Daily Papers

The current paradigm of test-time scaling relies on generating long reasoning traces ("thinking" more) before producing a response. In agent problems that require interaction, this can be done by generating thinking traces before acting in the world. However, this process does not allow agents to acquire new information from the environment or adapt their behavior over time. In this work, we propose to scale test-time interaction, an untapped dimension of test-time scaling that increases the agent's interaction horizon to enable running rich behaviors such as exploration, backtracking, and dynamic re-planning within a single rollout. To demonstrate the promise of this scaling dimension, we study the domain of web agents. We first show that even prompting-based interaction scaling without any training can improve task success on web benchmarks non-trivially. Building on this, we introduce TTI (Test-Time Interaction), a curriculum-based online reinforcement learning (RL) approach that trains agents by adaptively adjusting their rollout lengths. Using a Gemma 3 12B model, TTI produces state-of-the-art open-source, open-data web agents on WebVoyager and WebArena benchmarks. We further show that TTI enables agents to balance exploration and exploitation adaptively. Our results establish interaction scaling as a powerful, complementary axis to scaling per-step compute, offering new avenues for training adaptive agents.

Recent Large Reasoning Models (LRMs) with thinking traces have shown strong performance on English reasoning tasks. However, their ability to think in other languages is less studied. This capability is as important as answer accuracy for real world applications because users may find the reasoning trace useful for oversight only when it is expressed in their own language. We comprehensively evaluate two leading families of LRMs on our XReasoning benchmark and find that even the most advanced models often revert to English or produce fragmented reasoning in other languages, revealing a substantial gap in multilingual reasoning. Prompt based interventions that force models to reason in the users language improve readability and oversight but reduce answer accuracy, exposing an important trade off. We further show that targeted post training on just 100 examples mitigates this mismatch, though some accuracy loss remains. Our results highlight the limited multilingual reasoning capabilities of current LRMs and outline directions for future work. Code and data are available at https://github.com/Betswish/mCoT-XReasoning.

Distilling the thinking traces of a Large Language Model (LLM) with reasoning capabilities into a smaller model has been proven effective. Yet, there is a scarcity of work done on how model performances scale with the quantity of distillation data. In this work, we study the scaling trend of distilling competitive coding skills on two small non-reasoning LLMs. We validate the hypothesis that there is a valley of code reasoning: downstream performance on competitive coding first drops as data quantity increases, then it steadily increases in a sharper-than-log-linear fashion. Having identified the trend, we further fine-tune the models at two different distillation stages on the same data to ground conclusions on their respective learning phases. We learn that across stages in the low and medium-low data regimes, small models benefit significantly from easier coding questions than from harder ones. We also find that, surprisingly, the correctness of outputs in training data makes no difference to distillation outcomes. Our work represents a step forward in understanding the training dynamics of code reasoning distillation outside intuition

We introduce a variational reasoning framework for language models that treats thinking traces as latent variables and optimizes them through variational inference. Starting from the evidence lower bound (ELBO), we extend it to a multi-trace objective for tighter bounds and propose a forward-KL formulation that stabilizes the training of the variational posterior. We further show that rejection sampling finetuning and binary-reward RL, including GRPO, can be interpreted as local forward-KL objectives, where an implicit weighting by model accuracy naturally arises from the derivation and reveals a previously unnoticed bias toward easier questions. We empirically validate our method on the Qwen 2.5 and Qwen 3 model families across a wide range of reasoning tasks. Overall, our work provides a principled probabilistic perspective that unifies variational inference with RL-style methods and yields stable objectives for improving the reasoning ability of language models. Our code is available at https://github.com/sail-sg/variational-reasoning.

Despite substantial advances in scaling test-time compute, an ongoing debate in the community is how it should be scaled up to enable continued and efficient improvements with scaling. There are largely two approaches: first, distilling successful search or thinking traces; and second, using verification (e.g., 0/1 outcome rewards, reward models, or verifiers) to guide reinforcement learning (RL) and search algorithms. In this paper, we prove that finetuning LLMs with verifier-based (VB) methods based on RL or search is far superior to verifier-free (VF) approaches based on distilling or cloning search traces, given a fixed amount of compute/data budget. Further, we show that as we scale test-time compute (measured as the output token length) and training data, suboptimality of VF methods scales poorly compared to VB when the base pre-trained LLM presents a heterogeneous distribution over correct solution traces (e.g., different lengths, styles, etc.) and admits a non-sharp distribution over rewards on traces sampled from it. We formalize this condition using anti-concentration [Erdos, 1945]. This implies a stronger result that VB methods scale better asymptotically, with the performance gap between VB and VF methods widening as test-time budget grows. We corroborate our theory empirically on both didactic and math reasoning problems with 3/8/32B-sized pre-trained LLMs, where we find verification is crucial for scaling test-time compute.

The AM-DeepSeek-R1-Distilled is a large-scale dataset with thinking traces for general reasoning tasks, composed of high-quality and challenging reasoning problems. These problems are collected from a multitude of open-source datasets, subjected to semantic deduplication and meticulous cleaning to eliminate test set contamination. All responses within the dataset are distilled from reasoning models (predominantly DeepSeek-R1) and have undergone rigorous verification procedures. Mathematical problems are validated by checking against reference answers, code problems are verified using test cases, and other tasks are evaluated with the aid of a reward model. The AM-Distill-Qwen-32B model, which was trained through only simple Supervised Fine-Tuning (SFT) using this batch of data, outperformed the DeepSeek-R1-Distill-Qwen-32B model on four benchmarks: AIME2024, MATH-500, GPQA-Diamond, and LiveCodeBench. Additionally, the AM-Distill-Qwen-72B model surpassed the DeepSeek-R1-Distill-Llama-70B model on all benchmarks as well. We are releasing these 1.4 million problems and their corresponding responses to the research community with the objective of fostering the development of powerful reasoning-oriented Large Language Models (LLMs). The dataset was published in https://huggingface.co/datasets/a-m-team/AM-DeepSeek-R1-Distilled-1.4M{https://huggingface.co/datasets/a-m-team/AM-DeepSeek-R1-Distilled-1.4M}.

LLM-as-a-Judge refers to the automatic modeling of preferences for responses generated by Large Language Models (LLMs), which is of significant importance for both LLM evaluation and reward modeling. Although generative LLMs have made substantial progress in various tasks, their performance as LLM-Judge still falls short of expectations. In this work, we propose Think-J, which improves generative LLM-as-a-Judge by learning how to think. We first utilized a small amount of curated data to develop the model with initial judgment thinking capabilities. Subsequently, we optimize the judgment thinking traces based on reinforcement learning (RL). We propose two methods for judgment thinking optimization, based on offline and online RL, respectively. The offline RL requires training a critic model to construct positive and negative examples for learning. The online method defines rule-based reward as feedback for optimization. Experimental results showed that our approach can significantly enhance the evaluation capability of generative LLM-Judge, surpassing both generative and classifier-based LLM-Judge without requiring extra human annotations.

Recent reasoning Large Language Models (LLMs) demonstrate remarkable problem-solving abilities but often generate long thinking traces whose utility is unclear. Our work aims to improve their efficiency, enabling them to reach high performance without overthinking. First, we analyze the entropy of token probabilities in reasoning traces. Across three models, we observe a consistent U-shaped entropy pattern: high entropy on easy problems despite high accuracy, low entropy on problems with medium difficulty, and high entropy on hard problems reflecting uncertainty. Specifically, we notice 22--25\% entropy reduction from easy to medium difficulty regions, suggesting an {overthinking} phenomenon on easy instances. Building on these insights, we introduce DiffAdapt, a lightweight framework that selects Easy/Normal/Hard inference strategies per question based on their difficulty and reasoning trace entropy. Each inference strategy consists of a fixed prompt, temperature and maximum token length. In contrast to existing efficiency optimization methods, our approach does not fine-tune base LLM but a small probe that classifies LLM's final hidden state, allowing inexpensive adaptation. We comprehensively evaluate our method on five models and eight benchmarks. Our method achieves comparable or improved accuracy while reducing token usage by up to 22.4\%, establishing a practical path toward compute-efficient reasoning.

Recent advances in Multi-Modal Large Language Models (MLLMs) have enabled unified processing of language, vision, and structured inputs, opening the door to complex tasks such as logical deduction, spatial reasoning, and scientific analysis. Despite their promise, the reasoning capabilities of MLLMs, particularly those augmented with intermediate thinking traces (MLLMs-T), remain poorly understood and lack standardized evaluation benchmarks. Existing work focuses primarily on perception or final answer correctness, offering limited insight into how models reason or fail across modalities. To address this gap, we introduce the MMMR, a new benchmark designed to rigorously evaluate multi-modal reasoning with explicit thinking. The MMMR comprises 1) a high-difficulty dataset of 1,083 questions spanning six diverse reasoning types with symbolic depth and multi-hop demands and 2) a modular Reasoning Trace Evaluation Pipeline (RTEP) for assessing reasoning quality beyond accuracy through metrics like relevance, consistency, and structured error annotations. Empirical results show that MLLMs-T overall outperform non-thinking counterparts, but even top models like Claude-3.7-Sonnet and Gemini-2.5 Pro suffer from reasoning pathologies such as inconsistency and overthinking. This benchmark reveals persistent gaps between accuracy and reasoning quality and provides an actionable evaluation pipeline for future model development. Overall, the MMMR offers a scalable foundation for evaluating, comparing, and improving the next generation of multi-modal reasoning systems.

As AI systems progress, we rely more on them to make decisions with us and for us. To ensure that such decisions are aligned with human values, it is imperative for us to understand not only what decisions they make but also how they come to those decisions. Reasoning language models, which provide both final responses and (partially transparent) intermediate thinking traces, present a timely opportunity to study AI procedural reasoning. Unlike math and code problems which often have objectively correct answers, moral dilemmas are an excellent testbed for process-focused evaluation because they allow for multiple defensible conclusions. To do so, we present MoReBench: 1,000 moral scenarios, each paired with a set of rubric criteria that experts consider essential to include (or avoid) when reasoning about the scenarios. MoReBench contains over 23 thousand criteria including identifying moral considerations, weighing trade-offs, and giving actionable recommendations to cover cases on AI advising humans moral decisions as well as making moral decisions autonomously. Separately, we curate MoReBench-Theory: 150 examples to test whether AI can reason under five major frameworks in normative ethics. Our results show that scaling laws and existing benchmarks on math, code, and scientific reasoning tasks fail to predict models' abilities to perform moral reasoning. Models also show partiality towards specific moral frameworks (e.g., Benthamite Act Utilitarianism and Kantian Deontology), which might be side effects of popular training paradigms. Together, these benchmarks advance process-focused reasoning evaluation towards safer and more transparent AI.

Language models traditionally used for cross-domain generalization have recently demonstrated task-specific reasoning. However, their top-down training approach on general corpora is insufficient for acquiring abstractions needed for deep domain expertise. This may require a bottom-up approach that acquires expertise by learning to compose simple domain concepts into more complex ones. A knowledge graph (KG) provides this compositional structure, where domain primitives are represented as head-relation-tail edges and their paths encode higher-level concepts. We present a task generation pipeline that synthesizes tasks directly from KG primitives, enabling models to acquire and compose them for reasoning. We fine-tune language models on the resultant KG-grounded curriculum to demonstrate domain-specific superintelligence. While broadly applicable, we validate our approach in medicine, where reliable KGs exist. Using a medical KG, we curate 24,000 reasoning tasks paired with thinking traces derived from diverse medical primitives. We fine-tune the QwQ-32B model on this curriculum to obtain QwQ-Med-3 that takes a step towards medical superintelligence. We also introduce ICD-Bench, an evaluation suite to quantify reasoning abilities across 15 medical domains. Our experiments demonstrate that QwQ-Med-3 significantly outperforms state-of-the-art reasoning models on ICD-Bench categories. Further analysis reveals that QwQ-Med-3 utilizes acquired primitives to widen the performance gap on the hardest tasks of ICD-Bench. Finally, evaluation on medical question-answer benchmarks shows that QwQ-Med-3 transfers acquired expertise to enhance the base model's performance. While the industry's approach to artificial general intelligence (AGI) emphasizes broad expertise, we envision a future in which AGI emerges from the composable interaction of efficient domain-specific superintelligent agents.

We introduce Nemotron-Nano-9B-v2, a hybrid Mamba-Transformer language model designed to increase throughput for reasoning workloads while achieving state-of-the-art accuracy compared to similarly-sized models. Nemotron-Nano-9B-v2 builds on the Nemotron-H architecture, in which the majority of the self-attention layers in the common Transformer architecture are replaced with Mamba-2 layers, to achieve improved inference speed when generating the long thinking traces needed for reasoning. We create Nemotron-Nano-9B-v2 by first pre-training a 12-billion-parameter model (Nemotron-Nano-12B-v2-Base) on 20 trillion tokens using an FP8 training recipe. After aligning Nemotron-Nano-12B-v2-Base, we employ the Minitron strategy to compress and distill the model with the goal of enabling inference on up to 128k tokens on a single NVIDIA A10G GPU (22GiB of memory, bfloat16 precision). Compared to existing similarly-sized models (e.g., Qwen3-8B), we show that Nemotron-Nano-9B-v2 achieves on-par or better accuracy on reasoning benchmarks while achieving up to 6x higher inference throughput in reasoning settings like 8k input and 16k output tokens. We are releasing Nemotron-Nano-9B-v2, Nemotron-Nano12B-v2-Base, and Nemotron-Nano-9B-v2-Base checkpoints along with the majority of our pre- and post-training datasets on Hugging Face.

In human cognition theory, human thinking is governed by two systems: the fast and intuitive System 1 and the slower but more deliberative System 2. Recent studies have shown that incorporating System 2 process into Transformers including large language models (LLMs), significantly enhances their reasoning capabilities. Nevertheless, models that purely resemble System 2 thinking require substantially higher computational costs and are much slower to respond. To address this challenge, we present Dualformer, a single Transformer model that seamlessly integrates both the fast and slow reasoning modes. Dualformer is obtained by training on data with randomized reasoning traces, where different parts of the traces are dropped during training. The dropping strategies are specifically tailored according to the trace structure, analogous to analyzing our thinking process and creating shortcuts with patterns. At inference time, our model can be configured to output only the solutions (fast mode) or both the reasoning chain and the final solution (slow mode), or automatically decide which mode to engage (auto mode). In all cases, Dualformer outperforms the corresponding baseline models in both performance and computational efficiency: (1) in slow mode, Dualformer optimally solves unseen 30 x 30 maze navigation tasks 97.6% of the time, surpassing the Searchformer (trained on data with complete reasoning traces) baseline performance of 93.3%, while only using 45.5% fewer reasoning steps; (2) in fast mode, Dualformer completes those tasks with an 80% optimal rate, significantly outperforming the Solution-Only model (trained on solution-only data), which has an optimal rate of only 30%. For math problems, our techniques have also achieved improved performance with LLM fine-tuning, showing its generalization beyond task-specific models.

Large reasoning models (LRMs) have recently demonstrated impressive capabilities in complex reasoning tasks by leveraging increased test-time computation and exhibiting behaviors reminiscent of human-like self-reflection. While LRMs show a clear capacity for valuable self-reflection, how this ability interacts with other model behaviors remains underexplored. We investigate this connection by analyzing verbalized confidence, how models articulate their certainty, as a lens into the nature of self-reflection in LRMs. We find that supervised fine-tuning on reasoning traces (i.e., distillation) and reinforcement learning can improve verbalized calibration in reasoning-intensive settings in a progressive, laddered fashion. However, our results also indicate that reasoning models may possess a diminished awareness of their own knowledge boundaries, as evidenced by significantly lower "I don't know" response rates on factuality benchmarks. Moreover, we examine the relationship between verbalized confidence and reasoning chains, finding that models tend to express higher confidence when providing shorter or less elaborate reasoning. Our findings highlight how reasoning-oriented training can enhance performance in reasoning-centric tasks while potentially incurring a "reasoning tax," a cost reflected in the model's reduced ability to accurately recognize the limits of its own knowledge in small-scale models. More broadly, our work showcases how this erosion of knowledge boundaries can compromise model faithfulness, as models grow more confident without a commensurate understanding of when they should abstain.

Recent generations of language models have introduced Large Reasoning Models (LRMs) that generate detailed thinking processes before providing answers. While these models demonstrate improved performance on reasoning benchmarks, their fundamental capabilities, scaling properties, and limitations remain insufficiently understood. Current evaluations primarily focus on established math and coding benchmarks, emphasizing final answer accuracy. However, this evaluation paradigm often suffers from contamination and does not provide insights into the reasoning traces. In this work, we systematically investigate these gaps with the help of controllable puzzle environments that allow precise manipulation of complexity while maintaining consistent logical structures. This setup enables the analysis of not only final answers but also the internal reasoning traces, offering insights into how LRMs think. Through extensive experiments, we show that LRMs face a complete accuracy collapse beyond certain complexities. Moreover, they exhibit a counterintuitive scaling limit: their reasoning effort increases with problem complexity up to a point, then declines despite having remaining token budget. By comparing LRMs with their standard LLM counterparts under same inference compute, we identify three performance regimes: (1) low-complexity tasks where standard models outperform LRMs, (2) medium-complexity tasks where LRMs demonstrates advantage, and (3) high-complexity tasks where both models face complete collapse. We found that LRMs have limitations in exact computation: they fail to use explicit algorithms and reason inconsistently across scales. We also investigate the reasoning traces in more depth, studying the patterns of explored solutions and analyzing the models' computational behavior, shedding light on their strengths, limitations, and raising questions about their reasoning capabilities.

We propose a framework that enables neural models to "think while listening" to everyday sounds, thereby enhancing audio classification performance. Motivated by recent advances in the reasoning capabilities of large language models, we address two central questions: (i) how can thinking be incorporated into existing audio classification pipelines to enable reasoning in the category space and improve performance, and (ii) can a new architecture be designed from the ground up to support both thinking and test-time scaling? We demonstrate that in both settings, our models exhibit improved classification accuracy. Leveraging test-time scaling, we observe consistent gains as the number of sampled traces increases. Furthermore, we evaluate two open-source reasoning models, GPT-OSS-20B and Qwen3-14B, showing that while such models are capable of zero-shot reasoning, a lightweight approach--retraining only the embedding matrix of a frozen, smaller model like GPT-2--can surpass the performance of billion-parameter text-based reasoning models.

Large language models (LLMs) have demonstrated strong reasoning abilities in mathematical tasks, often enhanced through reinforcement learning (RL). However, RL-trained models frequently produce unnecessarily long reasoning traces -- even for simple queries -- leading to increased inference costs and latency. While recent approaches attempt to control verbosity by adding length penalties to the reward function, these methods rely on fixed penalty terms that are hard to tune and cannot adapt as the model's reasoning capability evolves, limiting their effectiveness. In this work, we propose an adaptive reward-shaping method that enables LLMs to "think fast and right" -- producing concise outputs without sacrificing correctness. Our method dynamically adjusts the reward trade-off between accuracy and response length based on model performance: when accuracy is high, the length penalty increases to encourage faster length reduction; when accuracy drops, the penalty is relaxed to preserve correctness. This adaptive reward accelerates early-stage length reduction while avoiding over-compression in later stages. Experiments across multiple datasets show that our approach consistently and dramatically reduces reasoning length while largely maintaining accuracy, offering a new direction for cost-efficient adaptive reasoning in large-scale language models.

Recent advances in post-training techniques have endowed Large Language Models (LLMs) with enhanced capabilities for tackling complex, logic-intensive tasks through the generation of supplementary planning tokens. This development raises a fundamental question: Are these models aware of what they "learn" and "think"? To address this, we define three core competencies: (1) awareness of learned latent policies, (2) generalization of these policies across domains, and (3) alignment between internal reasoning traces and final outputs. We empirically evaluate these abilities on several tasks, each designed to require learning a distinct policy. Furthermore, we contrast the profiles of models post-trained via Supervised Fine-Tuning (SFT), Direct Policy Optimization (DPO), and Group Relative Policy Optimization (GRPO). Our findings indicate that RL-trained models not only demonstrate greater awareness of their learned behaviors and stronger generalizability to novel, structurally similar tasks than SFT models but also often exhibit weak alignment between their reasoning traces and final outputs, an effect most pronounced in GRPO-trained models.

Large reasoning models (LRMs) achieve higher performance on challenging reasoning tasks by generating more tokens at inference time, but this verbosity often wastes computation on easy problems. Existing solutions, including supervised finetuning on shorter traces, user-controlled budgets, or RL with uniform penalties, either require data curation, manual configuration, or treat all problems alike regardless of difficulty. We introduce Adaptive Length Penalty (ALP), a reinforcement learning objective tailoring generation length to per-prompt solve rate. During training, ALP monitors each prompt's online solve rate through multiple rollouts and adds a differentiable penalty whose magnitude scales inversely with that rate, so confident (easy) prompts incur a high cost for extra tokens while hard prompts remain unhindered. Posttraining DeepScaleR-1.5B with ALP cuts average token usage by 50\% without significantly dropping performance. Relative to fixed-budget and uniform penalty baselines, ALP redistributes its reduced budget more intelligently by cutting compute on easy prompts and reallocating saved tokens to difficult ones, delivering higher accuracy on the hardest problems with higher cost.

Recent large vision-language models (LVLMs) can generate vision-text multimodal chain-of-thought (MCoT) traces after reinforcement fine-tuning (RFT). However, we observe that the visual information incorporated in MCoT is often inaccurate, though still yield correct answers, indicating a lack of faithfulness in the MCoT reasoning process. We attribute this unfaithfulness to the RL reward in RFT, which solely incentivizes the format of interleaved vision-text cues, ie, it encourages the model to incorporate visual information into its text reasoning steps without considering the correctness of the visual information. In this paper, we first probe the faithfulness of MCoT by measuring how much the prediction changes when its visual and textual thoughts are intervened. Surprisingly, the model's predictions remain nearly unchanged under visual intervention but change significantly under textual intervention, indicating that the visual evidence is largely ignored. To further analyze visual information, we introduce an automated LVLM-based evaluation metric that quantifies the faithfulness of visual cues from two perspectives: reliability and sufficiency. Our evaluation reveals that the visual information in current MCoT traces is simultaneously unreliable and insufficient. To address this issue, we propose a novel MCoT learning strategy termed Sufficient-Component Cause Model (SCCM) learning. This approach encourages the MCoT to generate sufficient yet minimal visual components that are independently capable of leading to correct answers. We note that the proposed SCCM is annotation-free and compatible with various RFT for MCoT in a plug-and-play manner. Empirical results demonstrate that SCCM consistently improves the visual faithfulness across a suite of fine-grained perception and reasoning benchmarks. Code is available at https://github.com/EugeneLiu01/Faithful_Thinking_with_Image.

While Large Reasoning Models (LRMs) generate extensive chain-of-thought reasoning, we lack a principled framework for understanding how these thoughts are structured. In this paper, we introduce a novel approach by applying Schoenfeld's Episode Theory, a classic cognitive framework for human mathematical problem-solving, to analyze the reasoning traces of LRMs. We annotated thousands of sentences and paragraphs from model-generated solutions to math problems using seven cognitive labels (e.g., Plan, Implement, Verify). The result is the first publicly available benchmark for the fine-grained analysis of machine reasoning, including a large annotated corpus and detailed annotation guidebooks. Our preliminary analysis reveals distinct patterns in LRM reasoning, such as the transition dynamics between cognitive states. This framework provides a theoretically grounded methodology for interpreting LRM cognition and enables future work on more controllable and transparent reasoning systems.

Recent advancements in multimodal reward models (RMs) have substantially improved post-training for visual generative models. However, current RMs face inherent limitations: (1) visual inputs consume large context budgets, forcing fewer frames and causing loss of fine-grained details; and (2) all visual information is packed into the initial prompt, exacerbating hallucination and forgetting during chain-of-thought reasoning. To overcome these issues, we introduce VideoReward Thinker (VR-Thinker), a thinking-with-image framework that equips the RM with visual reasoning operations (e.g., select frame) and a configurable visual memory window. This allows the RM to actively acquire and update visual evidence within context limits, improving reasoning fidelity and reliability. We activate visual reasoning via a reinforcement fine-tuning pipeline: (i) Cold Start with curated visual chain-of-thought data to distill basic reasoning skills and operation formatting; (ii) select samples whose per-dimension and overall judgments are all correct, then conduct Rejection sampling Fine-Tuning on these high-quality traces to further enhance reasoning; and (iii) apply Group Relative Policy Optimization (GRPO) to strengthen reasoning. Our approach delivers state-of-the-art accuracy among open-source models on video preference benchmarks, especially for longer videos: a 7B VR-Thinker achieves 80.5% on VideoGen Reward, 82.3% on GenAI-Bench, and 75.6% on MJ-Bench-Video. These results validate the effectiveness and promise of thinking-with-image multimodal reward modeling.

Reasoning models improve their problem-solving ability through inference-time scaling, allocating more compute via longer token budgets. Identifying which reasoning traces are likely to succeed remains a key opportunity: reliably predicting productive paths can substantially reduce wasted computation and improve overall efficiency. We introduce Latent-Trajectory signals that characterize the temporal evolution of a model's internal representations during the generation of intermediate reasoning tokens. By measuring the overall change in latent representations between the start and end of reasoning, the change accumulated across intermediate steps, and the extent to which these changes advance toward the final state, we show that these signals predict solution accuracy more reliably than both cross-layer metrics and output-based confidence measures. When used to guide answer selection across multiple sampled generations, Latent-Trajectory signals make test-time scaling more effective and efficient than majority voting, reducing token usage by up to 70% while preserving and even improving accuracy by 2.6% on average. Moreover, these predictive signals often emerge early in the reasoning trace, enabling early selection and allocation of compute to the most promising candidates. Our findings contribute not only practical strategies for inference-time efficiency, but also a deeper interpretability perspective on how reasoning processes are represented and differentiated in latent space.

In many environments only a tiny subset of all states yield high reward. In these cases, few of the interactions with the environment provide a relevant learning signal. Hence, we may want to preferentially train on those high-reward states and the probable trajectories leading to them. To this end, we advocate for the use of a backtracking model that predicts the preceding states that terminate at a given high-reward state. We can train a model which, starting from a high value state (or one that is estimated to have high value), predicts and sample for which the (state, action)-tuples may have led to that high value state. These traces of (state, action) pairs, which we refer to as Recall Traces, sampled from this backtracking model starting from a high value state, are informative as they terminate in good states, and hence we can use these traces to improve a policy. We provide a variational interpretation for this idea and a practical algorithm in which the backtracking model samples from an approximate posterior distribution over trajectories which lead to large rewards. Our method improves the sample efficiency of both on- and off-policy RL algorithms across several environments and tasks.

Large Reasoning Models (LRMs) extend large language models with explicit, multi-step reasoning traces to enhance transparency and performance on complex tasks. However, these reasoning traces can be redundant or logically inconsistent, making them a new source of hallucination that is difficult to detect. Existing hallucination detection methods focus primarily on answer-level uncertainty and often fail to detect hallucinations or logical inconsistencies arising from the model's reasoning trace. This oversight is particularly problematic for LRMs, where the explicit thinking trace is not only an important support to the model's decision-making process but also a key source of potential hallucination. To this end, we propose RACE (Reasoning and Answer Consistency Evaluation), a novel framework specifically tailored for hallucination detection in LRMs. RACE operates by extracting essential reasoning steps and computing four diagnostic signals: inter-sample consistency of reasoning traces, entropy-based answer uncertainty, semantic alignment between reasoning and answers, and internal coherence of reasoning. This joint analysis enables fine-grained hallucination detection even when the final answer appears correct. Experiments across datasets and different LLMs demonstrate that RACE outperforms existing hallucination detection baselines, offering a robust and generalizable solution for evaluating LRMs. Our code is available at: https://github.com/bebr2/RACE.

Large language models (LLMs) have made remarkable strides in various natural language processing tasks, but their performance on complex reasoning problems remains hindered by a lack of explainability and trustworthiness. This issue, often manifesting as hallucinations or unattributable reasoning processes, limits their applicability in complex reasoning scenarios. To address this, we propose Knowledge Graph-constrained Trajectory Reasoning Attribution and Chain Explanation Supervision (KG-TRACES), a novel framework that enhances the reasoning ability of LLMs through explicit supervision over reasoning paths and processes. KG-TRACES jointly supervises the model to: (1) predict symbolic relation paths, (2) predict full triple-level reasoning paths, and (3) generate attribution-aware reasoning processes grounded in the reasoning paths. At inference phase, the model adapts to both KG-available and KG-unavailable scenarios, retrieving reasoning paths from a KG when possible or predicting plausible reasoning paths with only intrinsic knowledge when not. This design enables the model to reason in an explainable and source-attributable pattern. Through extensive experiments on complex reasoning tasks, we demonstrate that KG-TRACES significantly outperforms existing SOTA: it improves Hits@1 by 1.6% and F1 by 4.7% on WebQSP, and achieves improvements of 4.8% in Hits@1 and 2.1% in F1 on CWQ. Moreover, we show its transferability to specialized domains such as medicine. By visualizing the intermediate steps of reasoning processes, we further show that the explicit supervision introduced by KG-TRACES leads to more stable and goal-directed reasoning processes, aligning closely with correct answers. Code is available at https://github.com/Edaizi/KG-TRACES.

Large reasoning models exhibit remarkable reasoning capabilities via long, elaborate reasoning trajectories. Supervised fine-tuning on such reasoning traces, also known as distillation, can be a cost-effective way to boost reasoning capabilities of student models. However, empirical observations reveal that these reasoning trajectories are often suboptimal, switching excessively between different lines of thought, resulting in under-thinking, over-thinking, and even degenerate responses. We introduce Retro-Search, an MCTS-inspired search algorithm, for distilling higher quality reasoning paths from large reasoning models. Retro-Search retrospectively revises reasoning paths to discover better, yet shorter traces, which can then lead to student models with enhanced reasoning capabilities with shorter, thus faster inference. Our approach can enable two use cases: self-improvement, where models are fine-tuned on their own Retro-Search-ed thought traces, and weak-to-strong improvement, where a weaker model revises stronger model's thought traces via Retro-Search. For self-improving, R1-distill-7B, fine-tuned on its own Retro-Search-ed traces, reduces the average reasoning length by 31.2% while improving performance by 7.7% across seven math benchmarks. For weak-to-strong improvement, we retrospectively revise R1-671B's traces from the OpenThoughts dataset using R1-distill-32B as the Retro-Search-er, a model 20x smaller. Qwen2.5-32B, fine-tuned on this refined data, achieves performance comparable to R1-distill-32B, yielding an 11.3% reduction in reasoning length and a 2.4% performance improvement compared to fine-tuning on the original OpenThoughts data. Our work counters recently emergent viewpoints that question the relevance of search algorithms in the era of large reasoning models, by demonstrating that there are still opportunities for algorithmic advancements, even for frontier models.

Chain-of-Thought (CoT) prompting has proven highly effective for enhancing complex reasoning in Large Language Models (LLMs) and Multimodal Large Language Models (MLLMs). Yet, it struggles in complex spatial reasoning tasks. Nonetheless, human cognition extends beyond language alone, enabling the remarkable capability to think in both words and images. Inspired by this mechanism, we propose a new reasoning paradigm, Multimodal Visualization-of-Thought (MVoT). It enables visual thinking in MLLMs by generating image visualizations of their reasoning traces. To ensure high-quality visualization, we introduce token discrepancy loss into autoregressive MLLMs. This innovation significantly improves both visual coherence and fidelity. We validate this approach through several dynamic spatial reasoning tasks. Experimental results reveal that MVoT demonstrates competitive performance across tasks. Moreover, it exhibits robust and reliable improvements in the most challenging scenarios where CoT fails. Ultimately, MVoT establishes new possibilities for complex reasoning tasks where visual thinking can effectively complement verbal reasoning.

Large Reasoning Models (LRMs) have achieved impressive performance on complex reasoning tasks by generating detailed chain-of-thought (CoT) explanations. However, these responses are often excessively long, containing redundant reasoning steps that inflate inference cost and reduce usability. Controlling the length of generated reasoning without sacrificing accuracy remains an open challenge. Through a systematic empirical analysis, we reveal a consistent positive correlation between model entropy and response length at different reasoning stages across diverse LRMs: the thinking phase exhibits higher entropy, reflecting exploratory behavior of longer responses, while the final answer phase shows lower entropy, indicating a more deterministic solution. This observation suggests that entropy at different reasoning stages can serve as a control knob for balancing conciseness and performance. Based on this insight, this paper introduces Phase Entropy Aware Reward (PEAR), a reward mechanism that incorporating phase-dependent entropy into the reward design. Instead of treating all tokens uniformly, PEAR penalize excessive entropy during the thinking phase and allowing moderate exploration at the final answer phase, which encourages models to generate concise reasoning traces that retain sufficient flexibility to solve the task correctly. This enables adaptive control of response length without relying on explicit length targets or rigid truncation rules. Extensive experiments across four benchmarks demonstrate that PEAR consistently reduces response length while sustaining competitive accuracy across model scales. In addition, PEAR demonstrates strong out-of-distribution (OOD) robustness beyond the training distribution. Our code is available at: https://github.com/iNLP-Lab/PEAR.

This work revisits the dominant supervised fine-tuning (SFT) then reinforcement learning (RL) paradigm for training Large Vision-Language Models (LVLMs), and reveals a key finding: SFT can significantly undermine subsequent RL by inducing ``pseudo reasoning paths'' imitated from expert models. While these paths may resemble the native reasoning paths of RL models, they often involve prolonged, hesitant, less informative steps, and incorrect reasoning. To systematically study this effect, we introduce VLAA-Thinking, a new multimodal dataset designed to support reasoning in LVLMs. Constructed via a six-step pipeline involving captioning, reasoning distillation, answer rewrite and verification, VLAA-Thinking comprises high-quality, step-by-step visual reasoning traces for SFT, along with a more challenging RL split from the same data source. Using this dataset, we conduct extensive experiments comparing SFT, RL and their combinations. Results show that while SFT helps models learn reasoning formats, it often locks aligned models into imitative, rigid reasoning modes that impede further learning. In contrast, building on the Group Relative Policy Optimization (GRPO) with a novel mixed reward module integrating both perception and cognition signals, our RL approach fosters more genuine, adaptive reasoning behavior. Notably, our model VLAA-Thinker, based on Qwen2.5VL 3B, achieves top-1 performance on Open LMM Reasoning Leaderboard (https://huggingface.co/spaces/opencompass/Open_LMM_Reasoning_Leaderboard) among 4B scale LVLMs, surpassing the previous state-of-the-art by 1.8%. We hope our findings provide valuable insights in developing reasoning-capable LVLMs and can inform future research in this area.

Large Language Models (LLMs) have shown impressive capabilities in transforming natural language questions about relational databases into SQL queries. Despite recent improvements, small LLMs struggle to handle questions involving multiple tables and complex SQL patterns under a Zero-Shot Learning (ZSL) setting. Supervised Fine-Tuning (SFT) partially compensate the knowledge deficits in pretrained models but falls short while dealing with queries involving multi-hop reasoning. To bridge this gap, different LLM training strategies to reinforce reasoning capabilities have been proposed, ranging from leveraging a thinking process within ZSL, including reasoning traces in SFT, or adopt Reinforcement Learning (RL) strategies. However, the influence of reasoning on Text2SQL performance is still largely unexplored. This paper investigates to what extent LLM reasoning capabilities influence their Text2SQL performance on four benchmark datasets. To this end, it considers the following LLM settings: (1) ZSL, including general-purpose reasoning or not; (2) SFT, with and without task-specific reasoning traces; (3) RL, leveraging execution accuracy as primary reward function; (4) SFT+RL, i.e, a two-stage approach that combines SFT and RL. The results show that general-purpose reasoning under ZSL proves to be ineffective in tackling complex Text2SQL cases. Small LLMs benefit from SFT with reasoning much more than larger ones, bridging the gap of their (weaker) model pretraining. RL is generally beneficial across all tested models and datasets, particularly when SQL queries involve multi-hop reasoning and multiple tables. Small LLMs with SFT+RL excel on most complex datasets thanks to a strategic balance between generality of the reasoning process and optimization of the execution accuracy. Thanks to RL, the7B Qwen-Coder-2.5 model performs on par with 100+ Billion ones on the Bird dataset.

Large reasoning models (LRMs) spend substantial test-time compute on long chain-of-thought (CoT) traces, but what *characterizes* an effective CoT remains unclear. While prior work reports gains from lengthening CoTs and increasing review (revisiting earlier steps) via appended *wait* tokens, recent studies suggest that shorter thinking can outperform longer traces. We therefore conduct a systematic evaluation across ten LRMs on math and scientific reasoning. Contrary to the "longer-is-better" narrative, we find that both naive CoT lengthening and increased review are associated with *lower* accuracy. As CoT unfolds step by step, token-level metrics can conflate verbosity with process quality. We introduce a graph view of CoT to extract structure and identify a single statistic-the *Failed-Step Fraction (FSF)*, the fraction of steps in abandoned branches-that consistently outpredicts length and review ratio for correctness across models. To probe causality, we design two interventions. First, we rank candidate CoTs by each metric at test time, where FSF yields the largest pass@1 gains; second, we edit CoTs to remove failed branches, which significantly improves accuracy, indicating that failed branches bias subsequent reasoning. Taken together, these results characterize effective CoTs as those that *fail less* and support *structure-aware* test-time scaling over indiscriminately generating long CoT.

The current focus of AI research is shifting from emphasizing model training towards enhancing evaluation quality, a transition that is crucial for driving further advancements in AI systems. Traditional evaluation methods typically rely on reward models assigning scalar preference scores to outputs. Although effective, such approaches lack interpretability, leaving users often uncertain about why a reward model rates a particular response as high or low. The advent of LLM-as-a-Judge provides a more scalable and interpretable method of supervision, offering insights into the decision-making process. Moreover, with the emergence of large reasoning models, which consume more tokens for deeper thinking and answer refinement, scaling test-time computation in the LLM-as-a-Judge paradigm presents an avenue for further boosting performance and providing more interpretability through reasoning traces. In this paper, we introduce J1-7B, which is first supervised fine-tuned on reflection-enhanced datasets collected via rejection-sampling and subsequently trained using Reinforcement Learning (RL) with verifiable rewards. At inference time, we apply Simple Test-Time Scaling (STTS) strategies for additional performance improvement. Experimental results demonstrate that J1-7B surpasses the previous state-of-the-art LLM-as-a-Judge by 4.8\% and exhibits a 5.1\% stronger scaling trend under STTS. Additionally, we present three key findings: (1) Existing LLM-as-a-Judge does not inherently exhibit such scaling trend. (2) Model simply fine-tuned on reflection-enhanced datasets continues to demonstrate similarly weak scaling behavior. (3) Significant scaling trend emerges primarily during the RL phase, suggesting that effective STTS capability is acquired predominantly through RL training.

This paper introduces UI-TARS, a native GUI agent model that solely perceives the screenshots as input and performs human-like interactions (e.g., keyboard and mouse operations). Unlike prevailing agent frameworks that depend on heavily wrapped commercial models (e.g., GPT-4o) with expert-crafted prompts and workflows, UI-TARS is an end-to-end model that outperforms these sophisticated frameworks. Experiments demonstrate its superior performance: UI-TARS achieves SOTA performance in 10+ GUI agent benchmarks evaluating perception, grounding, and GUI task execution. Notably, in the OSWorld benchmark, UI-TARS achieves scores of 24.6 with 50 steps and 22.7 with 15 steps, outperforming Claude (22.0 and 14.9 respectively). In AndroidWorld, UI-TARS achieves 46.6, surpassing GPT-4o (34.5). UI-TARS incorporates several key innovations: (1) Enhanced Perception: leveraging a large-scale dataset of GUI screenshots for context-aware understanding of UI elements and precise captioning; (2) Unified Action Modeling, which standardizes actions into a unified space across platforms and achieves precise grounding and interaction through large-scale action traces; (3) System-2 Reasoning, which incorporates deliberate reasoning into multi-step decision making, involving multiple reasoning patterns such as task decomposition, reflection thinking, milestone recognition, etc. (4) Iterative Training with Reflective Online Traces, which addresses the data bottleneck by automatically collecting, filtering, and reflectively refining new interaction traces on hundreds of virtual machines. Through iterative training and reflection tuning, UI-TARS continuously learns from its mistakes and adapts to unforeseen situations with minimal human intervention. We also analyze the evolution path of GUI agents to guide the further development of this domain.

Large language models (LLMs) have shown increasing capacity at planning and executing a high-level goal in a live computer environment (e.g. MiniWoB++). To perform a task, recent works often require a model to learn from trace examples of the task via either supervised learning or few/many-shot prompting. Without these trace examples, it remains a challenge how an agent can autonomously learn and improve its control on a computer, which limits the ability of an agent to perform a new task. We approach this problem with a zero-shot agent that requires no given expert traces. Our agent plans for executable actions on a partially observed environment, and iteratively progresses a task by identifying and learning from its mistakes via self-reflection and structured thought management. On the easy tasks of MiniWoB++, we show that our zero-shot agent often outperforms recent SoTAs, with more efficient reasoning. For tasks with more complexity, our reflective agent performs on par with prior best models, even though previous works had the advantages of accessing expert traces or additional screen information.

Reasoning large language models have recently achieved state-of-the-art performance in many fields. However, their long-form chain-of-thought reasoning creates interpretability challenges as each generated token depends on all previous ones, making the computation harder to decompose. We argue that analyzing reasoning traces at the sentence level is a promising approach to understanding reasoning processes. We present three complementary attribution methods: (1) a black-box method measuring each sentence's counterfactual importance by comparing final answers across 100 rollouts conditioned on the model generating that sentence or one with a different meaning; (2) a white-box method of aggregating attention patterns between pairs of sentences, which identified ``broadcasting'' sentences that receive disproportionate attention from all future sentences via ``receiver'' attention heads; (3) a causal attribution method measuring logical connections between sentences by suppressing attention toward one sentence and measuring the effect on each future sentence's tokens. Each method provides evidence for the existence of thought anchors, reasoning steps that have outsized importance and that disproportionately influence the subsequent reasoning process. These thought anchors are typically planning or backtracking sentences. We provide an open-source tool (www.thought-anchors.com) for visualizing the outputs of our methods, and present a case study showing converging patterns across methods that map how a model performs multi-step reasoning. The consistency across methods demonstrates the potential of sentence-level analysis for a deeper understanding of reasoning models.

Cognitive psychologists have documented that humans use cognitive heuristics, or mental shortcuts, to make quick decisions while expending less effort. While performing annotation work on crowdsourcing platforms, we hypothesize that such heuristic use among annotators cascades on to data quality and model robustness. In this work, we study cognitive heuristic use in the context of annotating multiple-choice reading comprehension datasets. We propose tracking annotator heuristic traces, where we tangibly measure low-effort annotation strategies that could indicate usage of various cognitive heuristics. We find evidence that annotators might be using multiple such heuristics, based on correlations with a battery of psychological tests. Importantly, heuristic use among annotators determines data quality along several dimensions: (1) known biased models, such as partial input models, more easily solve examples authored by annotators that rate highly on heuristic use, (2) models trained on annotators scoring highly on heuristic use don't generalize as well, and (3) heuristic-seeking annotators tend to create qualitatively less challenging examples. Our findings suggest that tracking heuristic usage among annotators can potentially help with collecting challenging datasets and diagnosing model biases.

Recent advances in natural language processing highlight two key factors for improving reasoning in large language models (LLMs): (i) allocating more test-time compute tends to help on harder problems but often introduces redundancy in the reasoning trace, and (ii) compute is most effective when reasoning is systematic and incremental, forming structured chains of thought (CoTs) akin to human problem-solving. To study these factors in isolation, we introduce a controlled setting based on shortest-path tasks in layered graphs. We train decoder-only transformers on question-trace-answer triples using a custom tokenizer, comparing models trained on optimal bottom-up dynamic programming traces with those trained on longer, valid traces involving backtracking. Surprisingly, with the same training-token budget, models trained on inefficient traces generalize better to unseen graphs. This benefit is not due to length alone-injecting arbitrary redundancy into reasoning traces fails to help and can even hurt performance. Instead, we find that generalization correlates with the model's confidence in next-token prediction, suggesting that long, coherent, and locally incremental traces make the training signal easier to optimize.

Recent advances in Large Language Models (LLMs) show that extending the length of reasoning chains significantly improves performance on complex tasks. While revealing these reasoning traces helps users better follow, verify, and learn from the model's problem-solving process, it also makes them highly vulnerable to unauthorized distillation. To mitigate this risk, proprietary model providers often adopt aggressive protection strategies, such as replacing detailed reasoning with brief summaries, which deprive users of valuable intermediate information. To address this trade-off, we propose PART, an information-preserving antidistillation reformulation of reasoning traces. Motivated by the difference between how humans understand reasoning traces and how LLMs exploit them for supervised fine-tuning, we design a simple but effective two-step reformulation: removing self-talk behaviors and reordering sub-conclusions. A small auxiliary model is trained to perform this reformulation, incurring minimal computational overhead. Extensive experiments demonstrate that PART consistently disrupts distillation across student models of different sizes and types on various reasoning benchmarks. For instance, when training on reformulated traces, even the performance of a large 32B student model decreases from 54.17 to 46.88 on AIME 2024, corresponding to a 13.5% degradation.

Specialized reasoning language models (RLMs) have demonstrated that scaling test-time computation through detailed reasoning traces significantly enhances performance. Although these traces effectively facilitate knowledge distillation into smaller, instruction-tuned models, the precise nature of transferred reasoning remains unclear. In this study, we investigate to what extent distilled models internalize replicated stylistic patterns during reasoning. To this end, we systematically analyze reasoning traces, identifying structural and lexical patterns that characterize successful reasoning. We then introduce two new datasets -- a dataset of emergent reasoning traces and a synthetic dataset explicitly constructed to replicate these stylistic patterns -- to precisely examine their influence on distilled models' reasoning capabilities. We find that models trained on the synthetic traces achieve comparable performance, indicating that distilled reasoning abilities rely significantly on surface-level patterns. Surprisingly, we observe an increase in performance even when the synthetic traces are altered to lead to the wrong answer. Our findings highlight how stylistic patterns can be leveraged to efficiently enhance LM reasoning across diverse model families.

Recent advancements in Large Language Models (LLMs) have revolutionized decision-making by breaking down complex problems into more manageable language sequences referred to as ``thoughts''. An effective thought design should consider three key perspectives: performance, efficiency, and flexibility. However, existing thought can at most exhibit two of these attributes. To address these limitations, we introduce a novel thought prompting approach called ``Everything of Thoughts'' (XoT) to defy the law of ``Penrose triangle of existing thought paradigms. XoT leverages pretrained reinforcement learning and Monte Carlo Tree Search (MCTS) to incorporate external domain knowledge into thoughts, thereby enhancing LLMs' capabilities and enabling them to generalize to unseen problems efficiently. Through the utilization of the MCTS-LLM collaborative thought revision framework, this approach autonomously produces high-quality comprehensive cognitive mappings with minimal LLM interactions. Additionally, XoT empowers LLMs to engage in unconstrained thinking, allowing for flexible cognitive mappings for problems with multiple solutions.

Language has long been conceived as an essential tool for human reasoning. The breakthrough of Large Language Models (LLMs) has sparked significant research interest in leveraging these models to tackle complex reasoning tasks. Researchers have moved beyond simple autoregressive token generation by introducing the concept of "thought" -- a sequence of tokens representing intermediate steps in the reasoning process. This innovative paradigm enables LLMs' to mimic complex human reasoning processes, such as tree search and reflective thinking. Recently, an emerging trend of learning to reason has applied reinforcement learning (RL) to train LLMs to master reasoning processes. This approach enables the automatic generation of high-quality reasoning trajectories through trial-and-error search algorithms, significantly expanding LLMs' reasoning capacity by providing substantially more training data. Furthermore, recent studies demonstrate that encouraging LLMs to "think" with more tokens during test-time inference can further significantly boost reasoning accuracy. Therefore, the train-time and test-time scaling combined to show a new research frontier -- a path toward Large Reasoning Model. The introduction of OpenAI's o1 series marks a significant milestone in this research direction. In this survey, we present a comprehensive review of recent progress in LLM reasoning. We begin by introducing the foundational background of LLMs and then explore the key technical components driving the development of large reasoning models, with a focus on automated data construction, learning-to-reason techniques, and test-time scaling. We also analyze popular open-source projects at building large reasoning models, and conclude with open challenges and future research directions.

Knowledge tracing (KT) has recently been an active research area of computational pedagogy. The task is to model students' mastery level of knowledge concepts based on their responses to the questions in the past, as well as predict the probabilities that they correctly answer subsequent questions in the future. KT tasks were historically solved using statistical modeling methods such as Bayesian inference and factor analysis, but recent advances in deep learning have led to the successive proposals that leverage deep neural networks, including long short-term memory networks, memory-augmented networks and self-attention networks. While those deep models demonstrate superior performance over the traditional approaches, they all neglect the explicit modeling of the learning curve theory, which generally says that more practice on the same knowledge concept enhances one's mastery level of the concept. Based on this theory, we propose a Convolution-Augmented Knowledge Tracing (CAKT) model in this paper. The model employs three-dimensional convolutional neural networks to explicitly learn a student's recent experience on applying the same knowledge concept with that in the next question, and fuses the learnt feature with the feature representing her overall latent knowledge state obtained using a classic LSTM network. The fused feature is then fed into a second LSTM network to predict the student's response to the next question. Experimental results show that CAKT achieves the new state-of-the-art performance in predicting students' responses compared with existing models. We also conduct extensive sensitivity analysis and ablation study to show the stability of the results and justify the particular architecture of CAKT, respectively.

Chain-of-thought traces have been shown to improve performance of large language models in a plethora of reasoning tasks, yet there is no consensus on the mechanism through which this performance boost is achieved. To shed more light on this, we introduce Causal CoT Graphs (CCGs), which are directed acyclic graphs automatically extracted from reasoning traces that model fine-grained causal dependencies in the language model output. A collection of 1671 mathematical reasoning problems from MATH500, GSM8K and AIME, and their associated CCGs are compiled into our dataset -- KisMATH. Our detailed empirical analysis with 15 open-weight LLMs shows that (i) reasoning nodes in the CCG are mediators for the final answer, a condition necessary for reasoning; and (ii) LLMs emphasise reasoning paths given by the CCG, indicating that models internally realise structures akin to our graphs. KisMATH enables controlled, graph-aligned interventions and opens up avenues for further investigation into the role of chain-of-thought in LLM reasoning.

Recent advances in large language models have demonstrated remarkable reasoning capabilities through Chain of Thought (CoT) prompting, but often at the cost of excessive verbosity in their intermediate outputs, which increases computational overhead. We introduce Sketch-of-Thought (SoT), a novel prompting framework that combines cognitive-inspired reasoning paradigms with linguistic constraints to minimize token usage while preserving reasoning accuracy. SoT is designed as a flexible framework that can incorporate any custom reasoning paradigms based on cognitive science, and we instantiate it with three such paradigms - Conceptual Chaining, Chunked Symbolism, and Expert Lexicons - each tailored to different reasoning tasks and selected dynamically via a lightweight routing model. Through comprehensive evaluation across 15 reasoning datasets with multiple languages and multimodal scenarios, we demonstrate that SoT achieves token reductions of 76% with negligible accuracy impact. In certain domains like mathematical and multi-hop reasoning, it even improves accuracy while using significantly fewer tokens. Our code is publicly available: https://www.github.com/SimonAytes/SoT.

We study privacy leakage in the reasoning traces of large reasoning models used as personal agents. Unlike final outputs, reasoning traces are often assumed to be internal and safe. We challenge this assumption by showing that reasoning traces frequently contain sensitive user data, which can be extracted via prompt injections or accidentally leak into outputs. Through probing and agentic evaluations, we demonstrate that test-time compute approaches, particularly increased reasoning steps, amplify such leakage. While increasing the budget of those test-time compute approaches makes models more cautious in their final answers, it also leads them to reason more verbosely and leak more in their own thinking. This reveals a core tension: reasoning improves utility but enlarges the privacy attack surface. We argue that safety efforts must extend to the model's internal thinking, not just its outputs.

Reasoning models such as OpenAI o3 and DeepSeek-R1 have demonstrated strong performance on reasoning-intensive tasks through extended Chain-of-Thought (CoT) prompting. While longer reasoning traces can facilitate a more thorough exploration of solution paths for complex problems, researchers have observed that these models often "overthink", leading to inefficient inference. In this paper, we introduce ShorterBetter, a simple yet effective reinforcement learning methed that enables reasoning language models to discover their own optimal CoT lengths without human intervention. By sampling multiple outputs per problem and defining the Sample Optimal Length (SOL) as the shortest correct response among all the outputs, our method dynamically guides the model toward optimal inference lengths. Applied to the DeepSeek-Distill-Qwen-1.5B model, ShorterBetter achieves up to an 80% reduction in output length on both in-domain and out-of-domain reasoning tasks while maintaining accuracy. Our analysis shows that overly long reasoning traces often reflect loss of reasoning direction, and thus suggests that the extended CoT produced by reasoning models is highly compressible.

Recently, with the chain of thought (CoT) prompting, large language models (LLMs), e.g., GPT-3, have shown strong reasoning ability in several natural language processing tasks such as arithmetic, commonsense, and logical reasoning. However, LLMs with CoT require multi-step prompting and multi-token prediction, which is highly sensitive to individual mistakes and vulnerable to error accumulation. The above issues make the LLMs need the ability to verify the answers. In fact, after inferring conclusions in some thinking decision tasks, people often check them by re-verifying steps to avoid some mistakes. In this paper, we propose and prove that LLMs also have similar self-verification abilities. We take the conclusion obtained by CoT as one of the conditions for solving the original problem. By taking turns masking the original conditions and predicting their results, we calculate an explainable answer verification score based on whether the re-predicted conditions are correct. Experimental results demonstrate that the proposed method can improve the reasoning performance on various arithmetic, commonsense, and logical reasoning datasets. Our code is publicly available at: https://github.com/WENGSYX/Self-Verification.

In most current research, large language models (LLMs) are able to perform reasoning tasks by generating chains of thought through the guidance of specific prompts. However, there still exists a significant discrepancy between their capability in solving complex reasoning problems and that of humans. At present, most approaches focus on chains of thought (COT) and tool use, without considering the adoption and application of human cognitive frameworks. It is well-known that when confronting complex reasoning challenges, humans typically employ various cognitive abilities, and necessitate interaction with all aspects of tools, knowledge, and the external environment information to accomplish intricate tasks. This paper introduces a novel intelligent framework, referred to as OlaGPT. OlaGPT carefully studied a cognitive architecture framework, and propose to simulate certain aspects of human cognition. The framework involves approximating different cognitive modules, including attention, memory, reasoning, learning, and corresponding scheduling and decision-making mechanisms. Inspired by the active learning mechanism of human beings, it proposes a learning unit to record previous mistakes and expert opinions, and dynamically refer to them to strengthen their ability to solve similar problems. The paper also outlines common effective reasoning frameworks for human problem-solving and designs Chain-of-Thought (COT) templates accordingly. A comprehensive decision-making mechanism is also proposed to maximize model accuracy. The efficacy of OlaGPT has been stringently evaluated on multiple reasoning datasets, and the experimental outcomes reveal that OlaGPT surpasses state-of-the-art benchmarks, demonstrating its superior performance. Our implementation of OlaGPT is available on GitHub: https://github.com/oladata-team/OlaGPT.

Information tasks such as writing surveys or analytical reports require complex search and reasoning, and have recently been grouped under the umbrella of deep research -- a term also adopted by recent models targeting these capabilities. Despite growing interest, the scope of the deep research task remains underdefined and its distinction from other reasoning-intensive problems is poorly understood. In this paper, we propose a formal characterization of the deep research (DR) task and introduce a benchmark to evaluate the performance of DR systems. We argue that the core defining feature of deep research is not the production of lengthy report-style outputs, but rather the high fan-out over concepts required during the search process, i.e., broad and reasoning-intensive exploration. To enable objective evaluation, we define DR using an intermediate output representation that encodes key claims uncovered during search-separating the reasoning challenge from surface-level report generation. Based on this formulation, we propose a diverse, challenging benchmark LiveDRBench with 100 challenging tasks over scientific topics (e.g., datasets, materials discovery, prior art search) and public interest events (e.g., flight incidents, movie awards). Across state-of-the-art DR systems, F1 score ranges between 0.02 and 0.72 for any sub-category. OpenAI's model performs the best with an overall F1 score of 0.55. Analysis of reasoning traces reveals the distribution over the number of referenced sources, branching, and backtracking events executed by current DR systems, motivating future directions for improving their search mechanisms and grounding capabilities. The benchmark is available at https://github.com/microsoft/LiveDRBench.

Large reasoning models (LRMs) have demonstrated impressive capabilities in complex problem-solving, yet their internal reasoning mechanisms remain poorly understood. In this paper, we investigate the reasoning trajectories of LRMs from an information-theoretic perspective. By tracking how mutual information (MI) between intermediate representations and the correct answer evolves during LRM reasoning, we observe an interesting MI peaks phenomenon: the MI at specific generative steps exhibits a sudden and significant increase during LRM's reasoning process. We theoretically analyze such phenomenon and show that as MI increases, the probability of model's prediction error decreases. Furthermore, these MI peaks often correspond to tokens expressing reflection or transition, such as ``Hmm'', ``Wait'' and ``Therefore,'' which we term as the thinking tokens. We then demonstrate that these thinking tokens are crucial for LRM's reasoning performance, while other tokens has minimal impacts. Building on these analyses, we propose two simple yet effective methods to improve LRM's reasoning performance, by delicately leveraging these thinking tokens. Overall, our work provides novel insights into the reasoning mechanisms of LRMs and offers practical ways to improve their reasoning capabilities. The code is available at https://github.com/ChnQ/MI-Peaks.

We present Thinking with Generated Images, a novel paradigm that fundamentally transforms how large multimodal models (LMMs) engage with visual reasoning by enabling them to natively think across text and vision modalities through spontaneous generation of intermediate visual thinking steps. Current visual reasoning with LMMs is constrained to either processing fixed user-provided images or reasoning solely through text-based chain-of-thought (CoT). Thinking with Generated Images unlocks a new dimension of cognitive capability where models can actively construct intermediate visual thoughts, critique their own visual hypotheses, and refine them as integral components of their reasoning process. We demonstrate the effectiveness of our approach through two complementary mechanisms: (1) vision generation with intermediate visual subgoals, where models decompose complex visual tasks into manageable components that are generated and integrated progressively, and (2) vision generation with self-critique, where models generate an initial visual hypothesis, analyze its shortcomings through textual reasoning, and produce refined outputs based on their own critiques. Our experiments on vision generation benchmarks show substantial improvements over baseline approaches, with our models achieving up to 50% (from 38% to 57%) relative improvement in handling complex multi-object scenarios. From biochemists exploring novel protein structures, and architects iterating on spatial designs, to forensic analysts reconstructing crime scenes, and basketball players envisioning strategic plays, our approach enables AI models to engage in the kind of visual imagination and iterative refinement that characterizes human creative, analytical, and strategic thinking. We release our open-source suite at https://github.com/GAIR-NLP/thinking-with-generated-images.

Recent advances in test-time scaling have led to the emergence of thinking LLMs that exhibit self-reflective behaviors and multi-step reasoning. While RL drives this self-improvement paradigm, a recent study (Gandhi et al., 2025) shows that RL alone does not truly instill these new reasoning abilities - it merely draws out behaviors already present in the base models. This raises a question: How can we train the models that don't exhibit such thinking behavior to develop it in the first place? To this end, we propose ThinkTuning, a GRPO-based interactive training approach where we augment the rollouts of a student model with the guidance from a teacher model. A simple idea from classroom practice inspires our method: a teacher poses a problem, lets the student try an answer, then gives corrective feedback -- enough to point the mind in the right direction and then show the solution. Each piece of feedback reshapes the student's thoughts, leading them to arrive at the correct solution. Similarly, we find that this type of implicit supervision through feedback from a teacher model of the same size improves the reasoning capabilities of the student model. In particular, on average, our method shows a 3.85% improvement over zero-shot baselines across benchmarks, and on MATH-500, AIME and GPQA-Diamond it shows 2.08%, 2.23% and 3.99% improvements over the vanilla-GRPO baseline. Source code is available at https://github.com/3rdAT/ThinkTuning.

Large Language Models (LLMs) leverage step-by-step reasoning to solve complex problems. Standard evaluation practice involves generating a complete reasoning trace and assessing the correctness of the final answer presented at its conclusion. In this paper, we challenge the reliance on the final answer by posing the following two questions: Does the final answer reliably represent the model's optimal conclusion? Can alternative reasoning paths yield different results? To answer these questions, we analyze intermediate reasoning steps, termed subthoughts, and propose a method based on our findings. Our approach involves segmenting a reasoning trace into sequential subthoughts based on linguistic cues. We start by prompting the model to generate continuations from the end-point of each intermediate subthought. We extract a potential answer from every completed continuation originating from different subthoughts. We find that aggregating these answers by selecting the most frequent one (the mode) often yields significantly higher accuracy compared to relying solely on the answer derived from the original complete trace. Analyzing the consistency among the answers derived from different subthoughts reveals characteristics that correlate with the model's confidence and correctness, suggesting potential for identifying less reliable answers. Our experiments across various LLMs and challenging mathematical reasoning datasets (AIME2024 and AIME2025) show consistent accuracy improvements, with gains reaching up to 13\% and 10\% respectively. Implementation is available at: https://github.com/hammoudhasan/SubthoughtReasoner.

Large language models (LLMs) have demonstrated enhanced performance through the Thinking then Responding paradigm, where models generate internal thoughts before final responses (aka, System 2 thinking). However, existing research lacks a systematic understanding of the mechanisms underlying how thinking patterns affect performance across model sizes. In this work, we conduct a comprehensive analysis of the impact of various thinking types on model performance and introduce ThinkPatterns-21k, a curated dataset comprising 21k instruction-response pairs (QA) collected from existing instruction-following datasets with five thinking types. For each pair, we augment it with five distinct internal thinking patterns: one unstructured thinking (monologue) and four structured variants (decomposition, self-ask, self-debate and self-critic), while maintaining the same instruction and response. Through extensive evaluation across different model sizes (3B-32B parameters), we have two key findings: (1) smaller models (<30B parameters) can benefit from most of structured thinking patterns, while larger models (32B) with structured thinking like decomposition would degrade performance and (2) unstructured monologue demonstrates broad effectiveness across different model sizes. Finally, we released all of our datasets, checkpoints, training logs of diverse thinking patterns to reproducibility, aiming to facilitate further research in this direction.

Large Reasoning Models (LRMs) have significantly enhanced their capabilities in complex problem-solving by introducing a thinking draft that enables multi-path Chain-of-Thought explorations before producing final answers. Ensuring the faithfulness of these intermediate reasoning processes is crucial for reliable monitoring, interpretation, and effective control. In this paper, we propose a systematic counterfactual intervention framework to rigorously evaluate thinking draft faithfulness. Our approach focuses on two complementary dimensions: (1) Intra-Draft Faithfulness, which assesses whether individual reasoning steps causally influence subsequent steps and the final draft conclusion through counterfactual step insertions; and (2) Draft-to-Answer Faithfulness, which evaluates whether final answers are logically consistent with and dependent on the thinking draft, by perturbing the draft's concluding logic. We conduct extensive experiments across six state-of-the-art LRMs. Our findings show that current LRMs demonstrate selective faithfulness to intermediate reasoning steps and frequently fail to faithfully align with the draft conclusions. These results underscore the need for more faithful and interpretable reasoning in advanced LRMs.

Large Reasoning Models (LRMs), which autonomously produce a reasoning Chain of Thought (CoT) before producing final responses, offer a promising approach to interpreting and monitoring model behaviors. Inspired by the observation that certain CoT patterns -- e.g., ``Wait, did I miss anything?'' -- consistently emerge across tasks, we explore whether LRMs exhibit human-like cognitive habits. Building on Habits of Mind, a well-established framework of cognitive habits associated with successful human problem-solving, we introduce CogTest, a principled benchmark designed to evaluate LRMs' cognitive habits. CogTest includes 16 cognitive habits, each instantiated with 25 diverse tasks, and employs an evidence-first extraction method to ensure reliable habit identification. With CogTest, we conduct a comprehensive evaluation of 16 widely used LLMs (13 LRMs and 3 non-reasoning ones). Our findings reveal that LRMs, unlike conventional LLMs, not only exhibit human-like habits but also adaptively deploy them according to different tasks. Finer-grained analyses further uncover patterns of similarity and difference in LRMs' cognitive habit profiles, particularly certain inter-family similarity (e.g., Qwen-3 models and DeepSeek-R1). Extending the study to safety-related tasks, we observe that certain habits, such as Taking Responsible Risks, are strongly associated with the generation of harmful responses. These findings suggest that studying persistent behavioral patterns in LRMs' CoTs is a valuable step toward deeper understanding of LLM misbehavior. The code is available at: https://github.com/jianshuod/CogTest.

Large language models (LLMs) have been routinely used to solve various tasks using step-by-step reasoning. However, the structure of intermediate reasoning steps, or thoughts, is rigid and unidirectional, such as chains, trees, or acyclic-directed graphs. Consequently, the resulting inflexible and forward-only reasoning may not address challenging tasks and fail when the LLM frequently gives false responses, i.e., ``hallucinations''. This paper proposes a new reasoning framework, called Thought Rollback (TR), allowing LLMs to adaptively build thought structure while maintaining effective reasoning toward problem-solving under ``hallucinations''. The core mechanism of TR is rolling back thoughts, which allows LLMs to perform error analysis on thoughts, and thus roll back to any previously mistaken thought for revision. Subsequently, by including such trial-and-error in the prompt to guide the LLM, each rollback leads to one more reliable reasoning path. Therefore, starting with a simple prompt without human annotations, LLM with TR adaptively and gradually explores thoughts for a correct solution. Comprehensive experiments on mathematical problems and multi-task reasoning demonstrate the state-of-the-art performance of TR in terms of problem-solving rate and interaction cost. For instance, the solving rate of GPT-4 with TR outperforms the current best by 9% on the MATH dataset.

Large Language Model can reasonably understand and generate human expressions but may lack of thorough thinking and reasoning mechanisms. Recently there have been several studies which enhance the thinking ability of language models but most of them are not data-driven or training-based. In this paper, we are motivated by the cognitive mechanism in the natural world, and design a novel model architecture called TaS which allows it to first consider the thoughts and then express the response based upon the query. We design several pipelines to annotate or generate the thought contents from prompt-response samples, then add language heads in a middle layer which behaves as the thinking layer. We train the language model by the thoughts-augmented data and successfully let the thinking layer automatically generate reasonable thoughts and finally output more reasonable responses. Both qualitative examples and quantitative results validate the effectiveness and performance of TaS. Our code is available at https://anonymous.4open.science/r/TadE.

Recently, slow-thinking reasoning systems, such as o1, have demonstrated remarkable capabilities in solving complex reasoning tasks. These systems typically engage in an extended thinking process before responding to a query, allowing them to generate more thorough, accurate, and well-reasoned solutions. These systems are primarily developed and maintained by industry, with their core techniques not publicly disclosed. In response, an increasing number of studies from the research community aim to explore the technical foundations underlying these powerful reasoning systems. Building on these prior efforts, this paper presents a reproduction report on implementing o1-like reasoning systems. We introduce an "imitate, explore, and self-improve" framework as our primary technical approach to train the reasoning model. In the initial phase, we use distilled long-form thought data to fine-tune the reasoning model, enabling it to invoke a slow-thinking mode. The model is then encouraged to explore challenging problems by generating multiple rollouts, which can result in increasingly more high-quality trajectories that lead to correct answers. Furthermore, the model undergoes self-improvement by iteratively refining its training dataset. To verify the effectiveness of this approach, we conduct extensive experiments on three challenging benchmarks. The experimental results demonstrate that our approach achieves competitive performance compared to industry-level reasoning systems on these benchmarks.

We find that the response length of reasoning LLMs, whether trained by reinforcement learning or supervised learning, drastically increases for ill-posed questions with missing premises (MiP), ending up with redundant and ineffective thinking. This newly introduced scenario exacerbates the general overthinking issue to a large extent, which we name as the MiP-Overthinking. Such failures are against the ``test-time scaling law'' but have been widely observed on multiple datasets we curated with MiP, indicating the harm of cheap overthinking and a lack of critical thinking. Surprisingly, LLMs not specifically trained for reasoning exhibit much better performance on the MiP scenario, producing much shorter responses that quickly identify ill-posed queries. This implies a critical flaw of the current training recipe for reasoning LLMs, which does not encourage efficient thinking adequately, leading to the abuse of thinking patterns. To further investigate the reasons behind such failures, we conduct fine-grained analyses of the reasoning length, overthinking patterns, and location of critical thinking on different types of LLMs. Moreover, our extended ablation study reveals that the overthinking is contagious through the distillation of reasoning models' responses. These results improve the understanding of overthinking and shed novel insights into mitigating the problem.

Recent Large Reasoning Models (LRMs), such as DeepSeek-R1 and OpenAI o1, have demonstrated strong performance gains by scaling up the length of Chain-of-Thought (CoT) reasoning during inference. However, a growing concern lies in their tendency to produce excessively long reasoning traces, which are often filled with redundant content (e.g., repeated definitions), over-analysis of simple problems, and superficial exploration of multiple reasoning paths for harder tasks. This inefficiency introduces significant challenges for training, inference, and real-world deployment (e.g., in agent-based systems), where token economy is critical. In this survey, we provide a comprehensive overview of recent efforts aimed at improving reasoning efficiency in LRMs, with a particular focus on the unique challenges that arise in this new paradigm. We identify common patterns of inefficiency, examine methods proposed across the LRM lifecycle, i.e., from pretraining to inference, and discuss promising future directions for research. To support ongoing development, we also maintain a real-time GitHub repository tracking recent progress in the field. We hope this survey serves as a foundation for further exploration and inspires innovation in this rapidly evolving area.

LLMs are typically trained to answer user questions or follow instructions similarly to how human experts respond. However, in the standard alignment framework they lack the basic ability of explicit thinking before answering. Thinking is important for complex questions that require reasoning and planning -- but can be applied to any task. We propose a training method for equipping existing LLMs with such thinking abilities for general instruction following without use of additional human data. We achieve this by an iterative search and optimization procedure that explores the space of possible thought generations, allowing the model to learn how to think without direct supervision. For each instruction, the thought candidates are scored using a judge model to evaluate their responses only, and then optimized via preference optimization. We show that this procedure leads to superior performance on AlpacaEval and Arena-Hard, and shows gains from thinking on non-reasoning categories such as marketing, health and general knowledge, in addition to more traditional reasoning & problem-solving tasks.

Chain-of-thought (CoT) prompting has become a widely used strategy for working with large language and multimodal models. While CoT has been shown to improve performance across many tasks, determining the settings in which it is effective remains an ongoing effort. In particular, it is still an open question in what settings CoT systematically reduces model performance. In this paper, we seek to identify the characteristics of tasks where CoT reduces performance by drawing inspiration from cognitive psychology, looking at cases where (i) verbal thinking or deliberation hurts performance in humans, and (ii) the constraints governing human performance generalize to language models. Three such cases are implicit statistical learning, visual recognition, and classifying with patterns containing exceptions. In extensive experiments across all three settings, we find that a diverse collection of state-of-the-art models exhibit significant drop-offs in performance (e.g., up to 36.3% absolute accuracy for OpenAI o1-preview compared to GPT-4o) when using inference-time reasoning compared to zero-shot counterparts. We also identify three tasks that satisfy condition (i) but not (ii), and find that while verbal thinking reduces human performance in these tasks, CoT retains or increases model performance. Overall, our results show that while there is not an exact parallel between the cognitive processes of models and those of humans, considering cases where thinking has negative consequences for human performance can help us identify settings where it negatively impacts models. By connecting the literature on human deliberation with evaluations of CoT, we offer a new tool that can be used in understanding the impact of prompt choices and inference-time reasoning.

Large language models' reasoning abilities benefit from methods that organize their thought processes, such as chain-of-thought prompting, which employs a sequential structure to guide the reasoning process step-by-step. However, existing approaches focus primarily on organizing the sequence of thoughts, leaving structure in individual thought steps underexplored. To address this gap, we propose Table as Thought, a framework inspired by cognitive neuroscience theories on human thought. Table as Thought organizes reasoning within a tabular schema, where rows represent sequential thought steps and columns capture critical constraints and contextual information to enhance reasoning. The reasoning process iteratively populates the table until self-verification ensures completeness and correctness. Our experiments show that Table as Thought excels in planning tasks and demonstrates a strong potential for enhancing LLM performance in mathematical reasoning compared to unstructured thought baselines. This work provides a novel exploration of refining thought representation within LLMs, paving the way for advancements in reasoning and AI cognition.

Recent large language models (LLMs) can generate long Chain-of-Thought (CoT) at test time, enabling them to solve complex tasks. These reasoning steps in CoT are often assumed as a faithful reflection of the model's internal thinking process, and used to monitor unsafe intentions. However, we find many reasoning steps don't truly contribute to LLMs' prediction. We measure the step-wise causal influence of each reasoning step on the model's final prediction with a proposed True Thinking Score (TTS). We reveal that LLMs often interleave between true-thinking steps (which are genuinely used to produce the final output) and decorative-thinking steps (which only give the appearance of reasoning but have minimal causal impact). Notably, only a small subset of the total reasoning steps have a high TTS that causally drive the model's prediction: e.g., for the AIME dataset, only an average of 2.3% of reasoning steps in CoT have a TTS >= 0.7 (range: 0-1) under the Qwen-2.5 model. Furthermore, we identify a TrueThinking direction in the latent space of LLMs. By steering along or against this direction, we can force the model to perform or disregard certain CoT steps when computing the final result. Finally, we highlight that self-verification steps in CoT (i.e., aha moments) can also be decorative, where LLMs do not truly verify their solution. Steering along the TrueThinking direction can force internal reasoning over these steps, resulting in a change in the final results. Overall, our work reveals that LLMs often verbalize reasoning steps without actually performing them internally, which undermines both the efficiency of LLM reasoning and the trustworthiness of CoT.

We introduce Diagram of Thought (DoT), a framework that models iterative reasoning in large language models (LLMs) as the construction of a directed acyclic graph (DAG) within a single model. Unlike traditional approaches that represent reasoning as linear chains or trees, DoT organizes propositions, critiques, refinements, and verifications into a cohesive DAG structure, allowing the model to explore complex reasoning pathways while maintaining logical consistency. Each node in the diagram corresponds to a proposition that has been proposed, critiqued, refined, or verified, enabling the LLM to iteratively improve its reasoning through natural language feedback. By leveraging auto-regressive next-token prediction with role-specific tokens, DoT facilitates seamless transitions between proposing ideas and critically evaluating them, providing richer feedback than binary signals. Furthermore, we formalize the DoT framework using Topos Theory, providing a mathematical foundation that ensures logical consistency and soundness in the reasoning process. This approach enhances both the training and inference processes within a single LLM, eliminating the need for multiple models or external control mechanisms. DoT offers a conceptual framework for designing next-generation reasoning-specialized models, emphasizing training efficiency, robust reasoning capabilities, and theoretical grounding. The code is available at https://github.com/diagram-of-thought/diagram-of-thought.

Large language models (LLMs) now solve multi-step problems by emitting extended chains of thought. During the process, they often re-derive the same intermediate steps across problems, inflating token usage and latency. This saturation of the context window leaves less capacity for exploration. We study a simple mechanism that converts recurring reasoning fragments into concise, reusable "behaviors" (name + instruction) via the model's own metacognitive analysis of prior traces. These behaviors are stored in a "behavior handbook" which supplies them to the model in-context at inference or distills them into parameters via supervised fine-tuning. This approach achieves improved test-time reasoning across three different settings - 1) Behavior-conditioned inference: Providing the LLM relevant behaviors in-context during reasoning reduces number of reasoning tokens by up to 46% while matching or improving baseline accuracy; 2) Behavior-guided self-improvement: Without any parameter updates, the model improves its own future reasoning by leveraging behaviors from its own past problem solving attempts. This yields up to 10% higher accuracy than a naive critique-and-revise baseline; and 3) Behavior-conditioned SFT: SFT on behavior-conditioned reasoning traces is more effective at converting non-reasoning models into reasoning models as compared to vanilla SFT. Together, these results indicate that turning slow derivations into fast procedural hints enables LLMs to remember how to reason, not just what to conclude.

Large Language Models (LLMs) have revolutionized natural language processing and hold immense potential for advancing Artificial Intelligence. However, the core architecture of most mainstream LLMs -- the Transformer -- has inherent limitations in computational depth, rendering them theoretically incapable of solving many reasoning tasks that demand increasingly deep computations. Chain of Thought (CoT) prompting has emerged as a technique to address these architectural limitations, as evidenced by several theoretical studies. It offers a promising approach to solving complex reasoning tasks that were previously beyond the capabilities of these models. Despite its successes, CoT and its variants (such as Tree of Thought, Graph of Thought, etc.) rely on a "one-prompt-for-all" approach, using a single prompt structure (e.g., "think step by step") for a wide range of tasks -- from counting and sorting to solving mathematical and algorithmic problems. This approach poses significant challenges for models to generate the correct reasoning steps, as the model must navigate through a vast prompt template space to find the appropriate template for each task. In this work, we build upon previous theoretical analyses of CoT to demonstrate how the one-prompt-for-all approach can negatively affect the computability of LLMs. We partition the solution search space into two: the prompt space and the answer space. Our findings show that task-specific supervision is essential for navigating the prompt space accurately and achieving optimal performance. Through experiments with state-of-the-art LLMs, we reveal a gap in reasoning performance when supervision is applied versus when it is not.

Large language models (LLMs) have exhibited impressive performance in language comprehension and various reasoning tasks. However, their abilities in spatial reasoning, a crucial aspect of human cognition, remain relatively unexplored. Human possess a remarkable ability to create mental images of unseen objects and actions through a process known as the Mind's Eye, enabling the imagination of the unseen world. Inspired by this cognitive capacity, we propose Visualization-of-Thought (VoT) prompting. VoT aims to elicit spatial reasoning of LLMs by visualizing their reasoning traces, thereby guiding subsequent reasoning steps. We employed VoT for multi-hop spatial reasoning tasks, including natural language navigation, visual navigation, and visual tiling in 2D grid worlds. Experimental results demonstrated that VoT significantly enhances the spatial reasoning abilities of LLMs. Notably, VoT outperformed existing multimodal large language models (MLLMs) in these tasks. While VoT works surprisingly well on LLMs, the ability to generate mental images to facilitate spatial reasoning resembles the mind's eye process, suggesting its potential viability in MLLMs.

Recent advances leverage post-training to enhance model reasoning performance, which typically requires costly training pipelines and still suffers from inefficient, overly lengthy outputs. We introduce Speculative Thinking, a training-free framework that enables large reasoning models to guide smaller ones during inference at the reasoning level, distinct from speculative decoding, which operates at the token level. Our approach is based on two observations: (1) reasoning-supportive tokens such as "wait" frequently appear after structural delimiters like "\n\n", serving as signals for reflection or continuation; and (2) larger models exhibit stronger control over reflective behavior, reducing unnecessary backtracking while improving reasoning quality. By strategically delegating reflective steps to a more capable model, our method significantly boosts the reasoning accuracy of reasoning models while shortening their output. With the assistance of the 32B reasoning model, the 1.5B model's accuracy on MATH500 increases from 83.2% to 89.4%, marking a substantial improvement of 6.2%. Simultaneously, the average output length is reduced from 5439 tokens to 4583 tokens, representing a 15.7% decrease. Moreover, when applied to a non-reasoning model (Qwen-2.5-7B-Instruct), our framework boosts its accuracy from 74.0% to 81.8% on the same benchmark, achieving a relative improvement of 7.8%.

Large reasoning models (LRMs), such as OpenAI o1 and DeepSeek-R1, have significantly enhanced their reasoning capabilities by generating longer chains of thought, demonstrating outstanding performance across a variety of tasks. However, this performance gain comes at the cost of a substantial increase in redundant reasoning during the generation process, leading to high computational overhead and exacerbating the issue of overthinking. Although numerous existing approaches aim to address the problem of overthinking, they often rely on external interventions. In this paper, we propose a novel framework, Self-Braking Tuning (SBT), which tackles overthinking from the perspective of allowing the model to regulate its own reasoning process, thus eliminating the reliance on external control mechanisms. We construct a set of overthinking identification metrics based on standard answers and design a systematic method to detect redundant reasoning. This method accurately identifies unnecessary steps within the reasoning trajectory and generates training signals for learning self-regulation behaviors. Building on this foundation, we develop a complete strategy for constructing data with adaptive reasoning lengths and introduce an innovative braking prompt mechanism that enables the model to naturally learn when to terminate reasoning at an appropriate point. Experiments across mathematical benchmarks (AIME, AMC, MATH500, GSM8K) demonstrate that our method reduces token consumption by up to 60% while maintaining comparable accuracy to unconstrained models.

Reasoning requires going beyond pattern matching or memorization of solutions to identify and implement "algorithmic procedures" that can be used to deduce answers to hard problems. Doing so requires realizing the most relevant primitives, intermediate results, or shared procedures, and building upon them. While RL post-training on long chains of thought ultimately aims to uncover this kind of algorithmic behavior, most reasoning traces learned by large models fail to consistently capture or reuse procedures, instead drifting into verbose and degenerate exploration. To address more effective reasoning, we introduce reasoning abstractions: concise natural language descriptions of procedural and factual knowledge that guide the model toward learning successful reasoning. We train models to be capable of proposing multiple abstractions given a problem, followed by RL that incentivizes building a solution while using the information provided by these abstractions. This results in a two-player RL training paradigm, abbreviated as RLAD, that jointly trains an abstraction generator and a solution generator. This setup effectively enables structured exploration, decouples learning signals of abstraction proposal and solution generation, and improves generalization to harder problems. We also show that allocating more test-time compute to generating abstractions is more beneficial for performance than generating more solutions at large test budgets, illustrating the role of abstractions in guiding meaningful exploration.

Recent advancements in large language models (LLMs) have demonstrated their impressive abilities in various reasoning and decision-making tasks. However, the quality and coherence of the reasoning process can still benefit from enhanced introspection and self-reflection. In this paper, we introduce Multiplex CoT (Chain of Thought), a method that enables LLMs to simulate a form of self-review while reasoning, by initiating double Chain of Thought (CoT) thinking. Multiplex CoT leverages the power of iterative reasoning, where the model generates an initial chain of thought and subsequently critiques and refines this reasoning with a second round of thought generation. This recursive approach allows for more coherent, logical, and robust answers, improving the overall decision-making process. We demonstrate how this method can be effectively implemented using simple prompt engineering in existing LLM architectures, achieving an effect similar to that of the Learning-Refinement Model (LRM) without the need for additional training. Additionally, we present a practical guide for implementing the method in Google Colab, enabling easy integration into real-world applications.

Recent studies on large language model (LLM) reasoning capabilities have demonstrated promising improvements in model performance by leveraging a lengthy thinking process and additional computational resources during inference, primarily in tasks involving mathematical reasoning (Muennighoff et al., 2025). However, it remains uncertain if longer reasoning chains inherently enhance factual accuracy, particularly beyond mathematical contexts. In this work, we thoroughly examine LLM reasoning within complex open-domain question-answering (QA) scenarios. We initially distill reasoning traces from advanced, large-scale reasoning models (QwQ-32B and DeepSeek-R1-671B), then fine-tune a variety of models ranging from smaller, instruction-tuned variants to larger architectures based on Qwen2.5. To enrich reasoning traces, we introduce factual information from knowledge graphs in the form of paths into our reasoning traces. Our experimental setup includes four baseline approaches and six different instruction-tuned models evaluated across a benchmark of six datasets, encompassing over 22.6K questions. Overall, we carry out 168 experimental runs and analyze approximately 1.7 million reasoning traces. Our findings indicate that, within a single run, smaller reasoning models achieve noticeable improvements in factual accuracy compared to their original instruction-tuned counterparts. Moreover, our analysis demonstrates that adding test-time compute and token budgets factual accuracy consistently improves by 2-8%, further confirming the effectiveness of test-time scaling for enhancing performance and consequently improving reasoning accuracy in open-domain QA tasks. We release all the experimental artifacts for further research.

Interpretability and explainability of deep neural networks are challenging due to their scale, complexity, and the agreeable notions on which the explaining process rests. Previous work, in particular, has focused on representing internal components of neural networks through human-friendly visuals and concepts. On the other hand, in real life, when making a decision, human tends to rely on similar situations and/or associations in the past. Hence arguably, a promising approach to make the model transparent is to design it in a way such that the model explicitly connects the current sample with the seen ones, and bases its decision on these samples. Grounded on that principle, we propose in this paper an explainable, evidence-based memory network architecture, which learns to summarize the dataset and extract supporting evidences to make its decision. Our model achieves state-of-the-art performance on two popular question answering datasets (i.e. TrecQA and WikiQA). Via further analysis, we show that this model can reliably trace the errors it has made in the validation step to the training instances that might have caused these errors. We believe that this error-tracing capability provides significant benefit in improving dataset quality in many applications.

Large Language Models (LLMs), such as OpenAI's o1-series have demonstrated compelling capabilities for complex reasoning tasks via the extended chain-of-thought (CoT) reasoning mechanism. However, recent studies reveal substantial redundancy in the CoT reasoning traces, which not only increases inference latency but also negatively impacts model performance by diverting attention to unnecessary reasoning paths. To address this issue, we investigate the internal reasoning structures of LLMs and categorize them into three primary thought types: execution, reflection, and transition thoughts. Moreover, our analysis reveals that excessive reflection and transition thoughts are strongly correlated with failure cases and these thought categories exhibit clear separation in the latent space. Based on these, we introduce SEAL (Steerable reasoning calibration), a training-free approach that seamlessly calibrates the CoT process, improving accuracy while demonstrating significant efficiency gains. SEAL consists of an offline stage for extracting the reasoning steering vector in the latent space, followed by an on-the-fly calibration of the reasoning trace through representation intervention using the steering vector. Notably, the steering vector exhibits strong transferability across various tasks. Extensive experiments across multiple models (DeepSeek-R1-Distill and QwQ-32B-Preview) and benchmarks (Math500, GSM8K, LiveCodeBench) validate the effectiveness of SEAL, up to a 11% improvement in accuracy while reducing reasoning tokens by 11.8% to 50.4%. Our code is publicly available at https://github.com/VITA-Group/SEAL.

Puzzlehunts are a genre of complex, multi-step puzzles lacking well-defined problem definitions. In contrast to conventional reasoning benchmarks consisting of tasks with clear instructions, puzzlehunts require models to discover the underlying problem structure from multimodal evidence and iterative reasoning, mirroring real-world domains such as scientific discovery, exploratory data analysis, or investigative problem-solving. Despite recent progress in foundation models, their performance on such open-ended settings remains largely untested. In this paper, we introduce PuzzleWorld, a large-scale benchmark of 667 puzzlehunt-style problems designed to assess step-by-step, open-ended, and creative multimodal reasoning. Each puzzle is annotated with the final solution, detailed reasoning traces, and cognitive skill labels, enabling holistic benchmarking and fine-grained diagnostic analysis. Most state-of-the-art models achieve only 1-2% final answer accuracy, with the best model solving only 14% of puzzles and reaching 40% stepwise accuracy. To demonstrate the value of our reasoning annotations, we show that fine-tuning a small model on reasoning traces improves stepwise reasoning from 4% to 11%, while training on final answers alone degrades performance to near zero. Our error analysis reveals that current models exhibit myopic reasoning, are bottlenecked by the limitations of language-based inference, and lack sketching capabilities crucial for visual and spatial reasoning. We release PuzzleWorld at https://github.com/MIT-MI/PuzzleWorld to support future work on building more general, open-ended, and creative reasoning systems.

"Search for" or "Navigate to"? When finding an object, the two choices always come up in our subconscious mind. Before seeing the target, we search for the target based on experience. After seeing the target, we remember the target location and navigate to. However, recently methods in object navigation field almost only consider using object association to enhance "search for" phase while neglect the importance of "navigate to" phase. Therefore, this paper proposes the dual adaptive thinking (DAT) method to flexibly adjust the different thinking strategies at different navigation stages. Dual thinking includes search thinking with the object association ability and navigation thinking with the target location ability. To make the navigation thinking more effective, we design the target-oriented memory graph (TOMG) to store historical target information and the target-aware multi-scale aggregator (TAMSA) to encode the relative target position. We assess our methods on the AI2-Thor dataset. Compared with the state-of-the-art (SOTA) method, our method reports 10.8%, 21.5% and 15.7% increase in success rate (SR), success weighted by path length (SPL) and success weighted by navigation efficiency (SNE), respectively.

Recently, Chain-of-Thought (CoT) prompting has delivered success on complex reasoning tasks, which aims at designing a simple prompt like ``Let's think step by step'' or multiple in-context exemplars with well-designed rationales to elicit Large Language Models (LLMs) to generate intermediate reasoning steps. However, the generated rationales often come with mistakes, making unfactual and unfaithful reasoning chains. To mitigate this brittleness, we propose a novel Chain-of-Knowledge (CoK) prompting, where we aim at eliciting LLMs to generate explicit pieces of knowledge evidence in the form of structure triple. This is inspired by our human behaviors, i.e., we can draw a mind map or knowledge map as the reasoning evidence in the brain before answering a complex question. Benefiting from CoK, we additionally introduce a F^2-Verification method to estimate the reliability of the reasoning chains in terms of factuality and faithfulness. For the unreliable response, the wrong evidence can be indicated to prompt the LLM to rethink. Extensive experiments demonstrate that our method can further improve the performance of commonsense, factual, symbolic, and arithmetic reasoning tasks.

Large language models (LLMs) such as OpenAI's o1 have demonstrated remarkable abilities in complex reasoning tasks by scaling test-time compute and exhibiting human-like deep thinking. However, we identify a phenomenon we term underthinking, where o1-like LLMs frequently switch between different reasoning thoughts without sufficiently exploring promising paths to reach a correct solution. This behavior leads to inadequate depth of reasoning and decreased performance, particularly on challenging mathematical problems. To systematically analyze this issue, we conduct experiments on three challenging test sets and two representative open-source o1-like models, revealing that frequent thought switching correlates with incorrect responses. We introduce a novel metric to quantify underthinking by measuring token efficiency in incorrect answers. To address underthinking, we propose a decoding strategy with thought switching penalty TIP that discourages premature transitions between thoughts, encouraging deeper exploration of each reasoning path. Experimental results demonstrate that our approach improves accuracy across challenging datasets without requiring model fine-tuning. Our findings contribute to understanding reasoning inefficiencies in o1-like LLMs and offer a practical solution to enhance their problem-solving capabilities.

Research on LLM technologies is rapidly emerging, with most of them employing a 'fast thinking' approach to inference. Most LLMs generate the final result based solely on a single query and LLM's reasoning capabilities. However, with the advent of OpenAI-o1, 'slow thinking' techniques have garnered increasing attention because its process is closer to the human thought process. Inspired by the human ability to constantly associate and replenish knowledge during thinking, we developed the novel Chain-of-Associated-Thoughts (CoAT) framework, which introduces an innovative synergy between the Monte Carlo Tree Search (MCTS) algorithm and a dynamic mechanism for integrating new key information, termed 'associative memory'. By combining the structured exploration capabilities of MCTS with the adaptive learning capacity of associative memory, CoAT significantly expands the LLM search space, enabling our framework to explore diverse reasoning pathways and dynamically update its knowledge base in real-time. This allows the framework to not only revisit and refine earlier inferences but also adaptively incorporate evolving information, ensuring that the final output is both accurate and comprehensive. To validate the effectiveness of our framework, we conducted extensive experiments across a range of generative and reasoning tasks. These experiments demonstrated that our framework outperforms conventional inference processes on accuracy, coherence, and diversity. The framework's ability to iteratively expand its search space while retaining contextually relevant information results.

Large language models have achieved substantial progress in mathematical reasoning, yet their advancement is limited by the scarcity of high-quality, high-difficulty training data. Existing synthesis methods largely rely on transforming human-written templates, limiting both diversity and scalability. We propose MathSmith, a novel framework for synthesizing challenging mathematical problems to enhance LLM reasoning. Rather than modifying existing problems, MathSmith constructs new ones from scratch by randomly sampling concept-explanation pairs from PlanetMath, ensuring data independence and avoiding contamination. To increase difficulty, we design nine predefined strategies as soft constraints during rationales. We further adopts reinforcement learning to jointly optimize structural validity, reasoning complexity, and answer consistency. The length of the reasoning trace generated under autoregressive prompting is used to reflect cognitive complexity, encouraging the creation of more demanding problems aligned with long-chain-of-thought reasoning. Experiments across five benchmarks, categorized as easy & medium (GSM8K, MATH-500) and hard (AIME2024, AIME2025, OlympiadBench), show that MathSmith consistently outperforms existing baselines under both short and long CoT settings. Additionally, a weakness-focused variant generation module enables targeted improvement on specific concepts. Overall, MathSmith exhibits strong scalability, generalization, and transferability, highlighting the promise of high-difficulty synthetic data in advancing LLM reasoning capabilities.

Passively collected behavioral health data from ubiquitous sensors holds significant promise to provide mental health professionals insights from patient's daily lives; however, developing analysis tools to use this data in clinical practice requires addressing challenges of generalization across devices and weak or ambiguous correlations between the measured signals and an individual's mental health. To address these challenges, we take a novel approach that leverages large language models (LLMs) to synthesize clinically useful insights from multi-sensor data. We develop chain of thought prompting methods that use LLMs to generate reasoning about how trends in data such as step count and sleep relate to conditions like depression and anxiety. We first demonstrate binary depression classification with LLMs achieving accuracies of 61.1% which exceed the state of the art. While it is not robust for clinical use, this leads us to our key finding: even more impactful and valued than classification is a new human-AI collaboration approach in which clinician experts interactively query these tools and combine their domain expertise and context about the patient with AI generated reasoning to support clinical decision-making. We find models like GPT-4 correctly reference numerical data 75% of the time, and clinician participants express strong interest in using this approach to interpret self-tracking data.

Large language models (LLMs) are becoming increasingly capable, but the mechanisms of their thinking and decision-making process remain unclear. Chain-of-thoughts (CoTs) have been commonly utilized to monitor LLMs, but this strategy fails to accurately reflect LLMs' thinking process. Techniques based on LLMs' hidden representations provide an inner perspective to monitor their latent thinking. However, previous methods only try to develop external monitors instead of making LLMs themselves easier to monitor. In this paper, we propose a novel method TELLME, improving the transparency of LLMs and helping monitors identify unsuitable and sensitive behaviors. Furthermore, we showcase the applications of TELLME on trustworthiness tasks (\eg, safety risks monitoring tasks and detoxification tasks), where LLMs achieve consistent improvement in transparency and task performance. More crucially, we theoretically analyze the improvement of TELLME on LLMs' generalization ability through optimal transport theory.

Large reasoning models (LRMs) generate intermediate reasoning traces before producing final answers, yielding strong gains on multi-step and mathematical tasks. Yet aligning LRMs with human preferences, a crucial prerequisite for model deployment, remains underexplored. The statistically correct objective for preference alignment requires marginalizing over reasoning traces, but this computation is intractable in practice. A common workaround optimizes a single sampled trajectory, which introduces substantial gradient variance from stochastic trace sampling. To address this challenge, we frame preference optimization for LRMs through the lens of the bias--variance trade-off and propose Bias--Variance Optimized Preference Optimization (BVPO), a simple, drop-in method that mixes two gradient estimators: a high-variance trace-based estimator and a low-variance empty-trace estimator obtained by disabling reasoning trace generation. Our theory shows that BVPO strictly reduces trace-induced variance for any nontrivial mixture, provides a closed-form choice of the mixing weight that minimizes mean-squared error relative to the true marginal gradient, and under standard smoothness and step-size conditions, tightens classical convergence bounds for stochastic gradient descent. Empirically, BVPO improves alignment over the best baseline by up to 7.8 points on AlpacaEval~2 and 6.8 points on Arena-Hard. Despite being trained only on general conversational data, BVPO also boosts reasoning performance for base models by up to 4.0 points on the average of six math reasoning benchmarks. These results identify variance from trace sampling as a key bottleneck and demonstrate that directly optimizing the bias--variance trade-off yields more stable training and stronger overall performance.

Why do thinking language models like DeepSeek R1 outperform their base counterparts? Despite consistent performance gains, it remains unclear to what extent thinking models learn entirely new reasoning capabilities or repurpose pre-existing base model ones. In this work, we propose a hybrid model where we activate reasoning mechanisms in base models at the right time to elicit thinking-model-level reasoning chains, implying that thinking models exploit already existing capabilities. To ground our analysis, we introduce an unsupervised, bottom-up approach for uncovering human-interpretable reasoning behaviors in thinking models. This approach provides an unbiased method to discover reasoning behaviors without imposing manual or LLM-derived assumptions. Across three base and four thinking models, using GSM8K and MATH500, our hybrid model recovers up to 91% of the performance gap to thinking models without any weight updates while steering only 12% of tokens. Concretely, our empirical setup provides a simple, causal way to test the effectiveness of existing reasoning mechanisms in base models by invoking them directly and measuring the resulting task performance. More broadly, these results reframe our understanding of how thinking models are trained: pre-training is when models acquire most of their reasoning mechanisms, and post-training teaches efficient deployment of these mechanisms at the right time, enabling efficient use of their inference-time compute.

When presented with questions involving visual thinking, humans naturally switch reasoning modalities, often forming mental images or drawing visual aids. Large language models have shown promising results in arithmetic and symbolic reasoning by expressing intermediate reasoning in text as a chain of thought, yet struggle to extend this capability to answer text queries that are easily solved by visual reasoning, even with extensive multimodal pretraining. We introduce a simple method, whiteboard-of-thought prompting, to unlock the visual reasoning capabilities of multimodal large language models across modalities. Whiteboard-of-thought prompting provides multimodal large language models with a metaphorical `whiteboard' to draw out reasoning steps as images, then returns these images back to the model for further processing. We find this can be accomplished with no demonstrations or specialized modules, instead leveraging models' existing ability to write code with libraries such as Matplotlib and Turtle. This simple approach shows state-of-the-art results on four difficult natural language tasks that involve visual and spatial reasoning. We identify multiple settings where GPT-4o using chain-of-thought fails dramatically, including more than one where it achieves 0% accuracy, while whiteboard-of-thought enables up to 92% accuracy in these same settings. We present a detailed exploration of where the technique succeeds as well as its sources of error.

Recent reasoning models through test-time scaling have demonstrated that long chain-of-thoughts can unlock substantial performance boosts in hard reasoning tasks such as math and code. However, the benefit of such long thoughts for system-2 reasoning is relatively less explored in other domains such as perceptual tasks where shallower, system-1 reasoning seems sufficient. In this paper, we introduce LongPerceptualThoughts, a new synthetic dataset with 30K long-thought traces for perceptual tasks. The key challenges in synthesizing elaborate reasoning thoughts for perceptual tasks are that off-the-shelf models are not yet equipped with such thinking behavior and that it is not straightforward to build a reliable process verifier for perceptual tasks. Thus, we propose a novel three-stage data synthesis framework that first synthesizes verifiable multiple-choice questions from dense image descriptions, then extracts simple CoTs from VLMs for those verifiable problems, and finally expands those simple thoughts to elaborate long thoughts via frontier reasoning models. In controlled experiments with a strong instruction-tuned 7B model, we demonstrate notable improvements over existing visual reasoning data-generation methods. Our model, trained on the generated dataset, achieves an average +3.4 points improvement over 5 vision-centric benchmarks, including +11.8 points on V^* Bench. Notably, despite being tuned for vision tasks, it also improves performance on the text reasoning benchmark, MMLU-Pro, by +2 points.

Aligned large language models (LLMs) demonstrate exceptional capabilities in task-solving, following instructions, and ensuring safety. However, the continual learning aspect of these aligned LLMs has been largely overlooked. Existing continual learning benchmarks lack sufficient challenge for leading aligned LLMs, owing to both their simplicity and the models' potential exposure during instruction tuning. In this paper, we introduce TRACE, a novel benchmark designed to evaluate continual learning in LLMs. TRACE consists of 8 distinct datasets spanning challenging tasks including domain-specific tasks, multilingual capabilities, code generation, and mathematical reasoning. All datasets are standardized into a unified format, allowing for effortless automatic evaluation of LLMs. Our experiments show that after training on TRACE, aligned LLMs exhibit significant declines in both general ability and instruction-following capabilities. For example, the accuracy of llama2-chat 13B on gsm8k dataset declined precipitously from 28.8\% to 2\% after training on our datasets. This highlights the challenge of finding a suitable tradeoff between achieving performance on specific tasks while preserving the original prowess of LLMs. Empirical findings suggest that tasks inherently equipped with reasoning paths contribute significantly to preserving certain capabilities of LLMs against potential declines. Motivated by this, we introduce the Reasoning-augmented Continual Learning (RCL) approach. RCL integrates task-specific cues with meta-rationales, effectively reducing catastrophic forgetting in LLMs while expediting convergence on novel tasks.

Intelligent tutoring systems optimize the selection and timing of learning materials to enhance understanding and long-term retention. This requires estimates of both the learner's progress (''knowledge tracing''; KT), and the prerequisite structure of the learning domain (''knowledge mapping''). While recent deep learning models achieve high KT accuracy, they do so at the expense of the interpretability of psychologically-inspired models. In this work, we present a solution to this trade-off. PSI-KT is a hierarchical generative approach that explicitly models how both individual cognitive traits and the prerequisite structure of knowledge influence learning dynamics, thus achieving interpretability by design. Moreover, by using scalable Bayesian inference, PSI-KT targets the real-world need for efficient personalization even with a growing body of learners and learning histories. Evaluated on three datasets from online learning platforms, PSI-KT achieves superior multi-step predictive accuracy and scalable inference in continual-learning settings, all while providing interpretable representations of learner-specific traits and the prerequisite structure of knowledge that causally supports learning. In sum, predictive, scalable and interpretable knowledge tracing with solid knowledge mapping lays a key foundation for effective personalized learning to make education accessible to a broad, global audience.

Chain-of-thought (CoT) outputs let us read a model's step-by-step reasoning. Since any long, serial reasoning process must pass through this textual trace, the quality of the CoT is a direct window into what the model is thinking. This visibility could help us spot unsafe or misaligned behavior (monitorability), but only if the CoT is transparent about its internal reasoning (faithfulness). Fully measuring faithfulness is difficult, so researchers often focus on examining the CoT in cases where the model changes its answer after adding a cue to the input. This proxy finds some instances of unfaithfulness but loses information when the model maintains its answer, and does not investigate aspects of reasoning not tied to the cue. We extend these results to a more holistic sense of monitorability by introducing verbosity: whether the CoT lists every factor needed to solve the task. We combine faithfulness and verbosity into a single monitorability score that shows how well the CoT serves as the model's external `working memory', a property that many safety schemes based on CoT monitoring depend on. We evaluate instruction-tuned and reasoning models on BBH, GPQA, and MMLU. Our results show that models can appear faithful yet remain hard to monitor when they leave out key factors, and that monitorability differs sharply across model families. We release our evaluation code using the Inspect library to support reproducible future work.

Parallel thinking has emerged as a novel approach for enhancing the reasoning capabilities of large language models (LLMs) by exploring multiple reasoning paths concurrently. However, activating such capabilities through training remains challenging, as existing methods predominantly rely on supervised fine-tuning (SFT) over synthetic data, which encourages teacher-forced imitation rather than exploration and generalization. Different from them, we propose Parallel-R1, the first reinforcement learning (RL) framework that enables parallel thinking behaviors for complex real-world reasoning tasks. Our framework employs a progressive curriculum that explicitly addresses the cold-start problem in training parallel thinking with RL. We first use SFT on prompt-generated trajectories from easier tasks to instill the parallel thinking ability, then transition to RL to explore and generalize this skill on harder problems. Experiments on various math benchmarks, including MATH, AMC23, and AIME, show that Parallel-R1 successfully instills parallel thinking, leading to 8.4% accuracy improvements over the sequential thinking model trained directly on challenging tasks with RL. Further analysis reveals a clear shift in the model's thinking behavior: at an early stage, it uses parallel thinking as an exploration strategy, while in a later stage, it uses the same capability for multi-perspective verification. Most significantly, we validate parallel thinking as a mid-training exploration scaffold, where this temporary exploratory phase unlocks a higher performance ceiling after RL, yielding a 42.9% improvement over the baseline on AIME25. Our model, data, and code will be open-source at https://github.com/zhengkid/Parallel-R1.

Multimodal reasoning requires iterative coordination between language and vision, yet it remains unclear what constitutes a meaningful interleaved chain of thought. We posit that text and image thoughts should function as complementary, rather than isomorphic, modalities that mutually advance reasoning. Guided by this principle, we build ThinkMorph, a unified model fine-tuned on 24K high-quality interleaved reasoning traces spanning tasks with varying visual engagement. ThinkMorph learns to generate progressive text-image reasoning steps that concretely manipulate visual content while maintaining coherent verbal logic. It delivers large gains on vision-centric benchmarks (averaging 34.7% over the base model) and generalizes to out-of-domain tasks, matching or surpassing larger and proprietary VLMs. Beyond performance, ThinkMorph exhibits emergent multimodal intelligence, including unseen visual manipulation skills, adaptive switching between reasoning modes, and better test-time scaling through diversified multimodal thoughts.These findings suggest promising directions for characterizing the emergent capabilities of unified models for multimodal reasoning.

Research on emergent patterns in Large Language Models (LLMs) has gained significant traction in both psychology and artificial intelligence, motivating the need for a comprehensive review that offers a synthesis of this complex landscape. In this article, we systematically review LLMs' capabilities across three important cognitive domains: decision-making biases, reasoning, and creativity. We use empirical studies drawing on established psychological tests and compare LLMs' performance to human benchmarks. On decision-making, our synthesis reveals that while LLMs demonstrate several human-like biases, some biases observed in humans are absent, indicating cognitive patterns that only partially align with human decision-making. On reasoning, advanced LLMs like GPT-4 exhibit deliberative reasoning akin to human System-2 thinking, while smaller models fall short of human-level performance. A distinct dichotomy emerges in creativity: while LLMs excel in language-based creative tasks, such as storytelling, they struggle with divergent thinking tasks that require real-world context. Nonetheless, studies suggest that LLMs hold considerable potential as collaborators, augmenting creativity in human-machine problem-solving settings. Discussing key limitations, we also offer guidance for future research in areas such as memory, attention, and open-source model development.

Chain-of-Thought (CoT) prompting enables complex reasoning in large language models (LLMs), including applications in information retrieval (IR). However, it often leads to overthinking, where models produce excessively long and semantically redundant traces with little or no benefit. We identify two key challenges in IR: redundant trajectories that revisit similar states and misguided reasoning that diverges from user intent. To address these, we propose State Machine Reasoning (SMR), a transition-based reasoning framework composed of discrete actions (Refine, Rerank, Stop) that support early stopping and fine-grained control. Experiments on the BEIR and BRIGHT benchmarks show that SMR improves retrieval performance (nDCG@10) by 3.4% while reducing token usage by 74.4%. It generalizes across LLMs and retrievers without requiring task-specific tuning, offering a practical alternative to conventional CoT reasoning. The code and details are available at https://github.com/ldilab/SMR.

Large Language Models, such as Generative Pre-trained Transformer 3 (aka. GPT-3), have been developed to understand language through the analysis of extensive text data, allowing them to identify patterns and connections between words. While LLMs have demonstrated impressive performance across various text-related tasks, they encounter challenges in tasks associated with reasoning. To address this challenge, Chain of Thought(CoT) prompting method has been proposed as a means to enhance LLMs' proficiency in complex reasoning tasks like solving math word problems and answering questions based on logical argumentative reasoning. The primary aim of this research is to assess how well four language models can grade reflective essays of third-year medical students. The assessment will specifically target the evaluation of critical thinking skills using CoT prompting. The research will provide the following contributions; to introduce and educate on the process of instructing models to evaluate reflective essays from a dataset they have not been previously trained on; to illustrate the use of CoT prompting as an instructional approach for training large models to carry out particular tasks. Our results suggest that among all the models, Llama-7b performs the least effectively, displaying the highest mean squared error. Conversely, ChatGPT emerges as the superior model, boasting a higher Cohen kappa score value of 0.53. Lastly, it's important to note that the selected models do prioritise user privacy by allowing users to delete their own conducted conversations.

While numerous works have assessed the generative performance of language models (LMs) on tasks requiring Theory of Mind reasoning, research into the models' internal representation of mental states remains limited. Recent work has used probing to demonstrate that LMs can represent beliefs of themselves and others. However, these claims are accompanied by limited evaluation, making it difficult to assess how mental state representations are affected by model design and training choices. We report an extensive benchmark with various LM types with different model sizes, fine-tuning approaches, and prompt designs to study the robustness of mental state representations and memorisation issues within the probes. Our results show that the quality of models' internal representations of the beliefs of others increases with model size and, more crucially, with fine-tuning. We are the first to study how prompt variations impact probing performance on theory of mind tasks. We demonstrate that models' representations are sensitive to prompt variations, even when such variations should be beneficial. Finally, we complement previous activation editing experiments on Theory of Mind tasks and show that it is possible to improve models' reasoning performance by steering their activations without the need to train any probe.

Test-time compute has led to remarkable success in the large language model (LLM) community, particularly for complex tasks, where longer chains of thought (CoTs) are generated to enhance reasoning capabilities. However, growing evidence reveals that such reasoning models often produce CoTs plagued by excessive redundancy, including unnecessary verification steps and repetitive reasoning shifts. The root cause lies in post-training of them that overly rely on outcome reward paradigms, as the data of process reward paradigms, which regulate intermediate reasoning steps, is difficult to construct at scale. To address this, we propose PI, a novel framework for Test-time Prompt Intervention. PI provides an interface to dynamically guide and regulate reasoning paths during inference through timely (When module) and proper (How module) interventions and post-intervention sampling (Which module). This allows human problem-solving expertise and cognitive science principles to be seamlessly integrated into LLMs' reasoning processes, enhancing controllability and interpretability. Extensive experiments across multiple models and datasets demonstrate that PI significantly shortens CoTs while reducing hallucination, yielding more concise and reliable reasoning.

Memory-augmented Large Language Models (LLMs) have demonstrated remarkable performance in long-term human-machine interactions, which basically relies on iterative recalling and reasoning of history to generate high-quality responses. However, such repeated recall-reason steps easily produce biased thoughts, i.e., inconsistent reasoning results when recalling the same history for different questions. On the contrary, humans can keep thoughts in the memory and recall them without repeated reasoning. Motivated by this human capability, we propose a novel memory mechanism called TiM (Think-in-Memory) that enables LLMs to maintain an evolved memory for storing historical thoughts along the conversation stream. The TiM framework consists of two crucial stages: (1) before generating a response, a LLM agent recalls relevant thoughts from memory, and (2) after generating a response, the LLM agent post-thinks and incorporates both historical and new thoughts to update the memory. Thus, TiM can eliminate the issue of repeated reasoning by saving the post-thinking thoughts as the history. Besides, we formulate the basic principles to organize the thoughts in memory based on the well-established operations, (i.e., insert, forget, and merge operations), allowing for dynamic updates and evolution of the thoughts. Furthermore, we introduce Locality-Sensitive Hashing into TiM to achieve efficient retrieval for the long-term conversations. We conduct qualitative and quantitative experiments on real-world and simulated dialogues covering a wide range of topics, demonstrating that equipping existing LLMs with TiM significantly enhances their performance in generating responses for long-term interactions.

Numerous applications of large language models (LLMs) rely on their ability to perform step-by-step reasoning. However, the reasoning behavior of LLMs remains poorly understood, posing challenges to research, development, and safety. To address this gap, we introduce landscape of thoughts-the first visualization tool for users to inspect the reasoning paths of chain-of-thought and its derivatives on any multi-choice dataset. Specifically, we represent the states in a reasoning path as feature vectors that quantify their distances to all answer choices. These features are then visualized in two-dimensional plots using t-SNE. Qualitative and quantitative analysis with the landscape of thoughts effectively distinguishes between strong and weak models, correct and incorrect answers, as well as different reasoning tasks. It also uncovers undesirable reasoning patterns, such as low consistency and high uncertainty. Additionally, users can adapt our tool to a model that predicts the property they observe. We showcase this advantage by adapting our tool to a lightweight verifier that evaluates the correctness of reasoning paths. The code is publicly available at: https://github.com/tmlr-group/landscape-of-thoughts.

Large Language Models (LLMs) have achieved remarkable success in reasoning tasks with the development of prompting methods. However, existing prompting approaches cannot reuse insights of solving similar problems and suffer from accumulated errors in multi-step reasoning, since they prompt LLMs to reason from scratch. To address these issues, we propose \textit{Thought Propagation (TP)}, which explores the analogous problems and leverages their solutions to enhance the complex reasoning ability of LLMs. These analogous problems are related to the input one, with reusable solutions and problem-solving strategies. Thus, it is promising to propagate insights of solving previous analogous problems to inspire new problem-solving. To achieve this, TP first prompts LLMs to propose and solve a set of analogous problems that are related to the input one. Then, TP reuses the results of analogous problems to directly yield a new solution or derive a knowledge-intensive plan for execution to amend the initial solution obtained from scratch. TP is compatible with existing prompting approaches, allowing plug-and-play generalization and enhancement in a wide range of tasks without much labor in task-specific prompt engineering. Experiments across three challenging tasks demonstrate TP enjoys a substantial improvement over the baselines by an average of 12\% absolute increase in finding the optimal solutions in Shortest-path Reasoning, 13\% improvement of human preference in Creative Writing, and 15\% enhancement in the task completion rate of LLM-Agent Planning.

Large language models have recently demonstrated significant gains in reasoning ability, often attributed to their capacity to generate longer chains of thought and engage in reflective reasoning. However, the contribution of reflections to performance improvement remains unclear. In this paper, we systematically analyze the rollouts of eight reasoning models on five mathematical datasets. We focus on reflective behaviours where the model has already produced an answer but continues reflecting before finalizing its output. Our analysis reveals that reflections are predominantly confirmatory and rarely alter the model's initial answer, a pattern consistent across models and datasets. To understand the role of reflections in training, we construct supervised fine-tuning (SFT) datasets with varying amounts of reflection steps. We observe that training models on rollouts with more reflection steps primarily enhances first-answer correctness rather than the ability to correct initially wrong answers through reflections. This motivates us to propose a question-aware early-stopping method that enhances inference-time token efficiency by stopping the reasoning process once a few plausible candidate answers are generated, thereby reducing unnecessary reflection steps. Motivated by this, we further propose to dynamically truncate the reflections after a candidate answer has appeared during generation, which reduces reasoning tokens by 24.5% across five mathematical datasets, within a 2.9% drop in accuracy.

Transferring reasoning capabilities from larger language models to smaller ones through supervised fine-tuning often fails counterintuitively, with performance degrading despite access to high-quality teacher demonstrations. We identify that this failure stems from distributional misalignment: reasoning traces from larger models contain tokens that are low probability under the student's distribution, exceeding the internal representation capacity of smaller architectures and creating learning barriers rather than helpful guidance. We propose Reverse Speculative Decoding (RSD), a mechanism for generating student-friendly reasoning traces in which the teacher model proposes candidate tokens but the student model determines acceptance based on its own probability distributions, filtering low probability tokens. When applied to Qwen3-0.6B, direct distillation of s1K-1.1 reasoning trace data degrades average performance across major reasoning benchmarks by 20.5\%, while the same model trained on RSD-generated reasoning traces achieves meaningful improvements of 4.9\%. Our analysis reveals that low probability tokens constitute the critical bottleneck in reasoning ability transfer. However, cross-model experiments demonstrate that RSD traces are model-specific rather than universally applicable, indicating that distributional alignment must be tailored for each student architecture's unique internal representation.

Recently, techniques such as explicit structured reasoning have demonstrated strong test-time scaling behavior by enforcing a separation between the model's internal "thinking" process and the final response. A key factor influencing answer quality in this setting is the length of the thinking stage. When the reasoning is too short, the model may fail to capture the complexity of the task. Conversely, when it is too long, the model may overthink, leading to unnecessary computation and degraded performance. This paper explores and exploits the underlying mechanisms by which LLMs understand and regulate the length of their reasoning during explicit thought processes. First, we show that LLMs encode their progress through the reasoning process and introduce an interactive progress bar visualization, which is then used to reveal insights on the model's planning dynamics. Second, we manipulate the internal progress encoding during inference to reduce unnecessary steps and generate a more concise and decisive chain of thoughts. Our empirical results demonstrate that this "overclocking" method mitigates overthinking, improves answer accuracy, and reduces inference latency. Our code is publicly available.

We design a suite of minimal algorithmic tasks that are a loose abstraction of open-ended real-world tasks. This allows us to cleanly and controllably quantify the creative limits of the present-day language model. Much like real-world tasks that require a creative, far-sighted leap of thought, our tasks require an implicit, open-ended stochastic planning step that either (a) discovers new connections in an abstract knowledge graph (like in wordplay, drawing analogies, or research) or (b) constructs new patterns (like in designing math problems or new proteins). In these tasks, we empirically and conceptually argue how next-token learning is myopic and memorizes excessively; comparatively, multi-token approaches, namely teacherless training and diffusion models, excel in producing diverse and original output. Secondly, in our tasks, we find that to elicit randomness from the Transformer without hurting coherence, it is better to inject noise right at the input layer (via a method we dub hash-conditioning) rather than defer to temperature sampling from the output layer. Thus, our work offers a principled, minimal test-bed for analyzing open-ended creative skills, and offers new arguments for going beyond next-token learning and softmax-based sampling. We make part of the code available under https://github.com/chenwu98/algorithmic-creativity

Recent Large Reasoning Models (LRMs) excel at complex reasoning tasks but often suffer from overthinking, generating overly long and redundant reasoning trajectories. To explore its essence, our empirical analysis reveals that LRMs are primarily limited to recognizing task properties (i.e., difficulty levels) like humans before solving the problem, leading to a one-size-fits-all reasoning process. Inspired by this, a pressing and natural question emerges: Can we explicitly bootstrap such ability to alleviate overthinking in LRMs? In this paper, we propose Think-How-to-Think (TH2T), a novel two-stage fine-tuning strategy that progressively inspires LRMs' difficulty cognition and redundancy cognition of LRMs. Specifically, we first inject difficulty hypnosis into output prefixes to guide the model toward adaptive reasoning depth, trained on a hybrid dataset mixing short and long reasoning paths. Then, we incorporate redundancy hypnosis, which supervises the intermediate reasoning steps to identify and eliminate unnecessary reasoning patterns. Experiments on 7B/14B/32B models demonstrate that TH2T significantly reduces inference costs by over 70% on easy tasks and 40% on hard tasks while maintaining performance stability. The resulting outputs exhibit clear signs of difficulty-aware capabilities and reduced redundancy (e.g., reflection and looping).

Vision-Language Models (VLMs) struggle to translate high-level instructions into the precise spatial affordances required for robotic manipulation. While visual Chain-of-Thought (CoT) methods exist, they are often computationally intensive. In this work, we introduce TRACE (Textual Reasoning for Affordance Coordinate Extraction), a novel methodology that integrates a textual Chain of Reasoning (CoR) into the affordance prediction process. We use this methodology to create the TRACE dataset, a large-scale collection created via an autonomous pipeline that pairs instructions with explicit textual rationales. By fine-tuning a VLM on this data, our model learns to externalize its spatial reasoning before acting. Our experiments show that our TRACE-tuned model achieves state-of-the-art performance, reaching 48.1% accuracy on the primary Where2Place (W2P) benchmark (a 9.6% relative improvement) and 55.0% on the more challenging W2P(h) subset. Crucially, an ablation study demonstrates that performance scales directly with the amount of reasoning data used, confirming the CoR's effectiveness. Furthermore, analysis of the model's attention maps reveals an interpretable reasoning process where focus shifts dynamically across reasoning steps. This work shows that training VLMs to generate a textual CoR is an effective and robust strategy for enhancing the precision, reliability, and interpretability of VLM-based robot control. Our dataset and code are available at https://github.com/jink-ucla/TRACE

Recent advancements in large language models have significantly improved their reasoning abilities, particularly through techniques involving search and backtracking. Backtracking naturally scales test-time compute by enabling sequential, linearized exploration via long chain-of-thought (CoT) generation. However, this is not the only strategy for scaling test-time compute: parallel sampling with best-of-n selection provides an alternative that generates diverse solutions simultaneously. Despite the growing adoption of sequential search, its advantages over parallel sampling--especially under a fixed compute budget remain poorly understood. In this paper, we systematically compare these two approaches on two challenging reasoning tasks: CountDown and Sudoku. Surprisingly, we find that sequential search underperforms parallel sampling on CountDown but outperforms it on Sudoku, suggesting that backtracking is not universally beneficial. We identify two factors that can cause backtracking to degrade performance: (1) training on fixed search traces can lock models into suboptimal strategies, and (2) explicit CoT supervision can discourage "implicit" (non-verbalized) reasoning. Extending our analysis to reinforcement learning (RL), we show that models with backtracking capabilities benefit significantly from RL fine-tuning, while models without backtracking see limited, mixed gains. Together, these findings challenge the assumption that backtracking universally enhances LLM reasoning, instead revealing a complex interaction between task structure, training data, model scale, and learning paradigm.

Reasoning-enhanced large language models (LLMs) explicitly generate intermediate reasoning steps prior to generating final answers, helping the model excel in complex problem-solving. In this paper, we demonstrate that this emerging generation framework offers a unique opportunity for more fine-grained control over model behavior. We propose Thinking Intervention, a novel paradigm designed to explicitly guide the internal reasoning processes of LLMs by strategically inserting or revising specific thinking tokens. We conduct comprehensive evaluations across multiple tasks, including instruction following on IFEval, instruction hierarchy on SEP, and safety alignment on XSTest and SORRY-Bench. Our results demonstrate that Thinking Intervention significantly outperforms baseline prompting approaches, achieving up to 6.7% accuracy gains in instruction-following scenarios, 15.4% improvements in reasoning about instruction hierarchies, and a 40.0% increase in refusal rates for unsafe prompts using open-source DeepSeek R1 models. Overall, our work opens a promising new research avenue for controlling reasoning LLMs.

In this paper, we investigate whether Large Language Models (LLMs) actively recall or retrieve their internal repositories of factual knowledge when faced with reasoning tasks. Through an analysis of LLMs' internal factual recall at each reasoning step via Knowledge Neurons, we reveal that LLMs fail to harness the critical factual associations under certain circumstances. Instead, they tend to opt for alternative, shortcut-like pathways to answer reasoning questions. By manually manipulating the recall process of parametric knowledge in LLMs, we demonstrate that enhancing this recall process directly improves reasoning performance whereas suppressing it leads to notable degradation. Furthermore, we assess the effect of Chain-of-Thought (CoT) prompting, a powerful technique for addressing complex reasoning tasks. Our findings indicate that CoT can intensify the recall of factual knowledge by encouraging LLMs to engage in orderly and reliable reasoning. Furthermore, we explored how contextual conflicts affect the retrieval of facts during the reasoning process to gain a comprehensive understanding of the factual recall behaviors of LLMs. Code and data will be available soon.

Spoken Language Models (SLMs) are designed to take speech inputs and produce spoken responses. However, current SLMs lack the ability to perform an internal, unspoken thinking process before responding. In contrast, humans typically engage in complex mental reasoning internally, enabling them to communicate ideas clearly and concisely. Thus, integrating an unspoken thought process into SLMs is highly desirable. While naively generating a complete chain-of-thought (CoT) reasoning before starting to talk can enable thinking for SLMs, this induces additional latency for the speech response, as the CoT reasoning can be arbitrarily long. To solve this issue, we propose Stitch, a novel generation method that alternates between the generation of unspoken reasoning chunks and spoken response chunks. Since the audio duration of a chunk of spoken response is much longer than the time to generate the tokens in a chunk of spoken response, we use the remaining free time to generate the unspoken reasoning tokens. When a chunk of audio is played to the user, the model continues to generate the next unspoken reasoning chunk, achieving simultaneous thinking and talking. Remarkably, Stitch matches the latency of baselines that cannot generate unspoken CoT by design while outperforming those baselines by 15% on math reasoning datasets; Stitch also performs equally well on non-reasoning datasets as those baseline models. Some animations and demonstrations are on the project page: https://d223302.github.io/STITCH.

Recently, there have been notable advancements in large language models (LLMs), demonstrating their growing abilities in complex reasoning. However, existing research largely overlooks a thorough and systematic comparison of these models' reasoning processes and outputs, particularly regarding their self-reflection pattern (also termed "Aha moment") and the interconnections across diverse domains. This paper proposes a novel framework for analyzing the reasoning characteristics of four cutting-edge large reasoning models (GPT-o1, DeepSeek-R1, Kimi-k1.5, and Grok-3) using keywords statistic and LLM-as-a-judge paradigm. Our approach connects their internal thinking processes with their final outputs. A diverse dataset consists of real-world scenario-based questions covering logical deduction, causal inference, and multi-step problem-solving. Additionally, a set of metrics is put forward to assess both the coherence of reasoning and the accuracy of the outputs. The research results uncover various patterns of how these models balance exploration and exploitation, deal with problems, and reach conclusions during the reasoning process. Through quantitative and qualitative comparisons, disparities among these models are identified in aspects such as the depth of reasoning, the reliance on intermediate steps, and the degree of similarity between their thinking processes and output patterns and those of GPT-o1. This work offers valuable insights into the trade-off between computational efficiency and reasoning robustness and provides practical recommendations for enhancing model design and evaluation in practical applications. We publicly release our project at: https://github.com/ChangWenhan/FromThinking2Output

Large Reasoning Models (LRMs) represent a breakthrough in AI problem-solving capabilities, but their effectiveness in interactive environments can be limited. This paper introduces and analyzes overthinking in LRMs. A phenomenon where models favor extended internal reasoning chains over environmental interaction. Through experiments on software engineering tasks using SWE Bench Verified, we observe three recurring patterns: Analysis Paralysis, Rogue Actions, and Premature Disengagement. We propose a framework to study these behaviors, which correlates with human expert assessments, and analyze 4018 trajectories. We observe that higher overthinking scores correlate with decreased performance, with reasoning models exhibiting stronger tendencies toward overthinking compared to non-reasoning models. Our analysis reveals that simple efforts to mitigate overthinking in agentic environments, such as selecting the solution with the lower overthinking score, can improve model performance by almost 30% while reducing computational costs by 43%. These results suggest that mitigating overthinking has strong practical implications. We suggest that by leveraging native function-calling capabilities and selective reinforcement learning overthinking tendencies could be mitigated. We also open-source our evaluation framework and dataset to facilitate research in this direction at https://github.com/AlexCuadron/Overthinking.

Reinforcement learning from human feedback (RLHF) has become a powerful post-training paradigm for aligning large language models with human preferences. A core challenge in RLHF is constructing accurate reward signals, where the conventional Bradley-Terry reward models (BT RMs) often suffer from sensitivity to data size and coverage, as well as vulnerability to reward hacking. Generative reward models (GenRMs) offer a more robust alternative by generating chain-of-thought (CoT) rationales followed by a final reward. However, existing GenRMs rely on shallow, vertically scaled reasoning, limiting their capacity to handle nuanced or complex (e.g., reasoning-intensive) tasks. Moreover, their pairwise preference outputs are incompatible with standard RLHF algorithms that require pointwise reward signals. In this work, we introduce Think-RM, a training framework that enables long-horizon reasoning in GenRMs by modeling an internal thinking process. Rather than producing structured, externally provided rationales, Think-RM generates flexible, self-guided reasoning traces that support advanced capabilities such as self-reflection, hypothetical reasoning, and divergent reasoning. To elicit these reasoning abilities, we first warm-up the models by supervised fine-tuning (SFT) over long CoT data. We then further improve the model's long-horizon abilities by rule-based reinforcement learning (RL). In addition, we propose a novel pairwise RLHF pipeline that directly optimizes policies using pairwise preference rewards, eliminating the need for pointwise reward conversion and enabling more effective use of Think-RM outputs. Experiments show that Think-RM achieves state-of-the-art results on RM-Bench, outperforming both BT RM and vertically scaled GenRM by 8%. When combined with our pairwise RLHF pipeline, it demonstrates superior end-policy performance compared to traditional approaches.

We investigate whether the success of a zero-shot Chain-of-Thought (CoT) process can be predicted before completion. We discover that a probing classifier, based on LLM representations, performs well even before a single token is generated, suggesting that crucial information about the reasoning process is already present in the initial steps representations. In contrast, a strong BERT-based baseline, which relies solely on the generated tokens, performs worse, likely because it depends on shallow linguistic cues rather than deeper reasoning dynamics. Surprisingly, using later reasoning steps does not always improve classification. When additional context is unhelpful, earlier representations resemble later ones more, suggesting LLMs encode key information early. This implies reasoning can often stop early without loss. To test this, we conduct early stopping experiments, showing that truncating CoT reasoning still improves performance over not using CoT at all, though a gap remains compared to full reasoning. However, approaches like supervised learning or reinforcement learning designed to shorten CoT chains could leverage our classifier's guidance to identify when early stopping is effective. Our findings provide insights that may support such methods, helping to optimize CoT's efficiency while preserving its benefits.

Recent deep-thinking large language models often reason extensively to improve performance, but such lengthy reasoning is not always desirable, as it incurs excessive inference costs with disproportionate performance gains. Controlling reasoning length without sacrificing performance is therefore important, but remains challenging, especially under tight thinking budgets. We propose budget guidance, a simple yet effective method for steering the reasoning process of LLMs toward a target budget without requiring any LLM fine-tuning. Our approach introduces a lightweight predictor that models a Gamma distribution over the remaining thinking length during next-token generation. This signal is then used to guide generation in a soft, token-level manner, ensuring that the overall reasoning trace adheres to the specified thinking budget. Budget guidance enables natural control of the thinking length, along with significant token efficiency improvements over baseline methods on challenging math benchmarks. For instance, it achieves up to a 26% accuracy gain on the MATH-500 benchmark under tight budgets compared to baseline methods, while maintaining competitive accuracy with only 63% of the thinking tokens used by the full-thinking model. Budget guidance also generalizes to broader task domains and exhibits emergent capabilities, such as estimating question difficulty. The source code is available at: https://github.com/UMass-Embodied-AGI/BudgetGuidance.

While large language models (LLMs) have demonstrated impressive capabilities across tasks in language understanding and interactive decision making, their abilities for reasoning (e.g. chain-of-thought prompting) and acting (e.g. action plan generation) have primarily been studied as separate topics. In this paper, we explore the use of LLMs to generate both reasoning traces and task-specific actions in an interleaved manner, allowing for greater synergy between the two: reasoning traces help the model induce, track, and update action plans as well as handle exceptions, while actions allow it to interface with external sources, such as knowledge bases or environments, to gather additional information. We apply our approach, named ReAct, to a diverse set of language and decision making tasks and demonstrate its effectiveness over state-of-the-art baselines, as well as improved human interpretability and trustworthiness over methods without reasoning or acting components. Concretely, on question answering (HotpotQA) and fact verification (Fever), ReAct overcomes issues of hallucination and error propagation prevalent in chain-of-thought reasoning by interacting with a simple Wikipedia API, and generates human-like task-solving trajectories that are more interpretable than baselines without reasoning traces. On two interactive decision making benchmarks (ALFWorld and WebShop), ReAct outperforms imitation and reinforcement learning methods by an absolute success rate of 34% and 10% respectively, while being prompted with only one or two in-context examples. Project site with code: https://react-lm.github.io

We explore how generating a chain of thought -- a series of intermediate reasoning steps -- significantly improves the ability of large language models to perform complex reasoning. In particular, we show how such reasoning abilities emerge naturally in sufficiently large language models via a simple method called chain of thought prompting, where a few chain of thought demonstrations are provided as exemplars in prompting. Experiments on three large language models show that chain of thought prompting improves performance on a range of arithmetic, commonsense, and symbolic reasoning tasks. The empirical gains can be striking. For instance, prompting a 540B-parameter language model with just eight chain of thought exemplars achieves state of the art accuracy on the GSM8K benchmark of math word problems, surpassing even finetuned GPT-3 with a verifier.

Chain-of-thought reasoning, a cognitive process fundamental to human intelligence, has garnered significant attention in the realm of artificial intelligence and natural language processing. However, there still remains a lack of a comprehensive survey for this arena. To this end, we take the first step and present a thorough survey of this research field carefully and widely. We use X-of-Thought to refer to Chain-of-Thought in a broad sense. In detail, we systematically organize the current research according to the taxonomies of methods, including XoT construction, XoT structure variants, and enhanced XoT. Additionally, we describe XoT with frontier applications, covering planning, tool use, and distillation. Furthermore, we address challenges and discuss some future directions, including faithfulness, multi-modal, and theory. We hope this survey serves as a valuable resource for researchers seeking to innovate within the domain of chain-of-thought reasoning.

Recent Large Language Models (LLMs) have reported high accuracy on reasoning benchmarks. However, it is still unclear whether the observed results arise from true reasoning or from statistical recall of the training set. Inspired by the ladder of causation (Pearl, 2009) and its three levels (associations, interventions and counterfactuals), this paper introduces RE-IMAGINE, a framework to characterize a hierarchy of reasoning ability in LLMs, alongside an automated pipeline to generate problem variations at different levels of the hierarchy. By altering problems in an intermediate symbolic representation, RE-IMAGINE generates arbitrarily many problems that are not solvable using memorization alone. Moreover, the framework is general and can work across reasoning domains, including math, code, and logic. We demonstrate our framework on four widely-used benchmarks to evaluate several families of LLMs, and observe reductions in performance when the models are queried with problem variations. These assessments indicate a degree of reliance on statistical recall for past performance, and open the door to further research targeting skills across the reasoning hierarchy.

Policy compliance assessment is a fundamental task of evaluating whether an input case strictly complies with a set of human-defined rules, more generally known as policies. In practice, human experts follow a systematic, step-by-step process to identify violations with respect to specific stipulations outlined in the policy. However, such documentation of gold-standard, expert-level reasoning processes is costly to acquire. In this paper, we introduce Policy Reasoning Traces (PRT), a form of specialized generated reasoning chains that serve as a reasoning bridge to improve an LLM's policy compliance assessment capabilities. Our empirical evaluations demonstrate that the use of PRTs for both inference-time and training-time scenarios significantly enhances the performance of open-weight and commercial models, setting a new state-of-the-art for HIPAA and GDPR policies. Beyond accuracy gains, we also highlight how PRTs can improve an LLM's ability to accurately cite policy clauses, as well as influence compliance decisions through their high utilization from the raw chains of thought.

Large Language Models (LLMs) have demonstrated promising capabilities in solving mathematical reasoning tasks, leveraging Chain-of-Thought (CoT) data as a vital component in guiding answer generation. Current paradigms typically generate CoT and answers directly for a given problem, diverging from human problem-solving strategies to some extent. Humans often solve problems by recalling analogous cases and leveraging their solutions to reason about the current task. Inspired by this cognitive process, we propose MetaLadder, a novel framework that explicitly prompts LLMs to recall and reflect on meta-problems, those structurally or semantically analogous problems, alongside their CoT solutions before addressing the target problem. Additionally, we introduce a problem-restating mechanism to enhance the model's comprehension of the target problem by regenerating the original question, which further improves reasoning accuracy. Therefore, the model can achieve reasoning transfer from analogical problems, mimicking human-like "learning from examples" and generalization abilities. Extensive experiments on mathematical benchmarks demonstrate that our MetaLadder significantly boosts LLMs' problem-solving accuracy, largely outperforming standard CoT-based methods (10.3\% accuracy gain) and other methods. Our code and data has been released at https://github.com/LHL3341/MetaLadder.

Humans draw to facilitate reasoning: we draw auxiliary lines when solving geometry problems; we mark and circle when reasoning on maps; we use sketches to amplify our ideas and relieve our limited-capacity working memory. However, such actions are missing in current multimodal language models (LMs). Current chain-of-thought and tool-use paradigms only use text as intermediate reasoning steps. In this work, we introduce Sketchpad, a framework that gives multimodal LMs a visual sketchpad and tools to draw on the sketchpad. The LM conducts planning and reasoning according to the visual artifacts it has drawn. Different from prior work, which uses text-to-image models to enable LMs to draw, Sketchpad enables LMs to draw with lines, boxes, marks, etc., which is closer to human sketching and better facilitates reasoning. Sketchpad can also use specialist vision models during the sketching process (e.g., draw bounding boxes with object detection models, draw masks with segmentation models), to further enhance visual perception and reasoning. We experiment with a wide range of math tasks (including geometry, functions, graphs, and chess) and complex visual reasoning tasks. Sketchpad substantially improves performance on all tasks over strong base models with no sketching, yielding an average gain of 12.7% on math tasks, and 8.6% on vision tasks. GPT-4o with Sketchpad sets a new state of the art on all tasks, including V*Bench (80.3%), BLINK spatial reasoning (83.9%), and visual correspondence (80.8%). All codes and data are in https://visualsketchpad.github.io/.

Chain-of-Thought (CoT) prompting enables large language models to solve complex reasoning problems by generating intermediate steps. However, confined by its inherent single-pass and sequential generation process, CoT heavily relies on the initial decisions, causing errors in early steps to accumulate and impact the final answers. In contrast, humans adopt recursive thinking when tackling complex reasoning problems, i.e., iteratively breaking the original problem into approachable sub-problems and aggregating their answers to resolve the original one. Inspired by the human cognitive process, we propose SOCRATIC QUESTIONING, a divide-and-conquer style algorithm that mimics the recursive thinking process. Specifically, SOCRATIC QUESTIONING leverages large language models to raise and answer sub-questions until collecting enough information to tackle the original question. Unlike CoT, SOCRATIC QUESTIONING explicitly navigates the thinking space, stimulates effective recursive thinking, and is more robust towards errors in the thinking process. Extensive experiments on several complex reasoning tasks, including MMLU, MATH, LogiQA, and visual question-answering demonstrate significant performance improvements over the state-of-the-art prompting methods, such as CoT, and Tree-of-Thought. The qualitative analysis clearly shows that the intermediate reasoning steps elicited by SOCRATIC QUESTIONING are similar to humans' recursively thinking process of complex reasoning problems.

Images usually convey richer detail than text, but often include redundant information which potentially downgrades multimodal reasoning performance. When faced with lengthy or complex messages, humans tend to employ abstract thinking to convert them into simple and concise abstracts. Inspired by this cognitive strategy, we introduce Visual Abstract Thinking (VAT), a novel thinking paradigm that prompts Multimodal Large Language Models (MLLMs) with visual abstract instead of explicit verbal thoughts or elaborate guidance, permitting a more concentrated visual reasoning mechanism. Explicit thinking, such as Chain-of-thought (CoT) or tool-augmented approaches, increases the complexity of reasoning process via inserting verbose intermediate steps, external knowledge or visual information. In contrast, VAT reduces redundant visual information and encourages models to focus their reasoning on more essential visual elements. Experimental results show that VAT consistently empowers different models, and achieves an average gain of 17% over GPT-4o baseline by employing diverse types of visual abstracts, demonstrating that VAT can enhance visual reasoning abilities for MLLMs regarding conceptual, structural and relational reasoning tasks. VAT is also compatible with CoT in knowledge-intensive multimodal reasoning tasks. These findings highlight the effectiveness of visual reasoning via abstract thinking and encourage further exploration of more diverse reasoning paradigms from the perspective of human cognition.

Recent developments, particularly OpenAI's O1 model, have demonstrated the remarkable potential of Large Language Models (LLMs) for complex reasoning tasks. Through analysis of O1's outputs and provided sample Chain-of-Thought (CoT) demonstrations, we observe that it approaches problem-solving in a distinctly human-like manner, systematically brainstorming ideas, testing hypotheses, verifying results, and planning comprehensive solutions. These sophisticated reasoning capabilities remain notably absent in other state-of-the-art language models. In this paper, we hypothesize that this performance gap stems from the limited availability of high-quality reasoning process data in current training sets. We demonstrate that by constructing a specialized dataset focused on explicit problem-solving workflows ("worked solutions"), we can elicit substantially improved planning capabilities from existing models. Additionally, we propose the Reasoning Enhancement Loop (REL), a method for generating synthetic worked solutions.

Researchers have long recognized the socio-technical gaps in personal tracking research, where machines can never fully model the complexity of human behavior, making it only able to produce basic rule-based outputs or "black-box" results that lack clear explanations. Real-world deployments rely on experts for this complex translation from sparse data to meaningful insights. In this study, we consider this translation process from data to insights by experts as "sensemaking" and explore how HCI researchers can support it through Vital Insight, an evidence-based 'sensemaking' system that combines direct representation and indirect inference through visualization and Large Language Models. We evaluate Vital Insight in user testing sessions with 14 experts in multi-modal tracking, synthesize design implications, and develop an expert sensemaking model where they iteratively move between direct data representations and AI-supported inferences to explore, retrieve, question, and validate insights.

Chain-of-thought (CoT) reasoning has enabled large language models (LLMs) to utilize additional computation through intermediate tokens to solve complex tasks. However, we posit that typical reasoning traces contain many redundant tokens, incurring extraneous inference costs. Upon examination of the output distribution of current LLMs, we find evidence on their latent ability to reason more concisely, relative to their default behavior. To elicit this capability, we propose simple fine-tuning methods which leverage self-generated concise reasoning paths obtained by best-of-N sampling and few-shot conditioning, in task-specific settings. Our combined method achieves a 30% reduction in output tokens on average, across five model families on GSM8K and MATH, while maintaining average accuracy. By exploiting the fundamental stochasticity and in-context learning capabilities of LLMs, our self-training approach robustly elicits concise reasoning on a wide range of models, including those with extensive post-training. Code is available at https://github.com/TergelMunkhbat/concise-reasoning

In this paper, we introduce the Tree-of-Thought (ToT) framework, a novel approach aimed at improving the problem-solving capabilities of auto-regressive large language models (LLMs). The ToT technique is inspired by the human mind's approach for solving complex reasoning tasks through trial and error. In this process, the human mind explores the solution space through a tree-like thought process, allowing for backtracking when necessary. To implement ToT as a software system, we augment an LLM with additional modules including a prompter agent, a checker module, a memory module, and a ToT controller. In order to solve a given problem, these modules engage in a multi-round conversation with the LLM. The memory module records the conversation and state history of the problem solving process, which allows the system to backtrack to the previous steps of the thought-process and explore other directions from there. To verify the effectiveness of the proposed technique, we implemented a ToT-based solver for the Sudoku Puzzle. Experimental results show that the ToT framework can significantly increase the success rate of Sudoku puzzle solving. Our implementation of the ToT-based Sudoku solver is available on GitHub: https://github.com/jieyilong/tree-of-thought-puzzle-solver.

Reinforcement learning (RL) has recently become a strong recipe for training reasoning LLMs that produce long chains of thought (LongCoT). Yet the standard RL "thinking environment", where the state is the prompt plus all prior reasoning tokens, makes the state unbounded and forces attention-based policies to pay quadratic compute as thoughts lengthen. We revisit the environment itself. We propose Markovian Thinking, a paradigm in which the policy advances reasoning while conditioning on a constant-size state, decoupling thinking length from context size. As an immediate consequence this yields linear compute with constant memory. We instantiate this idea with Delethink, an RL environment that structures reasoning into fixed-size chunks. Within each chunk, the model thinks as usual; at the boundary, the environment resets the context and reinitializes the prompt with a short carryover. Through RL, the policy learns to write a textual state near the end of each chunk sufficient for seamless continuation of reasoning after reset. Trained in this environment, an R1-Distill 1.5B model reasons in 8K-token chunks yet thinks up to 24K tokens, matching or surpassing LongCoT-RL trained with a 24K budget. With test-time scaling, Delethink continues to improve where LongCoT plateaus. The effect of linear compute is substantial: we empirically estimate at 96K average thinking length LongCoT-RL costs 27 H100-months vs. 7 for Delethink. Analysis at RL initialization shows off-the-shelf reasoning models (1.5B-120B) often sample Markovian traces zero-shot across diverse benchmarks, providing positive samples that make RL effective at scale. Our results show that redesigning the thinking environment is a powerful lever: it enables very long reasoning without quadratic overhead and opens a path toward efficient, scalable reasoning LLMs.

Human cognition typically involves thinking through abstract, fluid concepts rather than strictly using discrete linguistic tokens. Current reasoning models, however, are constrained to reasoning within the boundaries of human language, processing discrete token embeddings that represent fixed points in the semantic space. This discrete constraint restricts the expressive power and upper potential of such reasoning models, often causing incomplete exploration of reasoning paths, as standard Chain-of-Thought (CoT) methods rely on sampling one token per step. In this work, we introduce Soft Thinking, a training-free method that emulates human-like "soft" reasoning by generating soft, abstract concept tokens in a continuous concept space. These concept tokens are created by the probability-weighted mixture of token embeddings, which form the continuous concept space, enabling smooth transitions and richer representations that transcend traditional discrete boundaries. In essence, each generated concept token encapsulates multiple meanings from related discrete tokens, implicitly exploring various reasoning paths to converge effectively toward the correct answer. Empirical evaluations on diverse mathematical and coding benchmarks consistently demonstrate the effectiveness and efficiency of Soft Thinking, improving pass@1 accuracy by up to 2.48 points while simultaneously reducing token usage by up to 22.4% compared to standard CoT. Qualitative analysis further reveals that Soft Thinking outputs remain highly interpretable and readable, highlighting the potential of Soft Thinking to break the inherent bottleneck of discrete language-based reasoning. Code is available at https://github.com/eric-ai-lab/Soft-Thinking.

Due to the proliferation of short-form content and the rapid adoption of AI, opportunities for deep, reflective thinking have significantly diminished, undermining users' critical thinking and reducing engagement with the reasoning behind AI-generated outputs. To address this issue, we propose an Interactive Chain-of-Thought (CoT) Framework that enhances human-centered explainability and responsible AI usage by making the model's inference process transparent, modular, and user-editable. The framework decomposes reasoning into clearly defined blocks that users can inspect, modify, and re-execute, encouraging active cognitive engagement rather than passive consumption. It further integrates a lightweight edit-adaptation mechanism inspired by preference learning, allowing the system to align with diverse cognitive styles and user intentions. Ethical transparency is ensured through explicit metadata disclosure, built-in bias checkpoint functionality, and privacy-preserving safeguards. This work outlines the design principles and architecture necessary to promote critical engagement, responsible interaction, and inclusive adaptation in AI systems aimed at addressing complex societal challenges.

Large Language Models (LLMs) excel at reasoning and planning when trained on chainof-thought (CoT) data, where the step-by-step thought process is explicitly outlined by text tokens. However, this results in lengthy inputs where many words support textual coherence rather than core reasoning information, and processing these inputs consumes substantial computation resources. In this work, we propose a hybrid representation of the reasoning process, where we partially abstract away the initial reasoning steps using latent discrete tokens generated by VQ-VAE, significantly reducing the length of reasoning traces. We explore the use of latent trace abstractions in two scenarios: 1) training the model from scratch for the Keys-Finding Maze problem, 2) fine-tuning LLMs on this hybrid data with an extended vocabulary including unseen latent tokens, for both logical and mathematical reasoning problems. To facilitate effective learning, we introduce a simple training procedure that randomly mixes latent and text tokens, which enables fast adaptation to new latent tokens. Our approach consistently outperforms the baselines methods in various benchmarks.

Human interactions are deeply rooted in the interplay of thoughts, beliefs, and desires made possible by Theory of Mind (ToM): our cognitive ability to understand the mental states of ourselves and others. Although ToM may come naturally to us, emulating it presents a challenge to even the most advanced Large Language Models (LLMs). Recent improvements to LLMs' reasoning capabilities from simple yet effective prompting techniques such as Chain-of-Thought have seen limited applicability to ToM. In this paper, we turn to the prominent cognitive science theory "Simulation Theory" to bridge this gap. We introduce SimToM, a novel two-stage prompting framework inspired by Simulation Theory's notion of perspective-taking. To implement this idea on current ToM benchmarks, SimToM first filters context based on what the character in question knows before answering a question about their mental state. Our approach, which requires no additional training and minimal prompt-tuning, shows substantial improvement over existing methods, and our analysis reveals the importance of perspective-taking to Theory-of-Mind capabilities. Our findings suggest perspective-taking as a promising direction for future research into improving LLMs' ToM capabilities.

While recent success of large reasoning models (LRMs) significantly advanced LLMs' reasoning capability by optimizing the final answer accuracy using reinforcement learning, they may also drastically increase the output length due to overthinking, characterized by unnecessarily complex reasoning paths that waste computation and potentially degrade the performance. We hypothesize that such inefficiencies stem from LRMs' limited capability to dynamically select the proper modular reasoning strategies, termed thinking patterns at the right position. To investigate this hypothesis, we propose a dynamic optimization framework that segments model-generated reasoning paths into distinct thinking patterns, systematically identifying and promoting beneficial patterns that improve the answer while removing detrimental ones. Empirical analysis confirms that our optimized thinking paths yield more concise yet sufficiently informative trajectories, enhancing reasoning efficiency by reducing attention FLOPs by up to 47% while maintaining accuracy for originally correct responses. Moreover, a non-trivial portion of originally incorrect responses are transformed into correct ones, achieving a 15.6% accuracy improvement with reduced length. Motivated by the improvement brought by the optimized thinking paths, we apply a preference optimization technique supported by a pairwise dataset contrasting suboptimal and optimal reasoning paths. Experimental evaluations across multiple mathematical reasoning benchmarks reveal that our method notably reduces computational overhead while simultaneously improving reasoning accuracy, achieving up to a 12% accuracy improvement and reducing token usage from approximately 5,000 to 3,000 tokens.

Recent LLMs have significantly improved reasoning capabilities, primarily by including an explicit, lengthy Thinking process as part of generation. In this paper, we question whether this explicit thinking is necessary. Using the state-of-the-art DeepSeek-R1-Distill-Qwen, we find that bypassing the thinking process via simple prompting, denoted as NoThinking, can be surprisingly effective. When controlling for the number of tokens, NoThinking outperforms Thinking across a diverse set of seven challenging reasoning datasets--including mathematical problem solving, formal theorem proving, and coding--especially in low-budget settings, e.g., 51.3 vs. 28.9 on ACM 23 with 700 tokens. Notably, the performance of NoThinking becomes more competitive with pass@k as k increases. Building on this observation, we demonstrate that a parallel scaling approach that uses NoThinking to generate N outputs independently and aggregates them is highly effective. For aggregation, we use task-specific verifiers when available, or we apply simple best-of-N strategies such as confidence-based selection. Our method outperforms a range of baselines with similar latency using Thinking, and is comparable to Thinking with significantly longer latency (up to 9x). Together, our research encourages a reconsideration of the necessity of lengthy thinking processes, while also establishing a competitive reference for achieving strong reasoning performance in low-budget settings or at low latency using parallel scaling.

Test-Time Scaling (TTS) refers to approaches that improve reasoning performance by allocating extra computation during inference, without altering the model's parameters. While existing TTS methods operate in a discrete token space by generating more intermediate steps, recent studies in Coconut and SoftCoT have demonstrated that thinking in the continuous latent space can further enhance the reasoning performance. Such latent thoughts encode informative thinking without the information loss associated with autoregressive token generation, sparking increased interest in continuous-space reasoning. Unlike discrete decoding, where repeated sampling enables exploring diverse reasoning paths, latent representations in continuous space are fixed for a given input, which limits diverse exploration, as all decoded paths originate from the same latent thought. To overcome this limitation, we introduce SoftCoT++ to extend SoftCoT to the Test-Time Scaling paradigm by enabling diverse exploration of thinking paths. Specifically, we perturb latent thoughts via multiple specialized initial tokens and apply contrastive learning to promote diversity among soft thought representations. Experiments across five reasoning benchmarks and two distinct LLM architectures demonstrate that SoftCoT++ significantly boosts SoftCoT and also outperforms SoftCoT with self-consistency scaling. Moreover, it shows strong compatibility with conventional scaling techniques such as self-consistency. Source code is available at https://github.com/xuyige/SoftCoT.

Large language models have been shown to struggle with limited context memory and multi-step reasoning. We propose a simple method for solving both of these problems by allowing the model to take Self-Notes. Unlike recent scratchpad approaches, the model can deviate from the input context at any time to explicitly think. This allows the model to recall information and perform reasoning on the fly as it reads the context, thus extending its memory and enabling multi-step reasoning. Our experiments on multiple tasks demonstrate that our method can successfully generalize to longer and more complicated instances from their training setup by taking Self-Notes at inference time.

Artificial Intelligence Generated Content (AIGC) has shown remarkable progress in generating realistic images. However, in this paper, we take a step "backward" and address AIGC for the most rudimentary visual modality of human sketches. Our objective is on the creative nature of sketches, and that creative sketching should take the form of an interactive process. We further enable text to drive the sketch ideation process, allowing creativity to be freely defined, while simultaneously tackling the challenge of "I can't sketch". We present a method to generate controlled sketches using a text-conditioned diffusion model trained on pixel representations of images. Our proposed approach, referred to as SketchDreamer, integrates a differentiable rasteriser of Bezier curves that optimises an initial input to distil abstract semantic knowledge from a pretrained diffusion model. We utilise Score Distillation Sampling to learn a sketch that aligns with a given caption, which importantly enable both text and sketch to interact with the ideation process. Our objective is to empower non-professional users to create sketches and, through a series of optimisation processes, transform a narrative into a storyboard by expanding the text prompt while making minor adjustments to the sketch input. Through this work, we hope to aspire the way we create visual content, democratise the creative process, and inspire further research in enhancing human creativity in AIGC. The code is available at https://github.com/WinKawaks/SketchDreamer.

We introduce Graph of Thoughts (GoT): a framework that advances prompting capabilities in large language models (LLMs) beyond those offered by paradigms such as Chain-of-Thought or Tree of Thoughts (ToT). The key idea and primary advantage of GoT is the ability to model the information generated by an LLM as an arbitrary graph, where units of information ("LLM thoughts") are vertices, and edges correspond to dependencies between these vertices. This approach enables combining arbitrary LLM thoughts into synergistic outcomes, distilling the essence of whole networks of thoughts, or enhancing thoughts using feedback loops. We illustrate that GoT offers advantages over state of the art on different tasks, for example increasing the quality of sorting by 62% over ToT, while simultaneously reducing costs by >31%. We ensure that GoT is extensible with new thought transformations and thus can be used to spearhead new prompting schemes. This work brings the LLM reasoning closer to human thinking or brain mechanisms such as recurrence, both of which form complex networks.

Large Reasoning Models (LRMs) achieve superior performance by extending the thought length. However, a lengthy thinking trajectory leads to reduced efficiency. Most of the existing methods are stuck in the assumption of overthinking and attempt to reason efficiently by compressing the Chain-of-Thought, but this often leads to performance degradation. To address this problem, we introduce A*-Thought, an efficient tree search-based unified framework designed to identify and isolate the most essential thoughts from the extensive reasoning chains produced by these models. It formulates the reasoning process of LRMs as a search tree, where each node represents a reasoning span in the giant reasoning space. By combining the A* search algorithm with a cost function specific to the reasoning path, it can efficiently compress the chain of thought and determine a reasoning path with high information density and low cost. In addition, we also propose a bidirectional importance estimation mechanism, which further refines this search process and enhances its efficiency beyond uniform sampling. Extensive experiments on several advanced math tasks show that A*-Thought effectively balances performance and efficiency over a huge search space. Specifically, A*-Thought can improve the performance of QwQ-32B by 2.39times with low-budget and reduce the length of the output token by nearly 50% with high-budget. The proposed method is also compatible with several other LRMs, demonstrating its generalization capability. The code can be accessed at: https://github.com/AI9Stars/AStar-Thought.

Reasoning-capable language models achieve state-of-the-art performance in diverse complex tasks by generating long, explicit Chain-of-Thought (CoT) traces. While recent works show that base models can acquire such reasoning traces via reinforcement learning or distillation from stronger models like DeepSeek-R1, previous works demonstrate that even short CoT prompting without fine-tuning is able to improve reasoning. We ask whether long CoT can be induced in a base model using only prompting or minimal tuning. Using just 20 long CoT examples from the reasoning model QwQ-32B-Preview, we lightly fine-tune the base model Qwen2.5-32B. The resulting model outperforms the much larger Qwen2.5-Math-72B-Instruct, showing that a handful of high-quality examples can unlock strong reasoning capabilities. We further explore using CoT data from non-reasoning models and human annotators, enhanced with prompt engineering, multi-pass editing, and structural guidance. However, neither matches the performance of reasoning model traces, suggesting that certain latent qualities of expert CoT are difficult to replicate. We analyze key properties of reasoning data, such as problem difficulty, diversity, and answer length, that influence reasoning distillation. While challenges remain, we are optimistic that carefully curated human-written CoT, even in small quantities, can activate reasoning behaviors in base models. We release our human-authored dataset across refinement stages and invite further investigation into what makes small-scale reasoning supervision so effective.

We propose and test the LLM Brain Rot Hypothesis: continual exposure to junk web text induces lasting cognitive decline in large language models (LLMs). To causally isolate data quality, we run controlled experiments on real Twitter/X corpora, constructing junk and reversely controlled datasets via two orthogonal operationalizations: M1 (engagement degree) and M2 (semantic quality), with matched token scale and training operations across conditions. Contrary to the control group, continual pre-training of 4 LLMs on the junk dataset causes non-trivial declines (Hedges' g>0.3) on reasoning, long-context understanding, safety, and inflating "dark traits" (e.g., psychopathy, narcissism). The gradual mixtures of junk and control datasets also yield dose-response cognition decay: for example, under M1, ARC-Challenge with Chain Of Thoughts drops 74.9 rightarrow 57.2 and RULER-CWE 84.4 rightarrow 52.3 as junk ratio rises from 0% to 100%. Error forensics reveal several key insights. First, we identify thought-skipping as the primary lesion: models increasingly truncate or skip reasoning chains, explaining most of the error growth. Second, partial but incomplete healing is observed: scaling instruction tuning and clean data pre-training improve the declined cognition yet cannot restore baseline capability, suggesting persistent representational drift rather than format mismatch. Finally, we discover that the popularity, a non-semantic metric, of a tweet is a better indicator of the Brain Rot effect than the length in M1. Together, the results provide significant, multi-perspective evidence that data quality is a causal driver of LLM capability decay, reframing curation for continual pretraining as a training-time safety problem and motivating routine "cognitive health checks" for deployed LLMs.

Hallucinations (i.e., generating plausible but inaccurate content) and laziness (i.e. excessive refusals or defaulting to "I don't know") persist as major challenges in LLM reasoning. Current efforts to reduce hallucinations primarily focus on factual errors in knowledge-grounded tasks, often neglecting hallucinations related to faulty reasoning. Meanwhile, some approaches render LLMs overly conservative, limiting their problem-solving capabilities. To mitigate hallucination and laziness in reasoning tasks, we propose Automatic Curriculum Expert Iteration (Auto-CEI) to enhance LLM reasoning and align responses to the model's capabilities--assertively answering within its limits and declining when tasks exceed them. In our method, Expert Iteration explores the reasoning trajectories near the LLM policy, guiding incorrect paths back on track to reduce compounding errors and improve robustness; it also promotes appropriate "I don't know" responses after sufficient reasoning attempts. The curriculum automatically adjusts rewards, incentivizing extended reasoning before acknowledging incapability, thereby pushing the limits of LLM reasoning and aligning its behaviour with these limits. We compare Auto-CEI with various SOTA baselines across logical reasoning, mathematics, and planning tasks, where Auto-CEI achieves superior alignment by effectively balancing assertiveness and conservativeness.

While Multimodal Large Language Models (MLLMs) excel at visual understanding, they often struggle in complex scenarios that require visual planning and imagination. Inspired by how humans use sketching as a form of visual thinking to develop and communicate ideas, we introduce Latent Sketchpad, a framework that equips MLLMs with an internal visual scratchpad. The internal visual representations of MLLMs have traditionally been confined to perceptual understanding. We repurpose them to support generative visual thought without compromising reasoning ability. Building on frontier MLLMs, our approach integrates visual generation directly into their native autoregressive reasoning process. It allows the model to interleave textual reasoning with the generation of visual latents. These latents guide the internal thought process and can be translated into sketch images for interpretability. To realize this, we introduce two components: a Context-Aware Vision Head autoregressively produces visual representations, and a pretrained Sketch Decoder renders these into human-interpretable images. We evaluate the framework on our new dataset MazePlanning. Experiments across various MLLMs show that Latent Sketchpad delivers comparable or even superior reasoning performance to their backbone. It further generalizes across distinct frontier MLLMs, including Gemma3 and Qwen2.5-VL. By extending model's textual reasoning to visual thinking, our framework opens new opportunities for richer human-computer interaction and broader applications. More details and resources are available on our project page: https://latent-sketchpad.github.io/.

Divergent thinking, the cognitive process of generating diverse solutions, is a hallmark of human creativity and problem-solving. For machines, sampling diverse solution trajectories in complex reasoning problems is crucial for robust outcomes, data augmentation, and enhanced model generalization. Large language models (LLMs) often struggle with generating high-quality, diverse reasoning. While supervised fine-tuning helps with quality, it requires extensive supervision data to capture the full diversity of solutions. Alternatively, reinforcement learning methods like PPO aim to find limited highest-reward solutions while neglecting the solution diversity, akin to convergent thinking. To address these limitations, we propose Flow of Reasoning (FoR) -- an efficient LLM training approach enabling diverse reasoning with minimal data. FoR formulates multi-step LLM reasoning as a Markovian flow from an initial state to terminal states. The formulation allows to adapt principled GFlowNet approaches to train the LLM as a policy, which is able to sample multiple reasoning paths with probabilities proportional to the unnormalized reward. Empirical results show that, with limited training data (e.g., 15 examples), FoR can discover diverse high-quality solutions that excel greatly beyond current state-of-the-art methods across three tasks, including embodied reasoning (BlocksWorld), math puzzle solving (Game24), and logical reasoning (PrOntoQA). Code is available at https://github.com/Yu-Fangxu/FoR.

Chain-of-Thought (CoT) prompting reveals that large language models are capable of performing complex reasoning via intermediate steps. CoT prompting is primarily categorized into three approaches. The first approach utilizes straightforward prompts like ``Let's think step by step'' to generate a sequential thought process before yielding an answer. The second approach makes use of human-crafted, step-by-step demonstrations to guide the model's reasoning process. The third automates the generation of reasoned demonstrations with the 'Let's think step by step'.This approach sometimes leads to reasoning errors, highlighting the need to diversify demonstrations to mitigate its misleading effects. However, diverse demonstrations pose challenges for effective representations. In this work, we propose ECHO, a self-harmonized chain-of-thought prompting method. It consolidates diverse solution paths into a uniform and effective solution pattern.ECHO demonstrates the best overall performance across three reasoning domains.

Vision-Language Models (VLMs) excel at many multimodal tasks, yet their cognitive processes remain opaque on complex lateral thinking challenges like rebus puzzles. While recent work has demonstrated these models struggle significantly with rebus puzzle solving, the underlying reasoning processes and failure patterns remain largely unexplored. We address this gap through a comprehensive explainability analysis that moves beyond performance metrics to understand how VLMs approach these complex lateral thinking challenges. Our study contributes a systematically annotated dataset of 221 rebus puzzles across six cognitive categories, paired with an evaluation framework that separates reasoning quality from answer correctness. We investigate three prompting strategies designed to elicit different types of explanatory processes and reveal critical insights into VLM cognitive processes. Our findings demonstrate that reasoning quality varies dramatically across puzzle categories, with models showing systematic strengths in visual composition while exhibiting fundamental limitations in absence interpretation and cultural symbolism. We also discover that prompting strategy substantially influences both cognitive approach and problem-solving effectiveness, establishing explainability as an integral component of model performance rather than a post-hoc consideration.

Recent advancements in Large Language Models (LLMs) have demonstrated their potential in planning and reasoning tasks, offering a flexible alternative to classical pathfinding algorithms. However, most existing studies focus on LLMs' independent reasoning capabilities and overlook the potential synergy between LLMs and traditional algorithms. To fill this gap, we propose a comprehensive evaluation benchmark GridRoute to assess how LLMs can take advantage of traditional algorithms. We also propose a novel hybrid prompting technique called Algorithm of Thought (AoT), which introduces traditional algorithms' guidance into prompting. Our benchmark evaluates six LLMs ranging from 7B to 72B parameters across various map sizes, assessing their performance in correctness, optimality, and efficiency in grid environments with varying sizes. Our results show that AoT significantly boosts performance across all model sizes, particularly in larger or more complex environments, suggesting a promising approach to addressing path planning challenges. Our code is open-sourced at https://github.com/LinChance/GridRoute.

We study a class of optimization problems motivated by automating the design and update of AI systems like coding assistants, robots, and copilots. We propose an end-to-end optimization framework, Trace, which treats the computational workflow of an AI system as a graph akin to neural networks, based on a generalization of back-propagation. Optimization of computational workflows often involves rich feedback (e.g. console output or user's responses), heterogeneous parameters (e.g. prompts, hyper-parameters, codes), and intricate objectives (beyond maximizing a score). Moreover, its computation graph can change dynamically with the inputs and parameters. We frame a new mathematical setup of iterative optimization, Optimization with Trace Oracle (OPTO), to capture and abstract these properties so as to design optimizers that work across many domains. In OPTO, an optimizer receives an execution trace along with feedback on the computed output and updates parameters iteratively. Trace is the tool to implement OPTO in practice. Trace has a Python interface that efficiently converts a computational workflow into an OPTO instance using a PyTorch-like interface. Using Trace, we develop a general-purpose LLM-based optimizer called OptoPrime that can effectively solve OPTO problems. In empirical studies, we find that OptoPrime is capable of first-order numerical optimization, prompt optimization, hyper-parameter tuning, robot controller design, code debugging, etc., and is often competitive with specialized optimizers for each domain. We believe that Trace, OptoPrime and the OPTO framework will enable the next generation of interactive agents that automatically adapt using various kinds of feedback. Website: https://microsoft.github.io/Trace

Humans regularly engage in analogical thinking, relating personal experiences to current situations (X is analogous to Y because of Z). Analogical thinking allows humans to solve problems in creative ways, grasp difficult concepts, and articulate ideas more effectively. Can language models (LMs) do the same? To answer this question, we propose ANALOBENCH, a benchmark to determine analogical reasoning ability in LMs. Our benchmarking approach focuses on aspects of this ability that are common among humans: (i) recalling related experiences from a large amount of information, and (ii) applying analogical reasoning to complex and lengthy scenarios. We test a broad collection of proprietary models (e.g., GPT family, Claude V2) and open source models such as LLaMA2. As in prior results, scaling up LMs results in some performance boosts. Surprisingly, scale offers minimal gains when, (i) analogies involve lengthy scenarios, or (ii) recalling relevant scenarios from a large pool of information, a process analogous to finding a needle in a haystack. We hope these observations encourage further research in this field.

As Test-Time Scaling emerges as an active research focus in the large language model community, advanced post-training methods increasingly emphasize extending chain-of-thought (CoT) generation length, thereby enhancing reasoning capabilities to approach Deepseek R1-like reasoning models. However, recent studies reveal that reasoning models (even Qwen3) consistently exhibit excessive thought redundancy in CoT generation. This overthinking issue arises from the inherent limitations of conventional outcome-reward reinforcement learning, which systematically overlooks the regulation of intermediate reasoning processes. This paper introduces Serial-Group Decaying-Reward Policy Optimization (S-GRPO), a novel reinforcement learning paradigm that enables models to implicitly evaluate the sufficiency of intermediate reasoning steps, thereby facilitating early exit in CoT generation. Unlike GRPO, which samples multiple possible reasoning paths in parallel (parallel group), S-GRPO only samples one reasoning path and serially selects multiple temporal positions from the path to exit thinking and directly generate answers (serial group). For correct answers within a serial group, rewards gradually decrease based on the exit positions along the reasoning path from front to back. This design encourages the model to produce more accurate and concise thoughts, while also incentivizing early thinking termination when appropriate. Empirical evaluations demonstrate that S-GRPO is compatible with state-of-the-art reasoning models, including Qwen3 and Deepseek-distill. Across diverse benchmarks such as GSM8K, AIME 2024, AMC 2023, MATH-500, and GPQA Diamond, S-GRPO achieves a substantial reduction in sequence length (35.4% - 61.1%) while simultaneously improving accuracy (absolute 0.72% - 6.08%).

Mathematical reasoning is a crucial capability for Large Language Models (LLMs), yet generating detailed and accurate reasoning traces remains a significant challenge. This paper introduces a novel approach to produce high-quality reasoning traces for LLM fine-tuning using online learning Flows. Our method employs an incremental output production Flow, where component LLMs collaboratively construct solutions through iterative communication. We train the Flow using online Direct Preference Optimization (DPO) learning with rollouts, generating DPO pairs for each training example and updating models in real-time. We directly compare the quality of reasoning traces generated by our method with those produced through direct model inference, demonstrating the effectiveness of our approach in improving LLM performance in mathematical reasoning tasks.

We present THOUGHTSCULPT, a general reasoning and search method for tasks with outputs that can be decomposed into components. THOUGHTSCULPT explores a search tree of potential solutions using Monte Carlo Tree Search (MCTS), building solutions one action at a time and evaluating according to any domain-specific heuristic, which in practice is often simply an LLM evaluator. Critically, our action space includes revision actions: THOUGHTSCULPT may choose to revise part of its previous output rather than continuing to build the rest of its output. Empirically, THOUGHTSCULPT outperforms state-of-the-art reasoning methods across three challenging tasks: Story Outline Improvement (up to +30% interestingness), Mini-Crosswords Solving (up to +16% word success rate), and Constrained Generation (up to +10% concept coverage).

Interestingly, LLMs yet struggle with some basic tasks that humans find trivial to handle, e.g., counting the number of character r's in the word "strawberry". There are several popular conjectures (e.g., tokenization, architecture and training data) regarding the reason for deficiency of LLMs in simple word-based counting problems, sharing the similar belief that such failure stems from model pretraining hence probably inevitable during deployment. In this paper, we carefully design multiple evaluation settings to investigate validity of prevalent conjectures. Meanwhile, we measure transferability of advanced mathematical and coding reasoning capabilities from specialized LLMs to simple counting tasks. Although specialized LLMs suffer from counting problems as well, we find conjectures about inherent deficiency of LLMs invalid and further seek opportunities to elicit knowledge and capabilities from LLMs that are beneficial to counting tasks. Compared with strategies such as finetuning and in-context learning that are commonly adopted to enhance performance on new or challenging tasks, we show that engaging reasoning is the most robust and efficient way to help LLMs better perceive tasks with more accurate responses. We hope our conjecture validation design could provide insights into the study of future critical failure modes of LLMs. Based on challenges in transferring advanced capabilities to much simpler tasks, we call for more attention to model capability acquisition and evaluation. We also highlight the importance of cultivating consciousness of "reasoning before responding" during model pretraining.

Large reasoning models (LRMs), such as OpenAI's o1 and DeepSeek-R1, harness test-time scaling to perform multi-step reasoning for complex problem-solving. This reasoning process, executed before producing final answers, is often guided by special juncture tokens or textual segments that prompt self-evaluative reflection. We refer to these transition markers and reflective cues as "reflection tokens" (e.g., "wait", "but", "alternatively"). In this work, we treat reflection tokens as a "resource" and introduce the problem of resource allocation, aimed at improving the test-time compute performance of LRMs by adaptively regulating the frequency and placement of reflection tokens. Through empirical analysis, we show that both excessive and insufficient use of reflection tokens, referred to as over-reflection and under-reflection, can degrade model performance. To better understand and manage this trade-off, we draw an analogy between reflection token usage and learning rate scheduling in optimization. Building on this insight, we propose cyclical reflection token scheduling (termed CyclicReflex), a decoding strategy that dynamically modulates reflection token logits using a position-dependent triangular waveform. Experiments on MATH500, AIME2024/2025, and AMC2023 demonstrate that CyclicReflex consistently improves performance across model sizes (1.5B-8B), outperforming standard decoding and more recent approaches such as TIP (thought switching penalty) and S1. Codes are available at https://github.com/OPTML-Group/CyclicReflex.

We study how large language models (LLMs) ``think'' through their representation space. We propose a novel geometric framework that models an LLM's reasoning as flows -- embedding trajectories evolving where logic goes. We disentangle logical structure from semantics by employing the same natural deduction propositions with varied semantic carriers, allowing us to test whether LLMs internalize logic beyond surface form. This perspective connects reasoning with geometric quantities such as position, velocity, and curvature, enabling formal analysis in representation and concept spaces. Our theory establishes: (1) LLM reasoning corresponds to smooth flows in representation space, and (2) logical statements act as local controllers of these flows' velocities. Using learned representation proxies, we design controlled experiments to visualize and quantify reasoning flows, providing empirical validation of our theoretical framework. Our work serves as both a conceptual foundation and practical tools for studying reasoning phenomenon, offering a new lens for interpretability and formal analysis of LLMs' behavior.

Recent advances in Large Language Models (LLMs) have introduced Reasoning Large Language Models (RLLMs), which employ extended thinking processes with reflection and self-correction capabilities, demonstrating the effectiveness of test-time scaling. RLLMs exhibit innate Chain-of-Thought (CoT) reasoning capability obtained from training, leading to a natural question: "Is CoT prompting, a popular In-Context Learning (ICL) method for chat LLMs, necessary to enhance the reasoning capability of RLLMs?" In this work, we present the first comprehensive analysis of the impacts of Zero-shot CoT and Few-shot CoT on RLLMs across mathematical reasoning tasks. We examine models ranging from 1.5B to 32B parameters, finding that contrary to concerns, CoT prompting significantly enhances RLLMs' performance in most scenarios. Our results reveal distinct patterns: large-capacity models show minimal improvement on simple tasks but substantial gains on complex problems, while smaller models exhibit the opposite behavior. Further analysis demonstrates that CoT prompting effectively controls the distribution of the numbers of thinking tokens and reasoning steps, reducing excessive reflections by approximately 90% in some cases. Moreover, attention logits analysis reveals the RLLMs' overfitting to reflection-related words, which is mitigated by external CoT guidance. Notably, our experiments indicate that for RLLMs, one-shot CoT consistently yields superior performance compared to Few-shot CoT approaches. Our findings provide important insights for optimizing RLLMs' performance through appropriate prompting strategies.

According to the forgetting curve theory, we can enhance memory retention by learning extensive data and taking adequate rest. This means that in order to effectively retain new knowledge, it is essential to learn it thoroughly and ensure sufficient rest so that our brain can memorize without forgetting. The main takeaway from this theory is that learning extensive data at once necessitates sufficient rest before learning the same data again. This aspect of human long-term memory retention can be effectively utilized to address the continual learning of neural networks. Retaining new knowledge for a long period of time without catastrophic forgetting is the critical problem of continual learning. Therefore, based on Ebbinghaus' theory, we introduce the view-batch model that adjusts the learning schedules to optimize the recall interval between retraining the same samples. The proposed view-batch model allows the network to get enough rest to learn extensive knowledge from the same samples with a recall interval of sufficient length. To this end, we specifically present two approaches: 1) a replay method that guarantees the optimal recall interval, and 2) a self-supervised learning that acquires extensive knowledge from a single training sample at a time. We empirically show that these approaches of our method are aligned with the forgetting curve theory, which can enhance long-term memory. In our experiments, we also demonstrate that our method significantly improves many state-of-the-art continual learning methods in various protocols and scenarios. We open-source this project at https://github.com/hankyul2/ViewBatchModel.

"Thinking is for Doing." Humans can infer other people's mental states from observations--an ability called Theory-of-Mind (ToM)--and subsequently act pragmatically on those inferences. Existing question answering benchmarks such as ToMi ask models questions to make inferences about beliefs of characters in a story, but do not test whether models can then use these inferences to guide their actions. We propose a new evaluation paradigm for large language models (LLMs): Thinking for Doing (T4D), which requires models to connect inferences about others' mental states to actions in social scenarios. Experiments on T4D demonstrate that LLMs such as GPT-4 and PaLM 2 seemingly excel at tracking characters' beliefs in stories, but they struggle to translate this capability into strategic action. Our analysis reveals the core challenge for LLMs lies in identifying the implicit inferences about mental states without being explicitly asked about as in ToMi, that lead to choosing the correct action in T4D. To bridge this gap, we introduce a zero-shot prompting framework, Foresee and Reflect (FaR), which provides a reasoning structure that encourages LLMs to anticipate future challenges and reason about potential actions. FaR boosts GPT-4's performance from 50% to 71% on T4D, outperforming other prompting methods such as Chain-of-Thought and Self-Ask. Moreover, FaR generalizes to diverse out-of-distribution story structures and scenarios that also require ToM inferences to choose an action, consistently outperforming other methods including few-shot in-context learning.

Video reasoning using Large Multimodal Models (LMMs) relies on costly reinforcement learning (RL) and verbose chain-of-thought, resulting in substantial computational overhead during both training and inference. Moreover, the mechanisms that control the thinking process in these reasoning models are very limited. In this paper, using entropy of the model's output as a signal, we discover that the high-quality models go through a series of micro-explorations and micro-exploitations which keep the reasoning process grounded (i.e., avoid excessive randomness while the model is exploring or thinking through an answer). We further observe that once this "thinking" process is over, more accurate models demonstrate a better convergence by reducing the entropy significantly via a final exploitation phase (i.e., a more certain convergence towards a solution trajectory). We then use these novel, theoretically-grounded insights to tune the model's behavior directly at inference, without using any RL or supervised fine-tuning. Specifically, during inference, our proposed approach called V-Reason (Video-Reason) adapts the value cache of the LMM via a few optimization steps on a small, trainable controller using an entropy-based objective, i.e., no supervision from any dataset or RL is necessary. This tuning improves the model's micro-exploration and exploitation behavior during inference. Our experiments show that our proposed method achieves significant improvements over the base instruction-tuned models across several video reasoning datasets, narrowing the gap with RL-trained models to within 0.6% average accuracy without any training, while offering massive efficiency benefits: output tokens are reduced by 58.6% compared to the RL model.

Recent research developing neural network architectures with external memory have often used the benchmark bAbI question and answering dataset which provides a challenging number of tasks requiring reasoning. Here we employed a classic associative inference task from the memory-based reasoning neuroscience literature in order to more carefully probe the reasoning capacity of existing memory-augmented architectures. This task is thought to capture the essence of reasoning -- the appreciation of distant relationships among elements distributed across multiple facts or memories. Surprisingly, we found that current architectures struggle to reason over long distance associations. Similar results were obtained on a more complex task involving finding the shortest path between nodes in a path. We therefore developed MEMO, an architecture endowed with the capacity to reason over longer distances. This was accomplished with the addition of two novel components. First, it introduces a separation between memories (facts) stored in external memory and the items that comprise these facts in external memory. Second, it makes use of an adaptive retrieval mechanism, allowing a variable number of "memory hops" before the answer is produced. MEMO is capable of solving our novel reasoning tasks, as well as match state of the art results in bAbI.

The field of natural language processing (NLP) has witnessed significant progress in recent years, with a notable focus on improving large language models' (LLM) performance through innovative prompting techniques. Among these, prompt engineering coupled with structures has emerged as a promising paradigm, with designs such as Chain-of-Thought, Tree of Thoughts, or Graph of Thoughts, in which the overall LLM reasoning is guided by a structure such as a graph. As illustrated with numerous examples, this paradigm significantly enhances the LLM's capability to solve numerous tasks, ranging from logical or mathematical reasoning to planning or creative writing. To facilitate the understanding of this growing field and pave the way for future developments, we devise a general blueprint for effective and efficient LLM reasoning schemes. For this, we conduct an in-depth analysis of the prompt execution pipeline, clarifying and clearly defining different concepts. We then build the first taxonomy of structure-enhanced LLM reasoning schemes. We focus on identifying fundamental classes of harnessed structures, and we analyze the representations of these structures, algorithms executed with these structures, and many others. We refer to these structures as reasoning topologies, because their representation becomes to a degree spatial, as they are contained within the LLM context. Our study compares existing prompting schemes using the proposed taxonomy, discussing how certain design choices lead to different patterns in performance and cost. We also outline theoretical underpinnings, relationships between prompting and others parts of the LLM ecosystem such as knowledge bases, and the associated research challenges. Our work will help to advance future prompt engineering techniques.

To augment language models with the ability to reason, researchers usually prompt or finetune them to produce chain of thought reasoning steps before producing the final answer. However, although people use natural language to reason effectively, it may be that LMs could reason more effectively with some intermediate computation that is not in natural language. In this work, we explore an alternative reasoning approach: instead of explicitly producing the chain of thought reasoning steps, we use the language model's internal hidden states to perform implicit reasoning. The implicit reasoning steps are distilled from a teacher model trained on explicit chain-of-thought reasoning, and instead of doing reasoning "horizontally" by producing intermediate words one-by-one, we distill it such that the reasoning happens "vertically" among the hidden states in different layers. We conduct experiments on a multi-digit multiplication task and a grade school math problem dataset and find that this approach enables solving tasks previously not solvable without explicit chain-of-thought, at a speed comparable to no chain-of-thought.

Recently evolved large reasoning models (LRMs) show powerful performance in solving complex tasks with long chain-of-thought (CoT) reasoning capability. As these LRMs are mostly developed by post-training on formal reasoning tasks, whether they generalize the reasoning capability to help reduce hallucination in fact-seeking tasks remains unclear and debated. For instance, DeepSeek-R1 reports increased performance on SimpleQA, a fact-seeking benchmark, while OpenAI-o3 observes even severer hallucination. This discrepancy naturally raises the following research question: Are reasoning models more prone to hallucination? This paper addresses the question from three perspectives. (1) We first conduct a holistic evaluation for the hallucination in LRMs. Our analysis reveals that LRMs undergo a full post-training pipeline with cold start supervised fine-tuning (SFT) and verifiable reward RL generally alleviate their hallucination. In contrast, both distillation alone and RL training without cold start fine-tuning introduce more nuanced hallucinations. (2) To explore why different post-training pipelines alters the impact on hallucination in LRMs, we conduct behavior analysis. We characterize two critical cognitive behaviors that directly affect the factuality of a LRM: Flaw Repetition, where the surface-level reasoning attempts repeatedly follow the same underlying flawed logic, and Think-Answer Mismatch, where the final answer fails to faithfully match the previous CoT process. (3) Further, we investigate the mechanism behind the hallucination of LRMs from the perspective of model uncertainty. We find that increased hallucination of LRMs is usually associated with the misalignment between model uncertainty and factual accuracy. Our work provides an initial understanding of the hallucination in LRMs.

Existing chain-of-thought (CoT) distillation methods can effectively transfer reasoning abilities to base models but suffer from two major limitations: excessive verbosity of reasoning traces and inadequate adaptability to problem difficulty. Long reasoning traces significantly increase inference costs, and uniform-length solutions prevent base models from learning adaptive reasoning strategies. To address these issues, we propose a difficulty-aware prompting (DAP) method to dynamically shorten reasoning traces without performance loss. In our approach, a large teacher model first judges each problem's difficulty and then rewrites its reasoning traces to an appropriate shorter length, yielding concise yet complete reasoning traces. Leveraging the DAP pipeline, we curate a distilled dataset called LiteCoT consisting of 100K concise reasoning examples, with solutions averaging only 720 tokens (an order of magnitude shorter than typical CoTs). Using LiteCoT, we distilled a new family of reasoning models called Liter (1.5B, 7B, and 32B) based on the Qwen2.5 architecture. Experiments show that a student model fine-tuned on just 100K of these difficulty-pruned CoT samples outperforms a model distilled on 800K original Long CoT samples, while significantly reducing training and inference costs. Our method also generalizes well: across 11 diverse benchmarks, the shorter difficulty-aware CoTs achieve equal or better accuracy than Long chains, using far fewer tokens. For example, on the challenging AIME24 exam, our approach reaches 74.2% Pass@1 using only about 5K inference tokens, surpassing other methods that consume many more tokens. Our code and data are available at https://github.com/Evanwu1125/LiteCoT.

Enhancing the capability of large language models (LLMs) in reasoning has gained significant attention in recent years. Previous studies have demonstrated the effectiveness of various prompting strategies in aiding LLMs in reasoning (called "reasoning actions"), such as step-by-step thinking, reflecting before answering, solving with programs, and their combinations. However, these approaches often applied static, predefined reasoning actions uniformly to all questions, without considering the specific characteristics of each question or the capability of the task-solving LLM. In this paper, we propose DOTS, an approach enabling LLMs to reason dynamically via optimal reasoning trajectory search, tailored to the specific characteristics of each question and the inherent capability of the task-solving LLM. Our approach involves three key steps: i) defining atomic reasoning action modules that can be composed into various reasoning action trajectories; ii) searching for the optimal action trajectory for each training question through iterative exploration and evaluation for the specific task-solving LLM; and iii) using the collected optimal trajectories to train an LLM to plan for the reasoning trajectories of unseen questions. In particular, we propose two learning paradigms, i.e., fine-tuning an external LLM as a planner to guide the task-solving LLM, or directly fine-tuning the task-solving LLM with an internalized capability for reasoning actions planning. Our experiments across eight reasoning tasks show that our method consistently outperforms static reasoning techniques and the vanilla instruction tuning approach. Further analysis reveals that our method enables LLMs to adjust their computation based on problem complexity, allocating deeper thinking and reasoning to harder problems.

Recent Long-Context Language Models (LCLMs) can process hundreds of thousands of tokens in a single prompt, enabling new opportunities for knowledge-intensive multi-hop reasoning by integrating large sets of retrieved documents or, in some cases, directly all necessary information. However, simply feeding more documents into the context window fails to capture how evidence should be connected. We address this gap with thought templates, which recast reasoning as reusable thought caches, derived from prior problem solving traces, structuring how evidence is combined and guiding multi-hop inference with factual documents. To keep these templates effective, we propose an update strategy that iteratively refines templates derived from training data through natural-language feedback. Across diverse benchmarks and LCLM families, our approach delivers consistent gains over strong baselines in both retrieval-based and retrieval-free settings. Furthermore, we show that optimized templates can be distilled into smaller open-source models, demonstrating its broad applicability and transparent reasoning reuse. We refer to our framework as Thought Template Augmented LCLMs (ToTAL).

Compressing long chain-of-thought (CoT) from large language models (LLMs) is an emerging strategy to improve the reasoning efficiency of LLMs. Despite its promising benefits, existing studies equally compress all thoughts within a long CoT, hindering more concise and effective reasoning. To this end, we first investigate the importance of different thoughts by examining their effectiveness and efficiency in contributing to reasoning through automatic long CoT chunking and Monte Carlo rollouts. Building upon the insights, we propose a theoretically bounded metric to jointly measure the effectiveness and efficiency of different thoughts. We then propose LongotimesShort, an efficient reasoning framework that enables two LLMs to collaboratively solve the problem: a long-thought LLM for more effectively generating important thoughts, while a short-thought LLM for efficiently generating remaining thoughts. Specifically, we begin by synthesizing a small amount of cold-start data to fine-tune LLMs for long-thought and short-thought reasoning styles, respectively. Furthermore, we propose a synergizing-oriented multi-turn reinforcement learning, focusing on the model self-evolution and collaboration between long-thought and short-thought LLMs. Experimental results show that our method enables Qwen2.5-7B and Llama3.1-8B to achieve comparable performance compared to DeepSeek-R1-Distill-Qwen-7B and DeepSeek-R1-Distill-Llama-8B, while reducing token length by over 80% across the MATH500, AIME24/25, AMC23, and GPQA Diamond benchmarks. Our data and code are available at https://github.com/yasNing/Long-otimes-Short/.

We introduce thoughts of words (ToW), a novel training-time data-augmentation method for next-word prediction. ToW views next-word prediction as a core reasoning task and injects fine-grained thoughts explaining what the next word should be and how it is related to the previous contexts in pre-training texts. Our formulation addresses two fundamental drawbacks of existing next-word prediction learning schemes: they induce factual hallucination and are inefficient for models to learn the implicit reasoning processes in raw texts. While there are many ways to acquire such thoughts of words, we explore the first step of acquiring ToW annotations through distilling from larger models. After continual pre-training with only 70K ToW annotations, we effectively improve models' reasoning performances by 7% to 9% on average and reduce model hallucination by up to 10%. At the same time, ToW is entirely agnostic to tasks and applications, introducing no additional biases on labels or semantics.

Large language model (LLM) performance on reasoning problems typically does not generalize out of distribution. Previous work has claimed that this can be mitigated by modifying prompts to include examples with chains of thought--demonstrations of solution procedures--with the intuition that it is possible to in-context teach an LLM an algorithm for solving the problem. This paper presents a case study of chain of thought on problems from Blocksworld, a classical planning domain, and examine the performance of two state-of-the-art LLMs across two axes: generality of examples given in prompt, and complexity of problems queried with each prompt. While our problems are very simple, we only find meaningful performance improvements from chain of thought prompts when those prompts are exceedingly specific to their problem class, and that those improvements quickly deteriorate as the size n of the query-specified stack grows past the size of stacks shown in the examples. Our results hint that, contrary to previous claims in the literature, CoT's performance improvements do not stem from the model learning general algorithmic procedures via demonstrations and depend on carefully engineering highly problem specific prompts. This spotlights drawbacks of chain of thought, especially because of the sharp tradeoff between possible performance gains and the amount of human labor necessary to generate examples with correct reasoning traces.

We explore how iterative revising a chain of thoughts with the help of information retrieval significantly improves large language models' reasoning and generation ability in long-horizon generation tasks, while hugely mitigating hallucination. In particular, the proposed method -- *retrieval-augmented thoughts* (RAT) -- revises each thought step one by one with retrieved information relevant to the task query, the current and the past thought steps, after the initial zero-shot CoT is generated. Applying RAT to GPT-3.5, GPT-4, and CodeLLaMA-7b substantially improves their performances on various long-horizon generation tasks; on average of relatively increasing rating scores by 13.63% on code generation, 16.96% on mathematical reasoning, 19.2% on creative writing, and 42.78% on embodied task planning. The demo page can be found at https://craftjarvis.github.io/RAT

Large Reasoning Models (LRMs) demonstrate remarkable capabilities on complex tasks, exhibiting emergent, human-like thinking patterns. Despite their advances, we identify a fundamental limitation: current LRMs lack a dedicated meta-level cognitive system-an essential faculty in human cognition that enables "thinking about thinking". This absence leaves their emergent abilities uncontrollable (non-adaptive reasoning), unreliable (intermediate error), and inflexible (lack of a clear methodology). To address this gap, we introduce Meta-R1, a systematic and generic framework that endows LRMs with explicit metacognitive capabilities. Drawing on principles from cognitive science, Meta-R1 decomposes the reasoning process into distinct object-level and meta-level components, orchestrating proactive planning, online regulation, and adaptive early stopping within a cascaded framework. Experiments on three challenging benchmarks and against eight competitive baselines demonstrate that Meta-R1 is: (I) high-performing, surpassing state-of-the-art methods by up to 27.3%; (II) token-efficient, reducing token consumption to 15.7% ~ 32.7% and improving efficiency by up to 14.8% when compared to its vanilla counterparts; and (III) transferable, maintaining robust performance across datasets and model backbones.

The recent phenomenal success of language models has reinvigorated machine learning research, and large sequence models such as transformers are being applied to a variety of domains. One important problem class that has remained relatively elusive however is purposeful adaptive behavior. Currently there is a common perception that sequence models "lack the understanding of the cause and effect of their actions" leading them to draw incorrect inferences due to auto-suggestive delusions. In this report we explain where this mismatch originates, and show that it can be resolved by treating actions as causal interventions. Finally, we show that in supervised learning, one can teach a system to condition or intervene on data by training with factual and counterfactual error signals respectively.

Reasoning large language models (RLLMs) have recently demonstrated remarkable capabilities through structured and multi-step reasoning. While prior research has primarily focused on improving their training and inference strategies, their potential for in-context learning (ICL) remains largely underexplored. To fill this gap, we propose Thinking with Nothinking Calibration (JointThinking), a new ICL paradigm that leverages the structured difference between two reasoning modes, i.e., Thinking and Nothinking, to improve reasoning accuracy. Specifically, our method prompts the model to generate two answers in parallel: one in Thinking mode and the other in Nothinking mode. A second round of Thinking is triggered only when the two initial responses are inconsistent, using a single prompt that incorporates the original question and both candidate answers. Since such disagreement occurs infrequently (e.g., only 6\% in GSM8K), our method performs just one round of reasoning in most cases, resulting in minimal latency overhead. Extensive experiments across multiple reasoning benchmarks demonstrate that JointThinking significantly outperforms few-shot chain-of-thought (CoT) and majority voting with improved answer robustness. Moreover, It achieves comparable in-distribution performance to training-based SOTA method, while substantially outperforming on out-of-distribution tasks. We further conduct a systematic analysis of the calibration mechanism, showing that leveraging different reasoning modes consistently lowers the error rate and highlights the value of structural thinking diversity. Additionally, we observe that the performance gap between actual and ideal reasoning narrows as model size increases in the second round of thinking, indicating the strong scalability of our approach. Finally, we discuss current limitations and outline promising directions for future ICL research in RLLMs.

Class incremental learning (CIL) is a challenging setting of continual learning, which learns a series of tasks sequentially. Each task consists of a set of unique classes. The key feature of CIL is that no task identifier (or task-id) is provided at test time. Predicting the task-id for each test sample is a challenging problem. An emerging theory-guided approach (called TIL+OOD) is to train a task-specific model for each task in a shared network for all tasks based on a task-incremental learning (TIL) method to deal with catastrophic forgetting. The model for each task is an out-of-distribution (OOD) detector rather than a conventional classifier. The OOD detector can perform both within-task (in-distribution (IND)) class prediction and OOD detection. The OOD detection capability is the key to task-id prediction during inference. However, this paper argues that using a traditional OOD detector for task-id prediction is sub-optimal because additional information (e.g., the replay data and the learned tasks) available in CIL can be exploited to design a better and principled method for task-id prediction. We call the new method TPL (Task-id Prediction based on Likelihood Ratio). TPL markedly outperforms strong CIL baselines and has negligible catastrophic forgetting. The code of TPL is publicly available at https://github.com/linhaowei1/TPL.

Modern language models can imitate complex patterns through few-shot learning, enabling them to complete challenging tasks without fine-tuning. However, imitation can also lead models to reproduce inaccuracies or harmful content if present in the context. We study harmful imitation through the lens of a model's internal representations, and identify two related phenomena: "overthinking" and "false induction heads". The first phenomenon, overthinking, appears when we decode predictions from intermediate layers, given correct vs. incorrect few-shot demonstrations. At early layers, both demonstrations induce similar model behavior, but the behavior diverges sharply at some "critical layer", after which the accuracy given incorrect demonstrations progressively decreases. The second phenomenon, false induction heads, are a possible mechanistic cause of overthinking: these are heads in late layers that attend to and copy false information from previous demonstrations, and whose ablation reduces overthinking. Beyond scientific understanding, our results suggest that studying intermediate model computations could be a promising avenue for understanding and guarding against harmful model behaviors.

Recent advances in Chain-of-Thought (CoT) prompting have substantially improved the reasoning capabilities of Large Language Models (LLMs). However, these methods often suffer from overthinking, leading to unnecessarily lengthy or redundant reasoning traces. Existing approaches attempt to mitigate this issue through curating multiple reasoning chains for training LLMs, but their effectiveness is often constrained by the quality of the generated data and prone to overfitting. To address the challenge, we propose Reasoning Compression ThroUgh Stepwise Trials (ReCUT), a novel method aimed at balancing the accuracy and length of reasoning trajectory. Specifically, ReCUT employs a stepwise exploration mechanism and a long-short switched sampling strategy, enabling LLMs to incrementally generate diverse reasoning paths. These paths are evaluated and used to construct preference pairs to train two specialized models (Gemini LLMs)-one optimized for reasoning accuracy, the other for shorter reasoning. A final integrated model is obtained by interpolating the parameters of these two models. Experimental results across multiple math reasoning datasets and backbone models demonstrate that ReCUT significantly reduces reasoning lengths by approximately 30-50%, while maintaining or improving reasoning accuracy compared to various baselines. All codes and data will be released via https://github.com/NEUIR/ReCUT.

Large Language Models (LLMs) have demonstrated remarkable performance in solving complex reasoning tasks through mechanisms like Chain-of-Thought (CoT) prompting, which emphasizes verbose, step-by-step reasoning. However, humans typically employ a more efficient strategy: drafting concise intermediate thoughts that capture only essential information. In this work, we propose Chain of Draft (CoD), a novel paradigm inspired by human cognitive processes, where LLMs generate minimalistic yet informative intermediate reasoning outputs while solving tasks. By reducing verbosity and focusing on critical insights, CoD matches or surpasses CoT in accuracy while using as little as only 7.6% of the tokens, significantly reducing cost and latency across various reasoning tasks.

Test-time scaling (TTS), which involves dynamic allocation of compute during inference, offers a promising way to improve reasoning in large language models. While existing TTS methods work well, they often rely on long decoding paths or require a large number of samples to be generated, increasing the token usage and inference latency. We observe the surprising fact that for reasoning tasks, shorter traces are much more likely to be correct than longer ones. Motivated by this, we introduce First Finish Search (FFS), a training-free parallel decoding strategy that launches n independent samples and returns as soon as any one completes. We evaluate FFS alongside simple decoding, beam search, majority voting, and budget forcing on four reasoning models (DeepSeek-R1, R1-Distill-Qwen-32B, QwQ-32B and Phi-4-Reasoning-Plus) and across four datasets (AIME24, AIME25-I, AIME25-II and GPQA Diamond). With DeepSeek-R1, FFS achieves 82.23% accuracy on the AIME datasets, a 15% improvement over DeepSeek-R1's standalone accuracy, nearly matching OpenAI's o4-mini performance. Our theoretical analysis explains why stopping at the shortest trace is likely to yield a correct answer and identifies the conditions under which early stopping may be suboptimal. The elegance and simplicity of FFS demonstrate that straightforward TTS strategies can perform remarkably well, revealing the untapped potential of simple approaches at inference time.

Large Reasoning Models (LRMs) have demonstrated remarkable problem-solving abilities in mathematics, as evaluated by existing benchmarks exclusively on well-defined problems. However, such evaluation setup constitutes a critical gap, since a genuine intelligent agent should not only solve problems (as a math quiz solver), but also be able~to ask for information when the problems lack sufficient information, enabling proactivity in responding users' requests. To bridge such gap, we proposes a new dataset consisting of two types of incomplete problems with diverse contexts. Based on the dataset, our systematical evaluation of LRMs reveals their inability in proactively asking for information. In addition, we uncover the behaviors related to overthinking and hallucination of LRMs, and highlight the potential and challenges of supervised fine-tuning in learning such ability. We hope to provide new insights in developing LRMs with genuine intelligence, rather than just solving problems.