Daily Papers

We present IntPhys 2, a video benchmark designed to evaluate the intuitive physics understanding of deep learning models. Building on the original IntPhys benchmark, IntPhys 2 focuses on four core principles related to macroscopic objects: Permanence, Immutability, Spatio-Temporal Continuity, and Solidity. These conditions are inspired by research into intuitive physical understanding emerging during early childhood. IntPhys 2 offers a comprehensive suite of tests, based on the violation of expectation framework, that challenge models to differentiate between possible and impossible events within controlled and diverse virtual environments. Alongside the benchmark, we provide performance evaluations of several state-of-the-art models. Our findings indicate that while these models demonstrate basic visual understanding, they face significant challenges in grasping intuitive physics across the four principles in complex scenes, with most models performing at chance levels (50%), in stark contrast to human performance, which achieves near-perfect accuracy. This underscores the gap between current models and human-like intuitive physics understanding, highlighting the need for advancements in model architectures and training methodologies.

Recent advances in generative foundational models, often termed "world models," have propelled interest in applying them to critical tasks like robotic planning and autonomous system training. For reliable deployment, these models must exhibit high physical fidelity, accurately simulating real-world dynamics. Existing physics-based video benchmarks, however, suffer from entanglement, where a single test simultaneously evaluates multiple physical laws and concepts, fundamentally limiting their diagnostic capability. We introduce WorldBench, a novel video-based benchmark specifically designed for concept-specific, disentangled evaluation, allowing us to rigorously isolate and assess understanding of a single physical concept or law at a time. To make WorldBench comprehensive, we design benchmarks at two different levels: 1) an evaluation of intuitive physical understanding with concepts such as object permanence or scale/perspective, and 2) an evaluation of low-level physical constants and material properties such as friction coefficients or fluid viscosity. When SOTA video-based world models are evaluated on WorldBench, we find specific patterns of failure in particular physics concepts, with all tested models lacking the physical consistency required to generate reliable real-world interactions. Through its concept-specific evaluation, WorldBench offers a more nuanced and scalable framework for rigorously evaluating the physical reasoning capabilities of video generation and world models, paving the way for more robust and generalizable world-model-driven learning.

Large Language Models (LLMs), despite their advanced linguistic capabilities, fundamentally lack an intuitive understanding of physical dynamics, which limits their effectiveness in real-world scenarios that require causal reasoning. In this paper, we introduce Causal World Model Induction (CWMI), a novel framework designed to embed an explicit model of causal physics within an LLM. Our approach incorporates a dedicated Causal Physics Module (CPM) and a new training objective called Causal Intervention Loss, encouraging the model to learn cause-and-effect relationships from multimodal data. By training the model to predict the outcomes of hypothetical interventions instead of merely capturing statistical correlations, CWMI develops a robust internal representation of physical laws. Experimental results show that CWMI significantly outperforms state-of-the-art LLMs on zero-shot physical reasoning tasks, including the PIQA benchmark and our newly proposed PhysiCa-Bench dataset. These findings demonstrate that inducing a causal world model is a critical step toward more reliable and generalizable AI systems.

Intuitive physics understanding in video diffusion models plays an essential role in building general-purpose physically plausible world simulators, yet accurately evaluating such capacity remains a challenging task due to the difficulty in disentangling physics correctness from visual appearance in generation. To the end, we introduce LikePhys, a training-free method that evaluates intuitive physics in video diffusion models by distinguishing physically valid and impossible videos using the denoising objective as an ELBO-based likelihood surrogate on a curated dataset of valid-invalid pairs. By testing on our constructed benchmark of twelve scenarios spanning over four physics domains, we show that our evaluation metric, Plausibility Preference Error (PPE), demonstrates strong alignment with human preference, outperforming state-of-the-art evaluator baselines. We then systematically benchmark intuitive physics understanding in current video diffusion models. Our study further analyses how model design and inference settings affect intuitive physics understanding and highlights domain-specific capacity variations across physical laws. Empirical results show that, despite current models struggling with complex and chaotic dynamics, there is a clear trend of improvement in physics understanding as model capacity and inference settings scale.

Intuitive physics is pivotal for human understanding of the physical world, enabling prediction and interpretation of events even in infancy. Nonetheless, replicating this level of intuitive physics in artificial intelligence (AI) remains a formidable challenge. This study introduces X-VoE, a comprehensive benchmark dataset, to assess AI agents' grasp of intuitive physics. Built on the developmental psychology-rooted Violation of Expectation (VoE) paradigm, X-VoE establishes a higher bar for the explanatory capacities of intuitive physics models. Each VoE scenario within X-VoE encompasses three distinct settings, probing models' comprehension of events and their underlying explanations. Beyond model evaluation, we present an explanation-based learning system that captures physics dynamics and infers occluded object states solely from visual sequences, without explicit occlusion labels. Experimental outcomes highlight our model's alignment with human commonsense when tested against X-VoE. A remarkable feature is our model's ability to visually expound VoE events by reconstructing concealed scenes. Concluding, we discuss the findings' implications and outline future research directions. Through X-VoE, we catalyze the advancement of AI endowed with human-like intuitive physics capabilities.

While Multimodal Large Language Models (MLLMs) have become adept at recognizing objects, they often lack the intuitive, human-like understanding of the world's underlying physical and social principles. This high-level vision-grounded semantics, which we term visual knowledge, forms a bridge between perception and reasoning, yet remains an underexplored area in current MLLMs. To systematically evaluate this capability, we present VKnowU, a comprehensive benchmark featuring 1,680 questions in 1,249 videos, covering 8 core types of visual knowledge spanning both world-centric (e.g., intuitive physics) and human-centric (e.g., subjective intentions). Evaluation of 23 SOTA MLLMs reveals that leading models still fall short of human performance, with particularly notable gaps in the world-centric. To bridge this gap, we introduce a new dataset, VKnowQA, and VideoKnow+, a baseline model that explicitly incorporates visual knowledge into MLLMs. VideoKnow+ follows a structured See-Think-Answer paradigm and adopts reinforcement learning with visual knowledge reward, achieving a +3.7% improvement on VKnowU and consistent gains on MVBench, Video-MME, and MMVU. Our work highlights visual knowledge as a missing cornerstone for developing more generalizable MLLMs that can not only see but also truly understand our physical and social worlds.

Human commonsense understanding of the physical and social world is organized around intuitive theories. These theories support making causal and moral judgments. When something bad happens, we naturally ask: who did what, and why? A rich literature in cognitive science has studied people's causal and moral intuitions. This work has revealed a number of factors that systematically influence people's judgments, such as the violation of norms and whether the harm is avoidable or inevitable. We collected a dataset of stories from 24 cognitive science papers and developed a system to annotate each story with the factors they investigated. Using this dataset, we test whether large language models (LLMs) make causal and moral judgments about text-based scenarios that align with those of human participants. On the aggregate level, alignment has improved with more recent LLMs. However, using statistical analyses, we find that LLMs weigh the different factors quite differently from human participants. These results show how curated, challenge datasets combined with insights from cognitive science can help us go beyond comparisons based merely on aggregate metrics: we uncover LLMs implicit tendencies and show to what extent these align with human intuitions.

We investigate the emergence of intuitive physics understanding in general-purpose deep neural network models trained to predict masked regions in natural videos. Leveraging the violation-of-expectation framework, we find that video prediction models trained to predict outcomes in a learned representation space demonstrate an understanding of various intuitive physics properties, such as object permanence and shape consistency. In contrast, video prediction in pixel space and multimodal large language models, which reason through text, achieve performance closer to chance. Our comparisons of these architectures reveal that jointly learning an abstract representation space while predicting missing parts of sensory input, akin to predictive coding, is sufficient to acquire an understanding of intuitive physics, and that even models trained on one week of unique video achieve above chance performance. This challenges the idea that core knowledge -- a set of innate systems to help understand the world -- needs to be hardwired to develop an understanding of intuitive physics.

Humans develop an understanding of intuitive physics through active interaction with the world. This approach is in stark contrast to current video models, such as Sora, which rely on passive observation and therefore struggle with grasping physical causality. This observation leads to our central hypothesis: authentic physical intuition of the world model must be grounded in extensive, causally rich interactions with the real world. To test this hypothesis, we present WoW, a 14-billion-parameter generative world model trained on 2 million robot interaction trajectories. Our findings reveal that the model's understanding of physics is a probabilistic distribution of plausible outcomes, leading to stochastic instabilities and physical hallucinations. Furthermore, we demonstrate that this emergent capability can be actively constrained toward physical realism by SOPHIA, where vision-language model agents evaluate the DiT-generated output and guide its refinement by iteratively evolving the language instructions. In addition, a co-trained Inverse Dynamics Model translates these refined plans into executable robotic actions, thus closing the imagination-to-action loop. We establish WoWBench, a new benchmark focused on physical consistency and causal reasoning in video, where WoW achieves state-of-the-art performance in both human and autonomous evaluation, demonstrating strong ability in physical causality, collision dynamics, and object permanence. Our work provides systematic evidence that large-scale, real-world interaction is a cornerstone for developing physical intuition in AI. Models, data, and benchmarks will be open-sourced.

AI video generation is undergoing a revolution, with quality and realism advancing rapidly. These advances have led to a passionate scientific debate: Do video models learn ``world models'' that discover laws of physics -- or, alternatively, are they merely sophisticated pixel predictors that achieve visual realism without understanding the physical principles of reality? We address this question by developing Physics-IQ, a comprehensive benchmark dataset that can only be solved by acquiring a deep understanding of various physical principles, like fluid dynamics, optics, solid mechanics, magnetism and thermodynamics. We find that across a range of current models (Sora, Runway, Pika, Lumiere, Stable Video Diffusion, and VideoPoet), physical understanding is severely limited, and unrelated to visual realism. At the same time, some test cases can already be successfully solved. This indicates that acquiring certain physical principles from observation alone may be possible, but significant challenges remain. While we expect rapid advances ahead, our work demonstrates that visual realism does not imply physical understanding. Our project page is at https://physics-iq.github.io; code at https://github.com/google-deepmind/physics-IQ-benchmark.

Text-to-video (T2V) models like Sora have made significant strides in visualizing complex prompts, which is increasingly viewed as a promising path towards constructing the universal world simulator. Cognitive psychologists believe that the foundation for achieving this goal is the ability to understand intuitive physics. However, the capacity of these models to accurately represent intuitive physics remains largely unexplored. To bridge this gap, we introduce PhyGenBench, a comprehensive Physics Generation Benchmark designed to evaluate physical commonsense correctness in T2V generation. PhyGenBench comprises 160 carefully crafted prompts across 27 distinct physical laws, spanning four fundamental domains, which could comprehensively assesses models' understanding of physical commonsense. Alongside PhyGenBench, we propose a novel evaluation framework called PhyGenEval. This framework employs a hierarchical evaluation structure utilizing appropriate advanced vision-language models and large language models to assess physical commonsense. Through PhyGenBench and PhyGenEval, we can conduct large-scale automated assessments of T2V models' understanding of physical commonsense, which align closely with human feedback. Our evaluation results and in-depth analysis demonstrate that current models struggle to generate videos that comply with physical commonsense. Moreover, simply scaling up models or employing prompt engineering techniques is insufficient to fully address the challenges presented by PhyGenBench (e.g., dynamic scenarios). We hope this study will inspire the community to prioritize the learning of physical commonsense in these models beyond entertainment applications. We will release the data and codes at https://github.com/OpenGVLab/PhyGenBench

Common sense suggests that a particle must have a definite origin if its full path information is available. In quantum mechanics, the knowledge of path information is captured through the well-established duality relation between path distinguishability and interference visibility. If visibility is zero, high path distinguishability can be achieved, which enables one to determine with high predictive power where the particle originates. We investigate the complementarity between path information and interference visibility through an experiment involving three sources emitting into identical modes. Our findings challenge the classical intuition that a particle can be traced back to its origin through its trajectory when full path information is available. By grouping the crystals in different ways, we demonstrate that it is impossible to ascribe a definite physical origin to the photon pair, even if the emission probability of one individual source is zero and full path information is available. Our results shed new light on the physical interpretation of probability assignment and path information beyond its mathematical meaning and show that the interpretation of path information in quantum mechanics is subjective.

Reviewing the progress in artificial intelligence over the past decade, various significant advances (e.g. object detection, image generation, large language models) have enabled AI systems to produce more semantically meaningful outputs and achieve widespread adoption in internet scenarios. Nevertheless, AI systems still struggle when it comes to understanding and interacting with the physical world. This reveals an important issue: relying solely on semantic-level concepts learned from internet data (e.g. texts, images) to understand the physical world is far from sufficient -- machine intelligence currently lacks an effective way to learn about the physical world. This research introduces the idea of analytic concept -- representing the concepts related to the physical world through programs of mathematical procedures, providing machine intelligence a portal to perceive, reason about, and interact with the physical world. Except for detailing the design philosophy and providing guidelines for the application of analytic concepts, this research also introduce about the infrastructure that has been built around analytic concepts. I aim for my research to contribute to addressing these questions: What is a proper abstraction of general concepts in the physical world for machine intelligence? How to systematically integrate structured priors with neural networks to constrain AI systems to comply with physical laws?

The transition from symbolic manipulation to science-grade reasoning represents a pivotal frontier for Large Language Models (LLMs), with physics serving as the critical test anchor for binding abstract logic to physical reality. Physics demands that a model maintain physical consistency with the laws governing the universe, a task that fundamentally requires multimodal perception to ground abstract logic in reality. At the Olympiad level, diagrams are often constitutive rather than illustrative, containing essential constraints, such as boundary conditions and spatial symmetries, that are absent from the text. To bridge this visual-logical gap, we introduce P1-VL, a family of open-source vision-language models engineered for advanced scientific reasoning. Our method harmonizes Curriculum Reinforcement Learning, which employs progressive difficulty expansion to stabilize post-training, with Agentic Augmentation, enabling iterative self-verification at inference. Evaluated on HiPhO, a rigorous benchmark of 13 exams from 2024-2025, our flagship P1-VL-235B-A22B becomes the first open-source Vision-Language Model (VLM) to secure 12 gold medals and achieves the state-of-the-art performance in the open-source models. Our agent-augmented system achieves the No.2 overall rank globally, trailing only Gemini-3-Pro. Beyond physics, P1-VL demonstrates remarkable scientific reasoning capacity and generalizability, establishing significant leads over base models in STEM benchmarks. By open-sourcing P1-VL, we provide a foundational step toward general-purpose physical intelligence to better align visual perceptions with abstract physical laws for machine scientific discovery.

We investigate an experiential learning paradigm for acquiring an internal model of intuitive physics. Our model is evaluated on a real-world robotic manipulation task that requires displacing objects to target locations by poking. The robot gathered over 400 hours of experience by executing more than 100K pokes on different objects. We propose a novel approach based on deep neural networks for modeling the dynamics of robot's interactions directly from images, by jointly estimating forward and inverse models of dynamics. The inverse model objective provides supervision to construct informative visual features, which the forward model can then predict and in turn regularize the feature space for the inverse model. The interplay between these two objectives creates useful, accurate models that can then be used for multi-step decision making. This formulation has the additional benefit that it is possible to learn forward models in an abstract feature space and thus alleviate the need of predicting pixels. Our experiments show that this joint modeling approach outperforms alternative methods.

To apply eyeshadow without a brush, should I use a cotton swab or a toothpick? Questions requiring this kind of physical commonsense pose a challenge to today's natural language understanding systems. While recent pretrained models (such as BERT) have made progress on question answering over more abstract domains - such as news articles and encyclopedia entries, where text is plentiful - in more physical domains, text is inherently limited due to reporting bias. Can AI systems learn to reliably answer physical common-sense questions without experiencing the physical world? In this paper, we introduce the task of physical commonsense reasoning and a corresponding benchmark dataset Physical Interaction: Question Answering or PIQA. Though humans find the dataset easy (95% accuracy), large pretrained models struggle (77%). We provide analysis about the dimensions of knowledge that existing models lack, which offers significant opportunities for future research.

Automated discovery of physical laws from observational data in the real world is a grand challenge in AI. Current methods, relying on symbolic regression or LLMs, are limited to uni-modal data and overlook the rich, visual phenomenological representations of motion that are indispensable to physicists. This "sensory deprivation" severely weakens their ability to interpret the inherent spatio-temporal patterns within dynamic phenomena. To address this gap, we propose VIPER-R1, a multimodal model that performs Visual Induction for Physics-based Equation Reasoning to discover fundamental symbolic formulas. It integrates visual perception, trajectory data, and symbolic reasoning to emulate the scientific discovery process. The model is trained via a curriculum of Motion Structure Induction (MSI), using supervised fine-tuning to interpret kinematic phase portraits and to construct hypotheses guided by a Causal Chain of Thought (C-CoT), followed by Reward-Guided Symbolic Calibration (RGSC) to refine the formula structure with reinforcement learning. During inference, the trained VIPER-R1 acts as an agent: it first posits a high-confidence symbolic ansatz, then proactively invokes an external symbolic regression tool to perform Symbolic Residual Realignment (SR^2). This final step, analogous to a physicist's perturbation analysis, reconciles the theoretical model with empirical data. To support this research, we introduce PhysSymbol, a new 5,000-instance multimodal corpus. Experiments show that VIPER-R1 consistently outperforms state-of-the-art VLM baselines in accuracy and interpretability, enabling more precise discovery of physical laws. Project page: https://jiaaqiliu.github.io/VIPER-R1/

Recent advancements in video generation have witnessed significant progress, especially with the rapid advancement of diffusion models. Despite this, their deficiencies in physical cognition have gradually received widespread attention - generated content often violates the fundamental laws of physics, falling into the dilemma of ''visual realism but physical absurdity". Researchers began to increasingly recognize the importance of physical fidelity in video generation and attempted to integrate heuristic physical cognition such as motion representations and physical knowledge into generative systems to simulate real-world dynamic scenarios. Considering the lack of a systematic overview in this field, this survey aims to provide a comprehensive summary of architecture designs and their applications to fill this gap. Specifically, we discuss and organize the evolutionary process of physical cognition in video generation from a cognitive science perspective, while proposing a three-tier taxonomy: 1) basic schema perception for generation, 2) passive cognition of physical knowledge for generation, and 3) active cognition for world simulation, encompassing state-of-the-art methods, classical paradigms, and benchmarks. Subsequently, we emphasize the inherent key challenges in this domain and delineate potential pathways for future research, contributing to advancing the frontiers of discussion in both academia and industry. Through structured review and interdisciplinary analysis, this survey aims to provide directional guidance for developing interpretable, controllable, and physically consistent video generation paradigms, thereby propelling generative models from the stage of ''visual mimicry'' towards a new phase of ''human-like physical comprehension''.

Feynman famously asserted that interference is the only real mystery in quantum mechanics (QM). It is concluded that the reason for this mystery, and thereby the related mysteries of complementarity, non-commutativity of observables, the uncertainty principle and violation of Bell's equality, is that the axioms of QM depend vitally on the continuum nature of Hilbert Space, deemed unphysical. We develop a theory of quantum physics - Rational Quantum Mechanics (RaQM) - in which Hilbert Space is gravitationally discretised. The key to solving the mysteries of QM in RaQM is a number-theoretic property of the cosine function, concealed in QM when angles range over the continuum. This number-theoretic property describes mathematically the utter indivisibility of the quantum world and implies that the laws of physics are profoundly holistic. We contrast holism with nonlocality. In theories which embrace the continuum, the violation of Bell's inequality requires the laws of physics to be either nonlocal or not realistic; both incomprehensible concepts. By contrast, holism, as embodied in Mach's Principle or in the fractal geometry of a chaotic attractor, is neither incomprehensible nor unphysical. As part of this, we solve the deepest mystery of all; why nature makes use of complex numbers.

How does the brain predict physical outcomes while acting in the world? Machine learning world models compress visual input into latent spaces, discarding the spatial structure that characterizes sensory cortex. We propose isomorphic world models: architectures preserving sensory topology so that physics prediction becomes geometric propagation rather than abstract state transition. We implement this using neural fields with motor-gated channels, where activity evolves through local lateral connectivity and motor commands multiplicatively modulate specific populations. Three experiments support this approach: (1) local connectivity is sufficient to learn ballistic physics, with predictions traversing intermediate locations rather than "teleporting"; (2) policies trained entirely in imagination transfer to real physics at nearly twice the rate of latent-space alternatives; and (3) motor-gated channels spontaneously develop body-selective encoding through visuomotor prediction alone. These findings suggest intuitive physics and body schema may share a common origin in spatially structured neural dynamics.

Large language models (LLMs) have rapidly advanced and are increasingly capable of tackling complex scientific problems, including those in physics. Despite this progress, current LLMs often fail to emulate the concise, principle-based reasoning characteristic of human experts, instead generating lengthy and opaque solutions. This discrepancy highlights a crucial gap in their ability to apply core physical principles for efficient and interpretable problem solving. To systematically investigate this limitation, we introduce PhySense, a novel principle-based physics reasoning benchmark designed to be easily solvable by experts using guiding principles, yet deceptively difficult for LLMs without principle-first reasoning. Our evaluation across multiple state-of-the-art LLMs and prompt types reveals a consistent failure to align with expert-like reasoning paths, providing insights for developing AI systems with efficient, robust and interpretable principle-based scientific reasoning.

The Monty Hall problem is a classic probability puzzle known for its counterintuitive solution, revealing fundamental discrepancies between mathematical reasoning and human intuition. To bridge this gap, we introduce a novel explanatory framework inspired by quantum measurement theory. Specifically, we conceptualize the hosts' actions-opening doors to reveal non-prizes-as analogous to quantum measurements that cause asymmetric collapses of the probability distribution. This quantum-inspired interpretation not only clarifies why the intuitive misunderstanding arises but also provides generalized formulas consistent with standard Bayesian results. We further validate our analytical approach using Monte Carlo simulations across various problem settings, demonstrating precise agreement between theoretical predictions and empirical outcomes. Our quantum analogy thus offers a powerful pedagogical tool, enhancing intuitive understanding of conditional probability phenomena through the lens of probability redistribution and quantum-like measurement operations.

We discuss why AI is hard and why physics is simple. We discuss how physical intuition and the approach of theoretical physics can be brought to bear on the field of artificial intelligence and specifically machine learning. We suggest that the underlying project of machine learning and the underlying project of physics are strongly coupled through the principle of sparsity, and we call upon theoretical physicists to work on AI as physicists. As a first step in that direction, we discuss an upcoming book on the principles of deep learning theory that attempts to realize this approach.

Pre-trained on extensive text and image corpora, current Multi-Modal Large Language Models (MLLM) have shown strong capabilities in general visual reasoning tasks. However, their performance is still lacking in physical domains that require understanding diagrams with complex physical structures and quantitative analysis based on multi-modal information. To address this, we develop a new framework, named Multi-Modal Scientific Reasoning with Physics Perception and Simulation (MAPS) based on an MLLM. MAPS decomposes expert-level multi-modal reasoning task into physical diagram understanding via a Physical Perception Model (PPM) and reasoning with physical knowledge via a simulator. The PPM module is obtained by fine-tuning a visual language model using carefully designed synthetic data with paired physical diagrams and corresponding simulation language descriptions. At the inference stage, MAPS integrates the simulation language description of the input diagram provided by PPM and results obtained through a Chain-of-Simulation process with MLLM to derive the underlying rationale and the final answer. Validated using our collected college-level circuit analysis problems, MAPS significantly improves reasoning accuracy of MLLM and outperforms all existing models. The results confirm MAPS offers a promising direction for enhancing multi-modal scientific reasoning ability of MLLMs. We will release our code, model and dataset used for our experiments upon publishing of this paper.

Understanding the physical world is a fundamental challenge in embodied AI, critical for enabling agents to perform complex tasks and operate safely in real-world environments. While Vision-Language Models (VLMs) have shown great promise in reasoning and task planning for embodied agents, their ability to comprehend physical phenomena remains extremely limited. To close this gap, we introduce PhysBench, a comprehensive benchmark designed to evaluate VLMs' physical world understanding capability across a diverse set of tasks. PhysBench contains 10,002 entries of interleaved video-image-text data, categorized into four major domains: physical object properties, physical object relationships, physical scene understanding, and physics-based dynamics, further divided into 19 subclasses and 8 distinct capability dimensions. Our extensive experiments, conducted on 75 representative VLMs, reveal that while these models excel in common-sense reasoning, they struggle with understanding the physical world -- likely due to the absence of physical knowledge in their training data and the lack of embedded physical priors. To tackle the shortfall, we introduce PhysAgent, a novel framework that combines the generalization strengths of VLMs with the specialized expertise of vision models, significantly enhancing VLMs' physical understanding across a variety of tasks, including an 18.4\% improvement on GPT-4o. Furthermore, our results demonstrate that enhancing VLMs' physical world understanding capabilities can help embodied agents such as MOKA. We believe that PhysBench and PhysAgent offer valuable insights and contribute to bridging the gap between VLMs and physical world understanding.

Deep learning models are increasingly employed for perception, prediction, and control in complex systems. Embedding physical knowledge into these models is crucial for achieving realistic and consistent outputs, a challenge often addressed by physics-informed machine learning. However, integrating physical knowledge with representation learning becomes difficult when dealing with high-dimensional observation data, such as images, particularly under conditions of incomplete or imprecise state information. To address this, we propose Physically Interpretable World Models, a novel architecture that aligns learned latent representations with real-world physical quantities. Our method combines a variational autoencoder with a dynamical model that incorporates unknown system parameters, enabling the discovery of physically meaningful representations. By employing weak supervision with interval-based constraints, our approach eliminates the reliance on ground-truth physical annotations. Experimental results demonstrate that our method improves the quality of learned representations while achieving accurate predictions of future states, advancing the field of representation learning in dynamic systems.

Understanding the physical world is essential for generalist AI agents. However, it remains unclear whether state-of-the-art vision perception models (e.g., large VLMs) can reason physical properties quantitatively. Existing evaluations are predominantly VQA-based and qualitative, offering limited insight into whether these models can infer the kinematic quantities of moving objects from video observations. To address this, we present QuantiPhy, the first benchmark designed to quantitatively measure a VLM's physical reasoning ability. Comprising more than 3.3K video-text instances with numerical ground truth, QuantiPhy evaluates a VLM's performance on estimating an object's size, velocity, and acceleration at a given timestamp, using one of these properties as an input prior. The benchmark standardizes prompts and scoring to assess numerical accuracy, enabling fair comparisons across models. Our experiments on state-of-the-art VLMs reveal a consistent gap between their qualitative plausibility and actual numerical correctness. We further provide an in-depth analysis of key factors like background noise, counterfactual priors, and strategic prompting and find that state-of-the-art VLMs lean heavily on pre-trained world knowledge rather than faithfully using the provided visual and textual inputs as references when reasoning kinematic properties quantitatively. QuantiPhy offers the first rigorous, scalable testbed to move VLMs beyond mere verbal plausibility toward a numerically grounded physical understanding.

Humans learn by observing, interacting with environments, and internalizing physics and causality. Here, we aim to ask whether an agent can similarly acquire human-like reasoning from interaction and keep improving with more experience. We study this in a Game-to-Unseen (G2U) setting, curating 1,000+ heterogeneous games with diverse physical and causal mechanisms, and evaluate at three human-like levels: Survival, Curiosity, Utility, from primitive intuition to goal-driven reasoning. Our analysis reveals complementary failures: VLM/VLA agents reason but lack look-ahead in interactive settings, while world models imagine but imitate visual patterns rather than analyze physics and causality. We therefore propose IPR (Interactive Physical Reasoner), using world-model rollouts to score and reinforce a VLM's policy, and introduce PhysCode, a physics-centric action code aligning semantic intent with dynamics to provide a shared action space for prediction and reasoning. Pretrained on 1,000+ games, our IPR performs robustly on three levels, matches GPT-5 overall, and surpasses it on Curiosity. We find that performance improves with more training games and interaction steps, and that the model also zero-shot transfers to unseen games. These results support physics-centric interaction as a path to steadily improving physical reasoning.

Large Language Models (LLMs) are playing an expanding role in physics research by enhancing reasoning, symbolic manipulation, and numerical computation. However, ensuring the reliability and interpretability of their outputs remains a significant challenge. In our framework, we conceptualize the collaboration between AI and human scientists as a dynamic interplay among three modules: the reasoning module, the interpretation module, and the AI-scientist interaction module. Recognizing that effective physics reasoning demands rigorous logical consistency, quantitative precision, and deep integration with established theoretical models, we introduce the interpretation module to improve the understanding of AI-generated outputs, which is not previously explored in the literature. This module comprises multiple specialized agents, including summarizers, model builders, UI builders, and testers, which collaboratively structure LLM outputs within a physically grounded framework, by constructing a more interpretable science model. A case study demonstrates that our approach enhances transparency, facilitates validation, and strengthens AI-augmented reasoning in scientific discovery.

This work explores the hypothesis that subjectively attributed meaning constitutes the phenomenal content of conscious experience. That is, phenomenal content is semantic. This form of subjective meaning manifests as an intrinsic and non-representational character of qualia. Empirically, subjective meaning is ubiquitous in conscious experiences. We point to phenomenological studies that lend evidence to support this. Furthermore, this notion of meaning closely relates to what Frege refers to as "sense", in metaphysics and philosophy of language. It also aligns with Peirce's "interpretant", in semiotics. We discuss how Frege's sense can also be extended to the raw feels of consciousness. Sense and reference both play a role in phenomenal experience. Moreover, within the context of the mind-matter relation, we provide a formalization of subjective meaning associated to one's mental representations. Identifying the precise maps between the physical and mental domains, we argue that syntactic and semantic structures transcend language, and are realized within each of these domains. Formally, meaning is a relational attribute, realized via a map that interprets syntactic structures of a formal system within an appropriate semantic space. The image of this map within the mental domain is what is relevant for experience, and thus comprises the phenomenal content of qualia. We conclude with possible implications this may have for experience-based theories of consciousness.

We propose a formal reconstruction of quantum mechanics grounded not in external mathematical abstractions, but in the structured dynamics of subjective experience. The Qualia Abstraction Language (QAL) models physical systems as evolving streams of introspective units, structured sequences of modality, shape, and functional effect, rather than as state vectors in Hilbert space. This approach reimagines core quantum concepts: superposition becomes a form of structured ambiguity; collapse is reframed as an introspective contraction; and entanglement is modeled as semantic resonance across streams of qualia. Drawing on insights from nominalist philosophy and oversight theoretic limits in AI, we argue that the observer paradox in quantum mechanics reflects not an ontological lacuna, but a linguistic one: the absence of a formal vocabulary for modeling first person structure. QAL introduces such a vocabulary, providing a morphodynamic framework that embeds the observer within the system and replaces abstract projection with endogenous transformation. We analyze the alignment of QAL with endophysical approaches, contrast it with standard interpretations of quantum theory, and explore its implications for a post Platonist, introspectively grounded physics.

Physical AI systems need to perceive, understand, and perform complex actions in the physical world. In this paper, we present the Cosmos-Reason1 models that can understand the physical world and generate appropriate embodied decisions (e.g., next step action) in natural language through long chain-of-thought reasoning processes. We begin by defining key capabilities for Physical AI reasoning, with a focus on physical common sense and embodied reasoning. To represent physical common sense, we use a hierarchical ontology that captures fundamental knowledge about space, time, and physics. For embodied reasoning, we rely on a two-dimensional ontology that generalizes across different physical embodiments. Building on these capabilities, we develop two multimodal large language models, Cosmos-Reason1-8B and Cosmos-Reason1-56B. We curate data and train our models in four stages: vision pre-training, general supervised fine-tuning (SFT), Physical AI SFT, and Physical AI reinforcement learning (RL) as the post-training. To evaluate our models, we build comprehensive benchmarks for physical common sense and embodied reasoning according to our ontologies. Evaluation results show that Physical AI SFT and reinforcement learning bring significant improvements. To facilitate the development of Physical AI, we will make our code and pre-trained models available under the NVIDIA Open Model License at https://github.com/nvidia-cosmos/cosmos-reason1.

Understanding the physical world - governed by laws of motion, spatial relations, and causality - poses a fundamental challenge for multimodal large language models (MLLMs). While recent advances such as OpenAI o3 and GPT-4o demonstrate impressive perceptual and reasoning capabilities, our investigation reveals these models struggle profoundly with visual physical reasoning, failing to grasp basic physical laws, spatial interactions, and causal effects in complex scenes. More importantly, they often fail to follow coherent reasoning chains grounded in visual evidence, especially when multiple steps are needed to arrive at the correct answer. To rigorously evaluate this capability, we introduce MVPBench, a curated benchmark designed to rigorously evaluate visual physical reasoning through the lens of visual chain-of-thought (CoT). Each example features interleaved multi-image inputs and demands not only the correct final answer but also a coherent, step-by-step reasoning path grounded in evolving visual cues. This setup mirrors how humans reason through real-world physical processes over time. To ensure fine-grained evaluation, we introduce a graph-based CoT consistency metric that verifies whether the reasoning path of model adheres to valid physical logic. Additionally, we minimize shortcut exploitation from text priors, encouraging models to rely on visual understanding. Experimental results reveal a concerning trend: even cutting-edge MLLMs exhibit poor visual reasoning accuracy and weak image-text alignment in physical domains. Surprisingly, RL-based post-training alignment - commonly believed to improve visual reasoning performance - often harms spatial reasoning, suggesting a need to rethink current fine-tuning practices.

Large Language Models (LLMs) have achieved remarkable progress on advanced reasoning tasks such as mathematics and coding competitions. Meanwhile, physics, despite being both reasoning-intensive and essential to real-world understanding, received limited academic and industrial attention. This paper introduces PHYSICS, a dataset containing 16,568 high-quality physics problems spanning subjects and difficulty levels, to facilitate this issue. Specifically, PHYSICS is curated with exercises from over 100 textbooks through a carefully designed pipeline for quality control. It covers five major physics domains: Mechanics, Electromagnetism, Thermodynamics, Optics, and Modern Physics. It also spans a wide range of difficulty levels, from high school to graduate-level physics courses. To utilize the data for improving and evaluating the model's physical reasoning capabilities, we split the dataset into training and test sets, and provide reasoning paths generated by powerful reasoning models for the training data to facilitate model training. In addition, for the evaluation part, we find that existing evaluation frameworks exhibit biases in aspects such as units, simplification, and precision in physics domain. To balance efficiency and accuracy, we introduce a Rule+Model evaluation framework tailored to physics problems. Our evaluations on current state-of-the-art open-source and proprietary models highlight the limitations of current models in handling physics-related tasks. We hope that our dataset and evaluation methodology will jointly advance the development of LLMs in the field of physics.

Recent rapid advancements in text-to-video (T2V) generation, such as SoRA and Kling, have shown great potential for building world simulators. However, current T2V models struggle to grasp abstract physical principles and generate videos that adhere to physical laws. This challenge arises primarily from a lack of clear guidance on physical information due to a significant gap between abstract physical principles and generation models. To this end, we introduce the World Simulator Assistant (WISA), an effective framework for decomposing and incorporating physical principles into T2V models. Specifically, WISA decomposes physical principles into textual physical descriptions, qualitative physical categories, and quantitative physical properties. To effectively embed these physical attributes into the generation process, WISA incorporates several key designs, including Mixture-of-Physical-Experts Attention (MoPA) and a Physical Classifier, enhancing the model's physics awareness. Furthermore, most existing datasets feature videos where physical phenomena are either weakly represented or entangled with multiple co-occurring processes, limiting their suitability as dedicated resources for learning explicit physical principles. We propose a novel video dataset, WISA-32K, collected based on qualitative physical categories. It consists of 32,000 videos, representing 17 physical laws across three domains of physics: dynamics, thermodynamics, and optics. Experimental results demonstrate that WISA can effectively enhance the compatibility of T2V models with real-world physical laws, achieving a considerable improvement on the VideoPhy benchmark. The visual exhibitions of WISA and WISA-32K are available in the https://360cvgroup.github.io/WISA/.

Physical understanding remains brittle in omni-modal models because key physical attributes are visually ambiguous and sparsely represented in web-scale data. We present OmniFysics, a compact omni-modal model that unifies understanding across images, audio, video, and text, with integrated speech and image generation. To inject explicit physical knowledge, we build a physical data engine with two components. FysicsAny produces physics-grounded instruction--image supervision by mapping salient objects to verified physical attributes through hierarchical retrieval over a curated prototype database, followed by physics-law--constrained verification and caption rewriting. FysicsOmniCap distills web videos via audio--visual consistency filtering to generate high-fidelity video--instruction pairs emphasizing cross-modal physical cues. We train OmniFysics with staged multimodal alignment and instruction tuning, adopt latent-space flow matching for text-to-image generation, and use an intent router to activate generation only when needed. Experiments show competitive performance on standard multimodal benchmarks and improved results on physics-oriented evaluations.

Building future wireless systems that support services like digital twins (DTs) is challenging to achieve through advances to conventional technologies like meta-surfaces. While artificial intelligence (AI)-native networks promise to overcome some limitations of wireless technologies, developments still rely on AI tools like neural networks. Such tools struggle to cope with the non-trivial challenges of the network environment and the growing demands of emerging use cases. In this paper, we revisit the concept of AI-native wireless systems, equipping them with the common sense necessary to transform them into artificial general intelligence (AGI)-native systems. These systems acquire common sense by exploiting different cognitive abilities such as perception, analogy, and reasoning, that enable them to generalize and deal with unforeseen scenarios. Towards developing the components of such a system, we start by showing how the perception module can be built through abstracting real-world elements into generalizable representations. These representations are then used to create a world model, founded on principles of causality and hyper-dimensional (HD) computing, that aligns with intuitive physics and enables analogical reasoning, that define common sense. Then, we explain how methods such as integrated information theory play a role in the proposed intent-driven and objective-driven planning methods that maneuver the AGI-native network to take actions. Next, we discuss how an AGI-native network can enable use cases related to human and autonomous agents: a) analogical reasoning for next-generation DTs, b) synchronized and resilient experiences for cognitive avatars, and c) brain-level metaverse experiences like holographic teleportation. Finally, we conclude with a set of recommendations to build AGI-native systems. Ultimately, we envision this paper as a roadmap for the beyond 6G era.

Explainability has become an important topic in computer science and artificial intelligence, leading to a subfield called Explainable Artificial Intelligence (XAI). The goal of providing or seeking explanations is to achieve (better) 'understanding' on the part of the explainee. However, what it means to 'understand' is still not clearly defined, and the concept itself is rarely the subject of scientific investigation. This conceptual article aims to present a model of forms of understanding for XAI-explanations and beyond. From an interdisciplinary perspective bringing together computer science, linguistics, sociology, philosophy and psychology, a definition of understanding and its forms, assessment, and dynamics during the process of giving everyday explanations are explored. Two types of understanding are considered as possible outcomes of explanations, namely enabledness, 'knowing how' to do or decide something, and comprehension, 'knowing that' -- both in different degrees (from shallow to deep). Explanations regularly start with shallow understanding in a specific domain and can lead to deep comprehension and enabledness of the explanandum, which we see as a prerequisite for human users to gain agency. In this process, the increase of comprehension and enabledness are highly interdependent. Against the background of this systematization, special challenges of understanding in XAI are discussed.

Building AI systems that can plan, act, and create in the physical world requires more than pattern recognition. Such systems must understand the causal mechanisms and constraints governing physical processes in order to guide sequential decisions. This capability relies on internal representations, analogous to an internal language model, that relate observations, actions, and resulting environmental changes. However, many existing benchmarks treat visual perception and programmatic reasoning as separate problems, focusing either on visual recognition or on symbolic tasks. The domain of origami provides a natural testbed that integrates these modalities. Constructing shapes through folding operations requires visual perception, reasoning about geometric and physical constraints, and sequential planning, while remaining sufficiently structured for systematic evaluation. We introduce OrigamiBench, an interactive benchmark in which models iteratively propose folds and receive feedback on physical validity and similarity to a target configuration. Experiments with modern vision-language models show that scaling model size alone does not reliably produce causal reasoning about physical transformations. Models fail to generate coherent multi-step folding strategies, suggesting that visual and language representations remain weakly integrated.

Recent advances of data-driven machine learning have revolutionized fields like computer vision, reinforcement learning, and many scientific and engineering domains. In many real-world and scientific problems, systems that generate data are governed by physical laws. Recent work shows that it provides potential benefits for machine learning models by incorporating the physical prior and collected data, which makes the intersection of machine learning and physics become a prevailing paradigm. By integrating the data and mathematical physics models seamlessly, it can guide the machine learning model towards solutions that are physically plausible, improving accuracy and efficiency even in uncertain and high-dimensional contexts. In this survey, we present this learning paradigm called Physics-Informed Machine Learning (PIML) which is to build a model that leverages empirical data and available physical prior knowledge to improve performance on a set of tasks that involve a physical mechanism. We systematically review the recent development of physics-informed machine learning from three perspectives of machine learning tasks, representation of physical prior, and methods for incorporating physical prior. We also propose several important open research problems based on the current trends in the field. We argue that encoding different forms of physical prior into model architectures, optimizers, inference algorithms, and significant domain-specific applications like inverse engineering design and robotic control is far from being fully explored in the field of physics-informed machine learning. We believe that the interdisciplinary research of physics-informed machine learning will significantly propel research progress, foster the creation of more effective machine learning models, and also offer invaluable assistance in addressing long-standing problems in related disciplines.

Recent advances in mechanistic interpretability have revealed that large language models (LLMs) develop internal representations corresponding not only to concrete entities but also distinct, human-understandable abstract concepts and behaviour. Moreover, these hidden features can be directly manipulated to steer model behaviour. However, it remains an open question whether this phenomenon is unique to models trained on inherently structured data (ie. language, images) or if it is a general property of foundation models. In this work, we investigate the internal representations of a large physics-focused foundation model. Inspired by recent work identifying single directions in activation space for complex behaviours in LLMs, we extract activation vectors from the model during forward passes over simulation datasets for different physical regimes. We then compute "delta" representations between the two regimes. These delta tensors act as concept directions in activation space, encoding specific physical features. By injecting these concept directions back into the model during inference, we can steer its predictions, demonstrating causal control over physical behaviours, such as inducing or removing some particular physical feature from a simulation. These results suggest that scientific foundation models learn generalised representations of physical principles. They do not merely rely on superficial correlations and patterns in the simulations. Our findings open new avenues for understanding and controlling scientific foundation models and has implications for AI-enabled scientific discovery.

A longstanding goal in computer vision is to model motions from videos, while the representations behind motions, i.e. the invisible physical interactions that cause objects to deform and move, remain largely unexplored. In this paper, we study how to recover the invisible forces from visual observations, e.g., estimating the wind field by observing a leaf falling to the ground. Our key innovation is an end-to-end differentiable inverse graphics framework, which jointly models object geometry, physical properties, and interactions directly from videos. Through backpropagation, our approach enables the recovery of force representations from object motions. We validate our method on both synthetic and real-world scenarios, and the results demonstrate its ability to infer plausible force fields from videos. Furthermore, we show the potential applications of our approach, including physics-based video generation and editing. We hope our approach sheds light on understanding and modeling the physical process behind pixels, bridging the gap between vision and physics. Please check more video results in our https://chaoren2357.github.io/seeingthewind/{project page}.

Humans possess an exceptional ability to imagine 4D scenes, encompassing both motion and 3D geometry, from a single still image. This ability is rooted in our accumulated observations of similar scenes and an intuitive understanding of physics. In this paper, we aim to replicate this capacity in neural networks, specifically focusing on natural fluid imagery. Existing methods for this task typically employ simplistic 2D motion estimators to animate the image, leading to motion predictions that often defy physical principles, resulting in unrealistic animations. Our approach introduces a novel method for generating 4D scenes with physics-consistent animation from a single image. We propose the use of a physics-informed neural network that predicts motion for each surface point, guided by a loss term derived from fundamental physical principles, including the Navier-Stokes equations. To capture appearance, we predict feature-based 3D Gaussians from the input image and its estimated depth, which are then animated using the predicted motions and rendered from any desired camera perspective. Experimental results highlight the effectiveness of our method in producing physically plausible animations, showcasing significant performance improvements over existing methods. Our project page is https://physfluid.github.io/ .

Pre-trained language models (PLMs) have shown impressive performance in various language tasks. However, they are prone to spurious correlations, and often generate illusory information. In real-world applications, PLMs should justify decisions with formalized, coherent reasoning chains, but this challenge remains under-explored. Cognitive psychology theorizes that humans are capable of utilizing fast and intuitive heuristic thinking to make decisions based on past experience, then rationalizing the decisions through slower and deliberative analytic reasoning. We incorporate these interlinked dual processes in fine-tuning and in-context learning with PLMs, applying them to two language understanding tasks that require coherent physical commonsense reasoning. We show that our proposed Heuristic-Analytic Reasoning (HAR) strategies drastically improve the coherence of rationalizations for model decisions, yielding state-of-the-art results on Tiered Reasoning for Intuitive Physics (TRIP). We also find that this improved coherence is a direct result of more faithful attention to relevant language context in each step of reasoning. Our findings suggest that human-like reasoning strategies can effectively improve the coherence and reliability of PLM reasoning.

In this paper, we make the case that a scientific theory of deep learning is emerging. By this we mean a theory which characterizes important properties and statistics of the training process, hidden representations, final weights, and performance of neural networks. We pull together major strands of ongoing research in deep learning theory and identify five growing bodies of work that point toward such a theory: (a) solvable idealized settings that provide intuition for learning dynamics in realistic systems; (b) tractable limits that reveal insights into fundamental learning phenomena; (c) simple mathematical laws that capture important macroscopic observables; (d) theories of hyperparameters that disentangle them from the rest of the training process, leaving simpler systems behind; and (e) universal behaviors shared across systems and settings which clarify which phenomena call for explanation. Taken together, these bodies of work share certain broad traits: they are concerned with the dynamics of the training process; they primarily seek to describe coarse aggregate statistics; and they emphasize falsifiable quantitative predictions. We argue that the emerging theory is best thought of as a mechanics of the learning process, and suggest the name learning mechanics. We discuss the relationship between this mechanics perspective and other approaches for building a theory of deep learning, including the statistical and information-theoretic perspectives. In particular, we anticipate a symbiotic relationship between learning mechanics and mechanistic interpretability. We also review and address common arguments that fundamental theory will not be possible or is not important. We conclude with a portrait of important open directions in learning mechanics and advice for beginners. We host further introductory materials, perspectives, and open questions at learningmechanics.pub.

Machine learning methods can be a valuable aid in the scientific process, but they need to face challenging settings where data come from inhomogeneous experimental conditions. Recent meta-learning methods have made significant progress in multi-task learning, but they rely on black-box neural networks, resulting in high computational costs and limited interpretability. Leveraging the structure of the learning problem, we argue that multi-environment generalization can be achieved using a simpler learning model, with an affine structure with respect to the learning task. Crucially, we prove that this architecture can identify the physical parameters of the system, enabling interpreable learning. We demonstrate the competitive generalization performance and the low computational cost of our method by comparing it to state-of-the-art algorithms on physical systems, ranging from toy models to complex, non-analytical systems. The interpretability of our method is illustrated with original applications to physical-parameter-induced adaptation and to adaptive control.

Generative Artificial Intelligence (AI) has rapidly advanced the field of computer vision by enabling machines to create and interpret visual data with unprecedented sophistication. This transformation builds upon a foundation of generative models to produce realistic images, videos, and 3D/4D content. Conventional generative models primarily focus on visual fidelity while often neglecting the physical plausibility of the generated content. This gap limits their effectiveness in applications that require adherence to real-world physical laws, such as robotics, autonomous systems, and scientific simulations. As generative models evolve to increasingly integrate physical realism and dynamic simulation, their potential to function as "world simulators" expands. Therefore, the field of physics-aware generation in computer vision is rapidly growing, calling for a comprehensive survey to provide a structured analysis of current efforts. To serve this purpose, the survey presents a systematic review, categorizing methods based on how they incorporate physical knowledge, either through explicit simulation or implicit learning. It also analyzes key paradigms, discusses evaluation protocols, and identifies future research directions. By offering a comprehensive overview, this survey aims to help future developments in physically grounded generation for computer vision. The reviewed papers are summarized at https://tinyurl.com/Physics-Aware-Generation.

Modern foundational Multimodal Large Language Models (MLLMs) and video world models have advanced significantly in mathematical, common-sense, and visual reasoning, but their grasp of the underlying physics remains underexplored. Existing benchmarks attempting to measure this matter rely on synthetic, Visual Question Answer templates or focus on perceptual video quality that is tangential to measuring how well the video abides by physical laws. To address this fragmentation, we introduce PhysicsMind, a unified benchmark with both real and simulation environments that evaluates law-consistent reasoning and generation over three canonical principles: Center of Mass, Lever Equilibrium, and Newton's First Law. PhysicsMind comprises two main tasks: i) VQA tasks, testing whether models can reason and determine physical quantities and values from images or short videos, and ii) Video Generation(VG) tasks, evaluating if predicted motion trajectories obey the same center-of-mass, torque, and inertial constraints as the ground truth. A broad range of recent models and video generation models is evaluated on PhysicsMind and found to rely on appearance heuristics while often violating basic mechanics. These gaps indicate that current scaling and training are still insufficient for robust physical understanding, underscoring PhysicsMind as a focused testbed for physics-aware multimodal models. Our data will be released upon acceptance.

We present a technique for translating a black-box machine-learned classifier operating on a high-dimensional input space into a small set of human-interpretable observables that can be combined to make the same classification decisions. We iteratively select these observables from a large space of high-level discriminants by finding those with the highest decision similarity relative to the black box, quantified via a metric we introduce that evaluates the relative ordering of pairs of inputs. Successive iterations focus only on the subset of input pairs that are misordered by the current set of observables. This method enables simplification of the machine-learning strategy, interpretation of the results in terms of well-understood physical concepts, validation of the physical model, and the potential for new insights into the nature of the problem itself. As a demonstration, we apply our approach to the benchmark task of jet classification in collider physics, where a convolutional neural network acting on calorimeter jet images outperforms a set of six well-known jet substructure observables. Our method maps the convolutional neural network into a set of observables called energy flow polynomials, and it closes the performance gap by identifying a class of observables with an interesting physical interpretation that has been previously overlooked in the jet substructure literature.

Existing benchmarks fail to capture a crucial aspect of intelligence: physical reasoning, the integrated ability to combine domain knowledge, symbolic reasoning, and understanding of real-world constraints. To address this gap, we introduce PhyX: the first large-scale benchmark designed to assess models capacity for physics-grounded reasoning in visual scenarios. PhyX includes 3K meticulously curated multimodal questions spanning 6 reasoning types across 25 sub-domains and 6 core physics domains: thermodynamics, electromagnetism, mechanics, modern physics, optics, and wave\&acoustics. In our comprehensive evaluation, even state-of-the-art models struggle significantly with physical reasoning. GPT-4o, Claude3.7-Sonnet, and GPT-o4-mini achieve only 32.5\%, 42.2\%, and 45.8\% accuracy respectively-performance gaps exceeding 29\% compared to human experts. Our analysis exposes critical limitations in current models: over-reliance on memorized disciplinary knowledge, excessive dependence on mathematical formulations, and surface-level visual pattern matching rather than genuine physical understanding. We provide in-depth analysis through fine-grained statistics, detailed case studies, and multiple evaluation paradigms to thoroughly examine physical reasoning capabilities. To ensure reproducibility, we implement a compatible evaluation protocol based on widely-used toolkits such as VLMEvalKit, enabling one-click evaluation.

We introduce the Continuum Physical Dataset (ContPhy), a novel benchmark for assessing machine physical commonsense. ContPhy complements existing physical reasoning benchmarks by encompassing the inference of diverse physical properties, such as mass and density, across various scenarios and predicting corresponding dynamics. We evaluated a range of AI models and found that they still struggle to achieve satisfactory performance on ContPhy, which shows that the current AI models still lack physical commonsense for the continuum, especially soft-bodies, and illustrates the value of the proposed dataset. We also introduce an oracle model (ContPRO) that marries the particle-based physical dynamic models with the recent large language models, which enjoy the advantages of both models, precise dynamic predictions, and interpretable reasoning. ContPhy aims to spur progress in perception and reasoning within diverse physical settings, narrowing the divide between human and machine intelligence in understanding the physical world. Project page: https://physical-reasoning-project.github.io.

In this work, we describe strategies and provide case-study activities that can be used to examine the properties of superposition, entanglement, tagging, complementarity, and measurement in quantum curricula geared for teacher training. Having a solid foundation in these conceptual ideas is critical for educators who will be adopting quantum ideas within the classroom. Yet they are some of the most difficult concepts to master. We show how one can systematically develop these conceptual foundations with thought experiments on light and with thought experiments that employ the Stern-Gerlach experiment. We emphasize the importance of computer animations in aiding the instruction on these concepts.

Successful and effective communication between humans and AI relies on a shared experience of the world. By training solely on written text, current language models (LMs) miss the grounded experience of humans in the real-world -- their failure to relate language to the physical world causes knowledge to be misrepresented and obvious mistakes in their reasoning. We present Mind's Eye, a paradigm to ground language model reasoning in the physical world. Given a physical reasoning question, we use a computational physics engine (DeepMind's MuJoCo) to simulate the possible outcomes, and then use the simulation results as part of the input, which enables language models to perform reasoning. Experiments on 39 tasks in a physics alignment benchmark demonstrate that Mind's Eye can improve reasoning ability by a large margin (27.9% zero-shot, and 46.0% few-shot absolute accuracy improvement on average). Smaller language models armed with Mind's Eye can obtain similar performance to models that are 100x larger. Finally, we confirm the robustness of Mind's Eye through ablation studies.

In Marius von Senden's Space and Sight, a newly sighted blind patient describes the experience of a corner as lemon-like, because corners "prick" sight like lemons prick the tongue. Prickliness, here, is a dimension in the feature space of sensory experience, an effect of the perceived on the perceiver that arises where the two interact. In the account of the newly sighted, an effect familiar from one interaction translates to a novel context. Perception serves as the vehicle for generalization, in that an effect shared across different experiences produces a concrete abstraction grounded in those experiences. Cezanne and the post-impressionists, fluent in the language of experience translation, realized that the way to paint a concrete form that best reflected reality was to paint not what they saw, but what it was like to see. We envision a future of creation using AI where what it is like to see is replicable, transferrable, manipulable - part of the artist's palette that is both grounded in a particular context, and generalizable beyond it. An active line of research maps human-interpretable features onto directions in GAN latent space. Supervised and self-supervised approaches that search for anticipated directions or use off-the-shelf classifiers to drive image manipulation in embedding space are limited in the variety of features they can uncover. Unsupervised approaches that discover useful new directions show that the space of perceptually meaningful directions is nowhere close to being fully mapped. As this space is broad and full of creative potential, we want tools for direction discovery that capture the richness and generalizability of human perception. Our approach puts creators in the discovery loop during real-time tool use, in order to identify directions that are perceptually meaningful to them, and generate interpretable image translations along those directions.

This paper introduces an innovative approach to analyzing and improving multi-hop reasoning in AI systems by drawing inspiration from Hamiltonian mechanics. We propose a novel framework that maps reasoning chains in embedding spaces to Hamiltonian systems, allowing us to leverage powerful analytical tools from classical physics. Our method defines a Hamiltonian function that balances the progression of reasoning (kinetic energy) against the relevance to the question at hand (potential energy). Using this framework, we analyze a large dataset of reasoning chains from a multi-hop question-answering task, revealing intriguing patterns that distinguish valid from invalid reasoning. We show that valid reasoning chains have lower Hamiltonian energy and move in ways that make the best trade-off between getting more information and answering the right question. Furthermore, we demonstrate the application of this framework to steer the creation of more efficient reasoning algorithms within AI systems. Our results not only provide new insights into the nature of valid reasoning but also open up exciting possibilities for physics-inspired approaches to understanding and improving artificial intelligence.

We respond to the recent paper by Makelov et al. (2023), which reviews subspace interchange intervention methods like distributed alignment search (DAS; Geiger et al. 2023) and claims that these methods potentially cause "interpretability illusions". We first review Makelov et al. (2023)'s technical notion of what an "interpretability illusion" is, and then we show that even intuitive and desirable explanations can qualify as illusions in this sense. As a result, their method of discovering "illusions" can reject explanations they consider "non-illusory". We then argue that the illusions Makelov et al. (2023) see in practice are artifacts of their training and evaluation paradigms. We close by emphasizing that, though we disagree with their core characterization, Makelov et al. (2023)'s examples and discussion have undoubtedly pushed the field of interpretability forward.

Multimodal Large Language Models (MLLMs) have demonstrated remarkable capabilities in diverse reasoning tasks, yet their application to complex physics reasoning remains underexplored. Physics reasoning presents unique challenges, requiring grounding in physical conditions and the interpretation of multimodal information. Current physics benchmarks are limited, often focusing on text-only inputs or solely on problem-solving, thereby overlooking the critical intermediate steps of variable identification and process formulation. To address these limitations, we introduce PhysicsArena, the first multimodal physics reasoning benchmark designed to holistically evaluate MLLMs across three critical dimensions: variable identification, physical process formulation, and solution derivation. PhysicsArena aims to provide a comprehensive platform for assessing and advancing the multimodal physics reasoning abilities of MLLMs.

Physical reasoning, which involves the interpretation, understanding, and prediction of object behavior in dynamic environments, remains a significant challenge for current Vision-Language Models (VLMs). In this work, we propose two methods to enhance VLMs' physical reasoning capabilities using simulated data. First, we fine-tune a pre-trained VLM using question-answer (QA) pairs generated from simulations relevant to physical reasoning tasks. Second, we introduce Physics Context Builders (PCBs), specialized VLMs fine-tuned to create scene descriptions enriched with physical properties and processes. During physical reasoning tasks, these PCBs can be leveraged as context to assist a Large Language Model (LLM) to improve its performance. We evaluate both of our approaches using multiple benchmarks, including a new stability detection QA dataset called Falling Tower, which includes both simulated and real-world scenes, and CLEVRER. We demonstrate that a small QA fine-tuned VLM can significantly outperform larger state-of-the-art foundational models. We also show that integrating PCBs boosts the performance of foundational LLMs on physical reasoning tasks. Using the real-world scenes from the Falling Tower dataset, we also validate the robustness of both approaches in Sim2Real transfer. Our results highlight the utility that simulated data can have in the creation of learning systems capable of advanced physical reasoning.

The Mechanistic Interpretability (MI) program has mapped the Transformer as a precise computational graph. We extend this graph with a conservation law and time-varying AC dynamics, viewing it as a physical circuit. We introduce Momentum Attention, a symplectic augmentation embedding physical priors via the kinematic difference operator p_t = q_t - q_{t-1}, implementing the symplectic shear q_t = q_t + γp_t on queries and keys. We identify a fundamental Symplectic-Filter Duality: the physical shear is mathematically equivalent to a High-Pass Filter. This duality is our cornerstone contribution -- by injecting kinematic momentum, we sidestep the topological depth constraint (L geq 2) for induction head formation. While standard architectures require two layers for induction from static positions, our extension grants direct access to velocity, enabling Single-Layer Induction and Spectral Forensics via Bode Plots. We formalize an Orthogonality Theorem proving that DC (semantic) and AC (mechanistic) signals segregate into orthogonal frequency bands when Low-Pass RoPE interacts with High-Pass Momentum. Validated through 5,100+ controlled experiments (documented in Supplementary Appendices A--R and 27 Jupyter notebooks), our 125M Momentum model exceeds expectations on induction-heavy tasks while tracking a 350M baseline within sim2.9% validation loss. Dedicated associative recall experiments reveal a scaling law γ^* = 4.17 times N^{-0.74} establishing momentum-depth fungibility. We offer this framework as a complementary analytical toolkit connecting Generative AI, Hamiltonian Physics, and Signal Processing.

Physical commonsense reasoning represents a fundamental capability of human intelligence, enabling individuals to understand their environment, predict future events, and navigate physical spaces. Recent years have witnessed growing interest in reasoning tasks within Natural Language Processing (NLP). However, no prior research has examined the performance of Large Language Models (LLMs) on non-question-answering (non-QA) physical commonsense reasoning tasks in low-resource languages such as Basque. Taking the Italian GITA as a starting point, this paper addresses this gap by presenting BasPhyCo, the first non-QA physical commonsense reasoning dataset for Basque, available in both standard and dialectal variants. We evaluate model performance across three hierarchical levels of commonsense understanding: (1) distinguishing between plausible and implausible narratives (accuracy), (2) identifying the conflicting element that renders a narrative implausible (consistency), and (3) determining the specific physical state that creates the implausibility (verifiability). These tasks were assessed using multiple multilingual LLMs as well as models pretrained specifically for Italian and Basque. Results indicate that, in terms of verifiability, LLMs exhibit limited physical commonsense capabilities in low-resource languages such as Basque, especially when processing dialectal variants.

Understanding the physical structure is essential for real-world applications such as embodied agents, interactive design, and long-horizon manipulation. Yet, prevailing Vision-Language Model (VLM) evaluations still center on structure-agnostic, single-turn setups (e.g., VQA), which fail to assess agents' ability to reason about how geometry, contact, and support relations jointly constrain what actions are possible in a dynamic environment. To address this gap, we introduce the Causal Hierarchy of Actions and Interactions (CHAIN) benchmark, an interactive 3D, physics-driven testbed designed to evaluate whether models can understand, plan, and execute structured action sequences grounded in physical constraints. CHAIN shifts evaluation from passive perception to active problem solving, spanning tasks such as interlocking mechanical puzzles and 3D stacking and packing. We conduct a comprehensive study of state-of-the-art VLMs and diffusion-based models under unified interactive settings. Our results show that top-performing models still struggle to internalize physical structure and causal constraints, often failing to produce reliable long-horizon plans and cannot robustly translate perceived structure into effective actions. The project is available at https://social-ai-studio.github.io/CHAIN/.

In a systematic way, we investigate a widely asked question: Do LLMs really understand what they say?, which relates to the more familiar term Stochastic Parrot. To this end, we propose a summative assessment over a carefully designed physical concept understanding task, PhysiCo. Our task alleviates the memorization issue via the usage of grid-format inputs that abstractly describe physical phenomena. The grids represents varying levels of understanding, from the core phenomenon, application examples to analogies to other abstract patterns in the grid world. A comprehensive study on our task demonstrates: (1) state-of-the-art LLMs, including GPT-4o, o1 and Gemini 2.0 flash thinking, lag behind humans by ~40%; (2) the stochastic parrot phenomenon is present in LLMs, as they fail on our grid task but can describe and recognize the same concepts well in natural language; (3) our task challenges the LLMs due to intrinsic difficulties rather than the unfamiliar grid format, as in-context learning and fine-tuning on same formatted data added little to their performance.

We propose the Intuitive Reasoning Network (IRENE) - a novel neural model for intuitive psychological reasoning about agents' goals, preferences, and actions that can generalise previous experiences to new situations. IRENE combines a graph neural network for learning agent and world state representations with a transformer to encode the task context. When evaluated on the challenging Baby Intuitions Benchmark, IRENE achieves new state-of-the-art performance on three out of its five tasks - with up to 48.9% improvement. In contrast to existing methods, IRENE is able to bind preferences to specific agents, to better distinguish between rational and irrational agents, and to better understand the role of blocking obstacles. We also investigate, for the first time, the influence of the training tasks on test performance. Our analyses demonstrate the effectiveness of IRENE in combining prior knowledge gained during training for unseen evaluation tasks.

We present SeePhys, a large-scale multimodal benchmark for LLM reasoning grounded in physics questions ranging from middle school to PhD qualifying exams. The benchmark covers 7 fundamental domains spanning the physics discipline, incorporating 21 categories of highly heterogeneous diagrams. In contrast to prior works where visual elements mainly serve auxiliary purposes, our benchmark features a substantial proportion of vision-essential problems (75\%) that mandate visual information extraction for correct solutions. Through extensive evaluation, we observe that even the most advanced visual reasoning models (e.g., Gemini-2.5-pro and o4-mini) achieve sub-60\% accuracy on our benchmark. These results reveal fundamental challenges in current large language models' visual understanding capabilities, particularly in: (i) establishing rigorous coupling between diagram interpretation and physics reasoning, and (ii) overcoming their persistent reliance on textual cues as cognitive shortcuts.

Despite impressive visual fidelity, modern video generative models frequently produce sequences that violate intuitive physical laws, such as objects floating, teleporting, or morphing in ways that defy causality. While humans can easily detect such implausibilities, there remains no robust method for quantitatively assessing physical realism in video. In this work, we explore whether Video-Language Models (VLMs) can be trained to serve as reliable judges of physical plausibility. We find that existing VLMs struggle to identify physics violations, exposing fundamental limitations in their temporal and causal reasoning. To address this, we introduce TRAVL, a fine-tuning recipe that combines a balanced training dataset with a trajectory-aware attention module to improve motion encoding and discrimination in VLMs. To evaluate physical reasoning more rigorously, we propose ImplausiBench, a benchmark of 300 videos (150 real, 150 generated) that removes linguistic biases and isolates visual-temporal understanding. Performance is reported both with gold-standard human judgments and stricter LLM-as-judge metrics. Together, TRAVL and ImplausiBench offer a unified framework for probing and improving physical plausibility in multimodal models, shedding light on a challenging and underexplored aspect of visual-temporal understanding.

As Vision-Language Models (VLMs) grow in sophistication, their ability to perform reasoning is coming under increasing supervision. While they excel at many tasks, their grasp of fundamental scientific principles, such as physics, remains an underexplored frontier. To reflect the advancements in these capabilities, we introduce a novel and accessible framework designed to rigorously evaluate VLMs on their understanding of 2D physics. Our framework features a pragmatic scenario generator that creates a diverse testbed of over 400 problems across four core domains: Projectile Motion, Collision Dynamics, Mechanics, and Fluid Dynamics. Through comprehensive evaluation of four state-of-the-art VLMs, we demonstrate a strong correlation between model scale and reasoning ability, with our top-performing model, Qwen2.5-VL-7B, achieving an overall score of 0.815. We find that while models excel at formulaic problems, they struggle significantly with domains requiring abstract spatial reasoning. By designing this framework, we aim to democratize the study of scientific reasoning in VLMs and foster deeper insights into their capabilities and limitations.

Mechanical reasoning is a hallmark of human intelligence, defined by its ubiquitous yet irreplaceable role in human activities ranging from routine tasks to civil engineering. Embedding machines with mechanical reasoning is therefore an important step towards building human-level artificial intelligence. Here, we leveraged 155 cognitive experiments to test the understanding of system stability, gears and pulley systems, leverage principle, inertia and motion, and fluid mechanics in 26 Vision Language Models (VLMs). Results indicate that VLMs consistently perform worse than humans on all domains, while demonstrate significant difficulty in reasoning about gear systems and fluid mechanics. Notably, their performance on these tasks do not improve as number of parameters increase, suggesting that current attention-based architecture may fail to grasp certain underlying mechanisms required for mechanical reasoning, particularly those pertaining to mental simulations.

The advent of material databases provides an unprecedented opportunity to uncover predictive descriptors for emergent material properties from vast data space. However, common reliance on high-throughput ab initio data necessarily inherits limitations of such data: mismatch with experiments. On the other hand, experimental decisions are often guided by an expert's intuition honed from experiences that are rarely articulated. We propose using machine learning to "bottle" such operational intuition into quantifiable descriptors using expertly curated measurement-based data. We introduce "Materials Expert-Artificial Intelligence" (ME-AI) to encapsulate and articulate this human intuition. As a first step towards such a program, we focus on the topological semimetal (TSM) among square-net materials as the property inspired by the expert-identified descriptor based on structural information: the tolerance factor. We start by curating a dataset encompassing 12 primary features of 879 square-net materials, using experimental data whenever possible. We then use Dirichlet-based Gaussian process regression using a specialized kernel to reveal composite descriptors for square-net topological semimetals. The ME-AI learned descriptors independently reproduce expert intuition and expand upon it. Specifically, new descriptors point to hypervalency as a critical chemical feature predicting TSM within square-net compounds. Our success with a carefully defined problem points to the "machine bottling human insight" approach as promising for machine learning-aided material discovery.

We present a new probing dataset named PROST: Physical Reasoning about Objects Through Space and Time. This dataset contains 18,736 multiple-choice questions made from 14 manually curated templates, covering 10 physical reasoning concepts. All questions are designed to probe both causal and masked language models in a zero-shot setting. We conduct an extensive analysis which demonstrates that state-of-the-art pretrained models are inadequate at physical reasoning: they are influenced by the order in which answer options are presented to them, they struggle when the superlative in a question is inverted (e.g., most <-> least), and increasing the amount of pretraining data and parameters only yields minimal improvements. These results provide support for the hypothesis that current pretrained models' ability to reason about physical interactions is inherently limited by a lack of real world experience. By highlighting these limitations, we hope to motivate the development of models with a human-like understanding of the physical world.

In this work, we generalize the reaction-diffusion equation in statistical physics, Schr\"odinger equation in quantum mechanics, Helmholtz equation in paraxial optics into the neural partial differential equations (NPDE), which can be considered as the fundamental equations in the field of artificial intelligence research. We take finite difference method to discretize NPDE for finding numerical solution, and the basic building blocks of deep neural network architecture, including multi-layer perceptron, convolutional neural network and recurrent neural networks, are generated. The learning strategies, such as Adaptive moment estimation, L-BFGS, pseudoinverse learning algorithms and partial differential equation constrained optimization, are also presented. We believe it is of significance that presented clear physical image of interpretable deep neural networks, which makes it be possible for applying to analog computing device design, and pave the road to physical artificial intelligence.

We focus on the self-supervised discovery of manipulation concepts that can be adapted and reassembled to address various robotic tasks. We propose that the decision to conceptualize a physical procedure should not depend on how we name it (semantics) but rather on the significance of the informativeness in its representation regarding the low-level physical state and state changes. We model manipulation concepts (discrete symbols) as generative and discriminative goals and derive metrics that can autonomously link them to meaningful sub-trajectories from noisy, unlabeled demonstrations. Specifically, we employ a trainable codebook containing encodings (concepts) capable of synthesizing the end-state of a sub-trajectory given the current state (generative informativeness). Moreover, the encoding corresponding to a particular sub-trajectory should differentiate the state within and outside it and confidently predict the subsequent action based on the gradient of its discriminative score (discriminative informativeness). These metrics, which do not rely on human annotation, can be seamlessly integrated into a VQ-VAE framework, enabling the partitioning of demonstrations into semantically consistent sub-trajectories, fulfilling the purpose of discovering manipulation concepts and the corresponding sub-goal (key) states. We evaluate the effectiveness of the learned concepts by training policies that utilize them as guidance, demonstrating superior performance compared to other baselines. Additionally, our discovered manipulation concepts compare favorably to human-annotated ones while saving much manual effort.

Foundation models have emerged as effective backbones for many vision tasks. However, current self-supervised features entangle high-level semantics with low-level physical factors, such as geometry and illumination, hindering their use in tasks requiring explicit physical reasoning. In this paper, we introduce Φeat, a novel physically-grounded visual backbone that encourages a representation sensitive to material identity, including reflectance cues and geometric mesostructure. Our key idea is to employ a pretraining strategy that contrasts spatial crops and physical augmentations of the same material under varying shapes and lighting conditions. While similar data have been used in high-end supervised tasks such as intrinsic decomposition or material estimation, we demonstrate that a pure self-supervised training strategy, without explicit labels, already provides a strong prior for tasks requiring robust features invariant to external physical factors. We evaluate the learned representations through feature similarity analysis and material selection, showing that Φeat captures physically-grounded structure beyond semantic grouping. These findings highlight the promise of unsupervised physical feature learning as a foundation for physics-aware perception in vision and graphics. These findings highlight the promise of unsupervised physical feature learning as a foundation for physics-aware perception in vision and graphics.

In a recent paper, Erasmus et al. (2021) defend the idea that the ambiguity of the term "explanation" in explainable AI (XAI) can be solved by adopting any of four different extant accounts of explanation in the philosophy of science: the Deductive Nomological, Inductive Statistical, Causal Mechanical, and New Mechanist models. In this chapter, I show that the authors' claim that these accounts can be applied to deep neural networks as they would to any natural phenomenon is mistaken. I also provide a more general argument as to why the notion of explainability as it is currently used in the XAI literature bears little resemblance to the traditional concept of scientific explanation. It would be more fruitful to use the label "understandable AI" to avoid the confusion that surrounds the goal and purposes of XAI. In the second half of the chapter, I argue for a pragmatic conception of understanding that is better suited to play the central role attributed to explanation in XAI. Following Kuorikoski & Ylikoski (2015), the conditions of satisfaction for understanding an ML system are fleshed out in terms of an agent's success in using the system, in drawing correct inferences from it.

Recent advances in video generation have shown remarkable potential for constructing world simulators. However, current models still struggle to produce physically consistent results, particularly when handling large-scale or complex dynamics. This limitation arises primarily because existing approaches respond isotropically to physical prompts and neglect the fine-grained alignment between generated content and localized physical cues. To address these challenges, we propose ProPhy, a Progressive Physical Alignment Framework that enables explicit physics-aware conditioning and anisotropic generation. ProPhy employs a two-stage Mixture-of-Physics-Experts (MoPE) mechanism for discriminative physical prior extraction, where Semantic Experts infer semantic-level physical principles from textual descriptions, and Refinement Experts capture token-level physical dynamics. This mechanism allows the model to learn fine-grained, physics-aware video representations that better reflect underlying physical laws. Furthermore, we introduce a physical alignment strategy that transfers the physical reasoning capabilities of vision-language models (VLMs) into the Refinement Experts, facilitating a more accurate representation of dynamic physical phenomena. Extensive experiments on physics-aware video generation benchmarks demonstrate that ProPhy produces more realistic, dynamic, and physically coherent results than existing state-of-the-art methods.

We introduce Augmented Physics, a machine learning-integrated authoring tool designed for creating embedded interactive physics simulations from static textbook diagrams. Leveraging recent advancements in computer vision, such as Segment Anything and Multi-modal LLMs, our web-based system enables users to semi-automatically extract diagrams from physics textbooks and generate interactive simulations based on the extracted content. These interactive diagrams are seamlessly integrated into scanned textbook pages, facilitating interactive and personalized learning experiences across various physics concepts, such as optics, circuits, and kinematics. Drawing from an elicitation study with seven physics instructors, we explore four key augmentation strategies: 1) augmented experiments, 2) animated diagrams, 3) bi-directional binding, and 4) parameter visualization. We evaluate our system through technical evaluation, a usability study (N=12), and expert interviews (N=12). Study findings suggest that our system can facilitate more engaging and personalized learning experiences in physics education.

Recent advances in image and video generation raise hopes that these models possess world modeling capabilities, the ability to generate realistic, physically plausible videos. This could revolutionize applications in robotics, autonomous driving, and scientific simulation. However, before treating these models as world models, we must ask: Do they adhere to physical conservation laws? To answer this, we introduce Morpheus, a benchmark for evaluating video generation models on physical reasoning. It features 80 real-world videos capturing physical phenomena, guided by conservation laws. Since artificial generations lack ground truth, we assess physical plausibility using physics-informed metrics evaluated with respect to infallible conservation laws known per physical setting, leveraging advances in physics-informed neural networks and vision-language foundation models. Our findings reveal that even with advanced prompting and video conditioning, current models struggle to encode physical principles despite generating aesthetically pleasing videos. All data, leaderboard, and code are open-sourced at our project page.

Unified multimodal models are envisioned to bridge the gap between understanding and generation. Yet, to achieve competitive performance, state-of-the-art models adopt largely decoupled understanding and generation components. This design, while effective for individual tasks, weakens the connection required for mutual enhancement, leaving the potential synergy empirically uncertain. We propose to explicitly restore this synergy by introducing Understanding-Oriented Post-Training (UNO), a lightweight framework that treats understanding not only as a distinct task, but also a direct supervisory signal to steer generative representations. By incorporating objectives that encode semantic abstraction (captioning) and structural details (visual regression), we enable effective gradient flow from understanding to generation. Extensive experiments on image generation and editing demonstrate that understanding can serve as an effective catalyst for generation.

Neural networks are a powerful class of nonlinear functions that can be trained end-to-end on various applications. While the over-parametrization nature in many neural networks renders the ability to fit complex functions and the strong representation power to handle challenging tasks, it also leads to highly correlated neurons that can hurt the generalization ability and incur unnecessary computation cost. As a result, how to regularize the network to avoid undesired representation redundancy becomes an important issue. To this end, we draw inspiration from a well-known problem in physics -- Thomson problem, where one seeks to find a state that distributes N electrons on a unit sphere as evenly as possible with minimum potential energy. In light of this intuition, we reduce the redundancy regularization problem to generic energy minimization, and propose a minimum hyperspherical energy (MHE) objective as generic regularization for neural networks. We also propose a few novel variants of MHE, and provide some insights from a theoretical point of view. Finally, we apply neural networks with MHE regularization to several challenging tasks. Extensive experiments demonstrate the effectiveness of our intuition, by showing the superior performance with MHE regularization.

Recent advances in vision-language models (VLMs) have led to improved performance on tasks such as visual question answering and image captioning. Consequently, these models are now well-positioned to reason about the physical world, particularly within domains such as robotic manipulation. However, current VLMs are limited in their understanding of the physical concepts (e.g., material, fragility) of common objects, which restricts their usefulness for robotic manipulation tasks that involve interaction and physical reasoning about such objects. To address this limitation, we propose PhysObjects, an object-centric dataset of 36.9K crowd-sourced and 417K automated physical concept annotations of common household objects. We demonstrate that fine-tuning a VLM on PhysObjects improves its understanding of physical object concepts, by capturing human priors of these concepts from visual appearance. We incorporate this physically-grounded VLM in an interactive framework with a large language model-based robotic planner, and show improved planning performance on tasks that require reasoning about physical object concepts, compared to baselines that do not leverage physically-grounded VLMs. We additionally illustrate the benefits of our physically-grounded VLM on a real robot, where it improves task success rates. We release our dataset and provide further details and visualizations of our results at https://iliad.stanford.edu/pg-vlm/.

Vision-Language Models (VLMs) exhibit remarkable common-sense and semantic reasoning capabilities. However, they lack a grounded understanding of physical dynamics. This limitation arises from training VLMs on static internet-scale visual-language data that contain no causal interactions or action-conditioned changes. Consequently, it remains challenging to leverage VLMs for fine-grained robotic manipulation tasks that require physical understanding, reasoning, and corresponding action planning. To overcome this, we present SIMPACT, a test-time, SIMulation-enabled ACTion Planning framework that equips VLMs with physical reasoning through simulation-in-the-loop world modeling, without requiring any additional training. From a single RGB-D observation, SIMPACT efficiently constructs physics simulations, enabling the VLM to propose informed actions, observe simulated rollouts, and iteratively refine its reasoning. By integrating language reasoning with physics prediction, our simulation-enabled VLM can understand contact dynamics and action outcomes in a physically grounded way. Our method demonstrates state-of-the-art performance on five challenging, real-world rigid-body and deformable manipulation tasks that require fine-grained physical reasoning, outperforming existing general-purpose robotic manipulation models. Our results demonstrate that embedding physics understanding via efficient simulation into VLM reasoning at test time offers a promising path towards generalizable embodied intelligence. Project webpage can be found at https://simpact-bot.github.io

The ability to transform a flat sheet into a complex three-dimensional structure is a fundamental test of physical intelligence. Unlike cloth manipulation, origami is governed by strict geometric axioms and hard kinematic constraints, where a single invalid crease or collision can invalidate the entire folding sequence. As a result, origami demands long-horizon constructive reasoning that jointly satisfies precise physical laws and high-level semantic intent. Existing approaches fall into two disjoint paradigms: optimization-based methods enforce physical validity but require dense, precisely specified inputs, making them unsuitable for sparse natural language descriptions, while generative foundation models excel at semantic and perceptual synthesis yet fail to produce long-horizon, physics-consistent folding processes. Consequently, generating valid origami folding sequences directly from text remains an open challenge. To address this gap, we introduce Learn2Fold, a neuro-symbolic framework that formulates origami folding as conditional program induction over a crease-pattern graph. Our key insight is to decouple semantic proposal from physical verification. A large language model generates candidate folding programs from abstract text prompts, while a learned graph-structured world model serves as a differentiable surrogate simulator that predicts physical feasibility and failure modes before execution. Integrated within a lookahead planning loop, Learn2Fold enables robust generation of physically valid folding sequences for complex and out-of-distribution patterns, demonstrating that effective spatial intelligence arises from the synergy between symbolic reasoning and grounded physical simulation.

Recent diffusion-based video generation models can synthesize visually plausible videos, yet they often struggle to satisfy physical constraints. A key reason is that most existing approaches remain single-stage: they entangle high-level physical understanding with low-level visual synthesis, making it hard to generate content that require explicit physical reasoning. To address this limitation, we propose a training-free three-stage pipeline,PhyRPR:Phy\uline{Reason}--Phy\uline{Plan}--Phy\uline{Refine}, which decouples physical understanding from visual synthesis. Specifically, PhyReason uses a large multimodal model for physical state reasoning and an image generator for keyframe synthesis; PhyPlan deterministically synthesizes a controllable coarse motion scaffold; and PhyRefine injects this scaffold into diffusion sampling via a latent fusion strategy to refine appearance while preserving the planned dynamics. This staged design enables explicit physical control during generation. Extensive experiments under physics constraints show that our method consistently improves physical plausibility and motion controllability.

Understanding physical transformations is fundamental for reasoning in dynamic environments. While Vision Language Models (VLMs) show promise in embodied applications, whether they genuinely understand physical transformations remains unclear. We introduce ConservationBench evaluating conservation -- whether physical quantities remain invariant under transformations. Spanning four properties with paired conserving/non-conserving scenarios, we generate 23,040 questions across 112 VLMs. Results reveal systematic failure: performance remains near chance with improvements on conservation tasks accompanied by drops on controls. Control experiments show strong textual priors favoring invariance, yet models perform worse with visual content. Neither temporal resolution, prompting, nor curated sampling helps. These findings show that current VLMs fail to maintain transformation-invariant representations of physical properties across dynamic scenes.

Understanding the physical world requires perceptual models grounded in physical laws rather than mere statistical correlations. However, existing multimodal learning frameworks, focused on vision and language, lack physical consistency and overlook the intrinsic causal relationships among an object's geometry, material, vibration modes, and the sounds it produces. We introduce VibraVerse, a large-scale geometry-acoustics alignment dataset that explicitly bridges the causal chain from 3D geometry -> physical attributes -> modal parameters -> acoustic signals. Each 3D model has explicit physical properties (density, Young's modulus, Poisson's ratio) and volumetric geometry, from which modal eigenfrequencies and eigenvectors are computed for impact sound synthesis under controlled excitations. To establish this coherence, we introduce CLASP, a contrastive learning framework for cross-modal alignment that preserves the causal correspondence between an object's physical structure and its acoustic response. This framework enforces physically consistent alignment across modalities, ensuring that every sample is coherent, traceable to the governing equations, and embedded within a unified representation space spanning shape, image, and sound. Built upon VibraVerse, we define a suite of benchmark tasks for geometry-to-sound prediction, sound-guided shape reconstruction, and cross-modal representation learning. Extensive validations on these tasks demonstrate that models trained on VibraVerse exhibit superior accuracy, interpretability, and generalization across modalities. These results establish VibraVerse as a benchmark for physically consistent and causally interpretable multimodal learning, providing a foundation for sound-guided embodied perception and a deeper understanding of the physical world. The dataset will be open-sourced.

Generative video models achieve high visual fidelity but often violate basic physical principles, limiting reliability in real-world settings. Prior attempts to inject physics rely on conditioning: frame-level signals are domain-specific and short-horizon, while global text prompts are coarse and noisy, missing fine-grained dynamics. We present PhysVid, a physics-aware local conditioning scheme that operates over temporally contiguous chunks of frames. Each chunk is annotated with physics-grounded descriptions of states, interactions, and constraints, which are fused with the global prompt via chunk-aware cross-attention during training. At inference, we introduce negative physics prompts (descriptions of locally relevant law violations) to steer generation away from implausible trajectories. On VideoPhy, PhysVid improves physical commonsense scores by approx 33% over baseline video generators, and by up to approx 8% on VideoPhy2. These results show that local, physics-aware guidance substantially increases physical plausibility in generative video and marks a step toward physics-grounded video models.

Spatial intelligence unfolds through a perception-action loop: agents act to acquire observations, and reason about how observations vary as a function of action. Rather than passively processing what is seen, they actively uncover what is unseen - occluded structure, dynamics, containment, and functionality that cannot be resolved from passive sensing alone. We move beyond prior formulations of spatial intelligence that assume oracle observations by recasting the observer as an actor. We introduce ESI-BENCH, a comprehensive benchmark for embodied spatial intelligence spanning 10 task categories and 29 subcategories built on OmniGibson, grounded in Spelke's core knowledge systems. Agents must decide what abilities to deploy - perception, locomotion, and manipulation - and how to sequence them to actively accumulate task-relevant evidence. We conduct extensive experiments on state-of-the-art MLLMs and find that active exploration substantially outperforms passive counterparts, with agents spontaneously discovering emergent spatial strategies without explicit instructions, while random multi-view often adds noise rather than signal despite consuming far more images. Most failures stem not from weak perception but from action blindness: poor action choices lead to poor observations, which in turn drive cascading errors. While explicit 3D grounding stabilizes reasoning on depth-sensitive tasks, imperfect 3D representation proves more harmful than 2D baselines by distorting spatial relations. Human studies further reveal that unlike humans who seek falsifying viewpoints and revise beliefs under contradiction, models commit prematurely with high confidence regardless of evidence quality, exposing a metacognitive gap that neither better perception nor more embodied interaction alone can close.

AI explanations are often mentioned as a way to improve human-AI decision-making, but empirical studies have not found consistent evidence of explanations' effectiveness and, on the contrary, suggest that they can increase overreliance when the AI system is wrong. While many factors may affect reliance on AI support, one important factor is how decision-makers reconcile their own intuition -- beliefs or heuristics, based on prior knowledge, experience, or pattern recognition, used to make judgments -- with the information provided by the AI system to determine when to override AI predictions. We conduct a think-aloud, mixed-methods study with two explanation types (feature- and example-based) for two prediction tasks to explore how decision-makers' intuition affects their use of AI predictions and explanations, and ultimately their choice of when to rely on AI. Our results identify three types of intuition involved in reasoning about AI predictions and explanations: intuition about the task outcome, features, and AI limitations. Building on these, we summarize three observed pathways for decision-makers to apply their own intuition and override AI predictions. We use these pathways to explain why (1) the feature-based explanations we used did not improve participants' decision outcomes and increased their overreliance on AI, and (2) the example-based explanations we used improved decision-makers' performance over feature-based explanations and helped achieve complementary human-AI performance. Overall, our work identifies directions for further development of AI decision-support systems and explanation methods that help decision-makers effectively apply their intuition to achieve appropriate reliance on AI.

Physics problem-solving is a challenging domain for large AI models, requiring integration of conceptual understanding, mathematical reasoning, and interpretation of physical diagrams. Current evaluation methodologies show notable limitations in capturing the breadth and complexity of undergraduate-level physics, underscoring the need for more rigorous assessments. To this end, we present PhysUniBench, a large-scale multimodal benchmark designed to evaluate and improve the reasoning capabilities of multimodal large language models (MLLMs) specifically on undergraduate-level physics problems. PhysUniBench consists of 3,304 physics questions spanning 8 major sub-disciplines of physics, each accompanied by one visual diagrams. The benchmark includes both open-ended and multiple-choice questions, systematically curated and difficulty-rated through an iterative model-in-the-loop process. The benchmark's construction involved a rigorous multi-stage process, including multiple roll-outs, expert-level evaluation, automated filtering of easily solved problems, and a nuanced difficulty grading system with five levels. Through extensive experiments, we observe that current state-of-the-art models encounter substantial challenges in physics reasoning. For example, GPT-4o mini achieves only about 34.2\% accuracy in the proposed PhysUniBench. These results highlight that current MLLMs struggle with advanced physics reasoning, especially on multi-step problems and those requiring precise diagram interpretation. By providing a broad and rigorous assessment tool, PhysUniBench aims to drive progress in AI for Science, encouraging the development of models with stronger physical reasoning, problem-solving skills, and multimodal understanding. The benchmark and evaluation scripts are available at https://prismax-team.github.io/PhysUniBenchmark/.

A physically motivated equation that determines the number of electrons of a molecule is proposed based on chemical common sense. It shows that all molecules are entangled in the number of electrons and results in the fundamental assumption of molecular energy convexity that underpins molecular quantum mechanics. The proposed physical principle includes the molecular size consistency principle as a special case. Application of wavefunction theory to the principle shows that an individual molecule with a noninteger number of electrons is locally physical albeit locally unreal. The energy of a molecule is piecewise linear with respect to its continuous number of electrons. The continuity of the number of electrons allows the definition of an electronic chemical potential of a single molecule. A state function equivalent to the energy of a molecule can be defined using the chemical potential as a variable. The aforementioned physical principle can alternatively be expressed as a simple additivity with the new state function. The latter also shows that the quantum entanglement in the number of electrons can be viewed as all molecules sharing the same chemical potential.

Mechanistic Interpretability (MI) promises a path toward fully understanding how neural networks make their predictions. Prior work demonstrates that even when trained to perform simple arithmetic, models can implement a variety of algorithms (sometimes concurrently) depending on initialization and hyperparameters. Does this mean neuron-level interpretability techniques have limited applicability? We argue that high-dimensional neural networks can learn low-dimensional representations of their training data that are useful beyond simply making good predictions. Such representations can be understood through the mechanistic interpretability lens and provide insights that are surprisingly faithful to human-derived domain knowledge. This indicates that such approaches to interpretability can be useful for deriving a new understanding of a problem from models trained to solve it. As a case study, we extract nuclear physics concepts by studying models trained to reproduce nuclear data.

A critical gap exists between the general-purpose visual understanding of state-of-the-art physical AI models and the specialized perceptual demands of structured real-world deployment environments. We present PRISM, a 270K-sample multi-view video supervised fine-tuning (SFT) corpus for embodied vision-language-models (VLMs) in real-world retail environments. PRISM is motivated by a simple observation - physical AI systems fail not because of poor visual recognition, but because they do not understand space, physical dynamics and embodied action well enough to operate reliably in the world. To this end, PRISM is grounded in a novel three-dimensional knowledge ontology that spans spatial knowledge, temporal and physical knowledge, and embodied action knowledge. It covers 20+ capability probes across four evaluation dimensions - Embodied Reasoning (ER), Common Sense (CS), Spatial Perception (SP), and Intuitive Physics (IP), and to our knowledge, PRISM is the first dataset to instantiate all three knowledge dimensions within a single real-world deployment domain. The corpus captures data from egocentric, exocentric and 360° viewpoints across five supermarket locations and includes open-ended, chain-of-thought, and multiple-choice supervision. At 4 fps, PRISM spans approximately 11.8M video frames and approximately 730M tokens, placing it among the largest domain-specific video SFT corpora. Fine-tuning on PRISM reduces the error rate across all 20+ probes by 66.6% over the pre-trained baseline, with significant gains in embodied action understanding where the accuracy improves by 36.4%. Our results suggest that ontology-structured, domain specific SFT can meaningfully strengthen embodied VLMs for real-world settings. The PRISM dataset and more details are available at https://dreamvu.ai/prism

Scientific reasoning in materials science requires integrating multimodal experimental evidence with underlying physical theory. Existing benchmarks make it difficult to assess whether incorporating visual experimental data during post-training improves mechanism-grounded explanation reasoning beyond text-only supervision. We introduce MATRIX, a multimodal benchmark for materials science reasoning that evaluates foundational theory, research-level reasoning, and the interpretation of real experimental artifacts across multiple characterization modalities. Using MATRIX as a controlled diagnostic, we isolate the effect of visual grounding by comparing post-training on structured materials science text alone with post-training that incorporates paired experimental images. Despite using relatively small amounts of multimodal data, visual supervision improves experimental interpretation by 10-25% and yields 5-16% gains on text-only scientific reasoning tasks. Our results demonstrate that these improvements rely on correct image-text alignment during post-training, highlighting cross-modal representational transfer. We also observe consistent improvements on ScienceQA and PubMedQA, demonstrating that the benefits of structured multimodal post-training extend beyond materials science. The MATRIX dataset is available at https://huggingface.co/datasets/radical-ai/MATRIX and the model at https://huggingface.co/radical-ai/MATRIX-PT.

Vision-Language Models (VLMs) are increasingly pivotal for generalist robot manipulation, enabling tasks such as physical reasoning, policy generation, and failure detection. However, their proficiency in these high-level applications often assumes a deep understanding of low-level physical prerequisites, a capability that remains largely unverified. For robots to perform actions reliably, they must comprehend intrinsic object properties (e.g., material, weight), action affordances (e.g., graspable, stackable), and physical constraints (e.g., stability, reachability, or an object's state, such as being closed). Despite the widespread use of VLMs in manipulation tasks, we argue that off-the-shelf models may lack this granular, physically grounded understanding, as such prerequisites are often overlooked during training. To address this critical gap, we introduce PAC Bench, a comprehensive benchmark designed to systematically evaluate VLMs on their understanding of core Properties, Affordances, and Constraints (PAC) from a task executability perspective. PAC Bench features a diverse dataset with over 30,000 annotations, comprising 673 real-world images (115 object classes, 15 property types, and 1 to 3 affordances defined per class), 100 real-world humanoid-view scenarios, and 120 unique simulated constraint scenarios across four tasks. Our evaluations reveal significant gaps in the ability of current VLMs to grasp fundamental physical concepts, highlighting limitations in their suitability for reliable robot manipulation and pointing to key areas for targeted research. PAC Bench also serves as a standardized benchmark for rigorously evaluating physical reasoning in VLMs and guiding the development of more robust, physically grounded models for robotic applications. Project Page: https://pacbench.github.io/

This paper explores the intersection of identity, individuality, and reality through competing frameworks, including classical metaphysics, quantum mechanics, and computational theories. Traditional metaphysical notions of fixed identity are challenged by advancements in cloning, teletransportation, and digital replication, which reveal the fluid and relational nature of individuality. Quantum mechanics further complicates these notions, emphasizing the indistinguishability and contextuality of fundamental particles. Computational approaches, such as the Ruliad and Constructor Theory, offer expansive views of emergent realities but often lack practical constraints for observer relevance. Algorithmic idealism is introduced as a unifying framework, proposing that reality is an emergent construct governed by computational rules prioritizing coherence, sufficiency, and observer-dependent experiences. By redefining identity as an informational construct and reality as a process shaped by algorithmic transitions, algorithmic idealism resolves foundational paradoxes and offers a superior lens for understanding existence in an increasingly digital and interconnected world. The framework bridges gaps between competing theories, providing a coherent and pragmatic model for addressing ethical, metaphysical, and technological challenges.

We present a theory of information expressed solely in terms of which transformations of physical systems are possible and which are impossible - i.e. in constructor-theoretic terms. Although it includes conjectured laws of physics that are directly about information, independently of the details of particular physical instantiations, it does not regard information as an a priori mathematical or logical concept, but as something whose nature and properties are determined by the laws of physics alone. It does not suffer from the circularity at the foundations of existing information theory (namely that information and distinguishability are each defined in terms of the other). It explains the relationship between classical and quantum information, and reveals the single, constructor-theoretic property underlying the most distinctive phenomena associated with the latter, including the lack of in-principle distinguishability of some states, the impossibility of cloning, the existence of pairs of variables that cannot simultaneously have sharp values, the fact that measurement processes can be both deterministic and unpredictable, the irreducible perturbation caused by measurement, and entanglement (locally inaccessible information).

The ability to use, understand, and create tools is a hallmark of human intelligence, enabling sophisticated interaction with the physical world. For any general-purpose intelligent agent to achieve true versatility, it must also master these fundamental skills. While modern Multimodal Large Language Models (MLLMs) leverage their extensive common knowledge for high-level planning in embodied AI and in downstream Vision-Language-Action (VLA) models, the extent of their true understanding of physical tools remains unquantified. To bridge this gap, we present PhysToolBench, the first benchmark dedicated to evaluating the comprehension of physical tools by MLLMs. Our benchmark is structured as a Visual Question Answering (VQA) dataset comprising over 1,000 image-text pairs. It assesses capabilities across three distinct difficulty levels: (1) Tool Recognition: Requiring the recognition of a tool's primary function. (2) Tool Understanding: Testing the ability to grasp the underlying principles of a tool's operation. (3) Tool Creation: Challenging the model to fashion a new tool from surrounding objects when conventional options are unavailable. Our comprehensive evaluation of 32 MLLMs-spanning proprietary, open-source, specialized embodied, and backbones in VLAs-reveals a significant deficiency in tool understanding. Furthermore, we provide an in-depth analysis and propose preliminary solutions. Code and dataset are publicly available.

Video generation models are increasingly used as world simulators for storytelling, simulation, and embodied AI. As these models advance, a key question arises: do generated videos obey the physical laws of the real world? Existing evaluations largely rely on automated metrics or coarse human judgments such as preferences or rubric-based checks. While useful for assessing perceptual quality, these methods provide limited insight into when and why generated dynamics violate real-world physical constraints. We introduce Physion-Eval, a large-scale benchmark of expert human reasoning for diagnosing physical realism failures in videos generated by five state-of-the-art models across egocentric and exocentric views, containing 10,990 expert reasoning traces spanning 22 fine-grained physical categories. Each generated video is derived from a corresponding real-world reference video depicting a clear physical process, and annotated with temporally localized glitches, structured failure categories, and natural-language explanations of the violated physical behavior. Using this dataset, we reveal a striking limitation of current video generation models: in physics-critical scenarios, 83.3% of exocentric and 93.5% of egocentric generated videos exhibit at least one human-identifiable physical glitch. We hope Physion-Eval will set a new standard for physical realism evaluation and guide the development of physics-grounded video generation. The benchmark is publicly available at https://huggingface.co/datasets/PhysionLabs/Physion-Eval.

All current formulations of thermodynamics invoke some form of coarse-graining or ensembles as the supposed link between their own laws and the microscopic laws of motion. They deal only with ensemble-averages, expectation values, macroscopic limits, infinite heat baths, etc., not with the details of physical variables of individual microscopic systems. They are consistent with the laws of motion for finite systems only in certain approximations, which improve with increasing scale, given various assumptions about initial conditions which are neither specified precisely nor even thought to hold exactly in nature. Here I propose a new formulation of the zeroth, first and second laws, improving upon the axiomatic approach to thermodynamics (Carath\'eodory, 1909; Lieb & Yngvason, 1999), via the principles of the recently proposed constructor theory. Specifically, I provide a non-approximative, scale-independent formulation of 'adiabatic accessibility'; this in turn provides a non-approximative, scale-independent distinction between work and heat and reveals an unexpected connection between information theory and the first law of thermodynamics (not just the second). It also achieves the long-sought unification of the axiomatic approach with Kelvin's.

The discipline of physics stands as a cornerstone of human intellect, driving the evolution of technology and deepening our understanding of the fundamental principles of the cosmos. Contemporary literature includes some works centered on the task of solving physics problems - a crucial domain of natural language reasoning. In this paper, we evaluate the performance of frontier LLMs in solving physics problems, both mathematical and descriptive. We also employ a plethora of inference-time techniques and agentic frameworks to improve the performance of the models. This includes the verification of proposed solutions in a cumulative fashion by other, smaller LLM agents, and we perform a comparative analysis of the performance that the techniques entail. There are significant improvements when the multi-agent framework is applied to problems that the models initially perform poorly on. Furthermore, we introduce a new evaluation benchmark for physics problems, {rm P{small HYSICS}E{small VAL}}, consisting of 19,609 problems sourced from various physics textbooks and their corresponding correct solutions scraped from physics forums and educational websites. Our code and data are publicly available at https://github.com/areebuzair/PhysicsEval.

We introduce Explanatory Learning (EL), a framework to let machines use existing knowledge buried in symbolic sequences -- e.g. explanations written in hieroglyphic -- by autonomously learning to interpret them. In EL, the burden of interpreting symbols is not left to humans or rigid human-coded compilers, as done in Program Synthesis. Rather, EL calls for a learned interpreter, built upon a limited collection of symbolic sequences paired with observations of several phenomena. This interpreter can be used to make predictions on a novel phenomenon given its explanation, and even to find that explanation using only a handful of observations, like human scientists do. We formulate the EL problem as a simple binary classification task, so that common end-to-end approaches aligned with the dominant empiricist view of machine learning could, in principle, solve it. To these models, we oppose Critical Rationalist Networks (CRNs), which instead embrace a rationalist view on the acquisition of knowledge. CRNs express several desired properties by construction, they are truly explainable, can adjust their processing at test-time for harder inferences, and can offer strong confidence guarantees on their predictions. As a final contribution, we introduce Odeen, a basic EL environment that simulates a small flatland-style universe full of phenomena to explain. Using Odeen as a testbed, we show how CRNs outperform empiricist end-to-end approaches of similar size and architecture (Transformers) in discovering explanations for novel phenomena.

The next frontier for video generation lies in developing models capable of zero-shot reasoning, where understanding real-world scientific laws is crucial for accurate physical outcome modeling under diverse conditions. However, existing video benchmarks are physical commonsense-based, offering limited insight into video models' scientific reasoning capability. We introduce VideoScience-Bench, a benchmark designed to evaluate undergraduate-level scientific understanding in video models. Each prompt encodes a composite scientific scenario that requires understanding and reasoning across multiple scientific concepts to generate the correct phenomenon. The benchmark comprises 200 carefully curated prompts spanning 14 topics and 103 concepts in physics and chemistry. We conduct expert-annotated evaluations across seven state-of-the-art video models in T2V and I2V settings along five dimensions: Prompt Consistency, Phenomenon Congruency, Correct Dynamism, Immutability, and Spatio-Temporal Continuity. Using a VLM-as-a-Judge to assess video generations, we observe strong correlation with human assessments. To the best of our knowledge, VideoScience-Bench is the first benchmark to evaluate video models not only as generators but also as reasoners, requiring their generations to demonstrate scientific understanding consistent with expected physical and chemical phenomena. Our data and evaluation code are available at: https://github.com/hao-ai-lab/VideoScience{github.com/hao-ai-lab/VideoScience}.

Concept-based explanation methods, such as Concept Activation Vectors, are potent means to quantify how abstract or high-level characteristics of input data influence the predictions of complex deep neural networks. However, applying them to industrial prediction problems is challenging as it is not immediately clear how to define and access appropriate concepts for individual use cases and specific data types. In this work, we investigate how to leverage established concept-based explanation techniques in the context of bearing fault detection with deep neural networks trained on vibration signals. Since bearings are prevalent in almost every rotating equipment, ensuring the reliability of intransparent fault detection models is crucial to prevent costly repairs and downtimes of industrial machinery. Our evaluations demonstrate that explaining opaque models in terms of vibration concepts enables human-comprehensible and intuitive insights about their inner workings, but the underlying assumptions need to be carefully validated first.

Methods for understanding the decisions of and mechanisms underlying deep neural networks (DNNs) typically rely on building intuition by emphasizing sensory or semantic features of individual examples. For instance, methods aim to visualize the components of an input which are "important" to a network's decision, or to measure the semantic properties of single neurons. Here, we argue that interpretability research suffers from an over-reliance on intuition-based approaches that risk-and in some cases have caused-illusory progress and misleading conclusions. We identify a set of limitations that we argue impede meaningful progress in interpretability research, and examine two popular classes of interpretability methods-saliency and single-neuron-based approaches-that serve as case studies for how overreliance on intuition and lack of falsifiability can undermine interpretability research. To address these concerns, we propose a strategy to address these impediments in the form of a framework for strongly falsifiable interpretability research. We encourage researchers to use their intuitions as a starting point to develop and test clear, falsifiable hypotheses, and hope that our framework yields robust, evidence-based interpretability methods that generate meaningful advances in our understanding of DNNs.

Understanding objects is a central building block of artificial intelligence, especially for embodied AI. Even though object recognition excels with deep learning, current machines still struggle to learn higher-level knowledge, e.g., what attributes an object has, and what can we do with an object. In this work, we propose a challenging Object Concept Learning (OCL) task to push the envelope of object understanding. It requires machines to reason out object affordances and simultaneously give the reason: what attributes make an object possesses these affordances. To support OCL, we build a densely annotated knowledge base including extensive labels for three levels of object concept (category, attribute, affordance), and the causal relations of three levels. By analyzing the causal structure of OCL, we present a baseline, Object Concept Reasoning Network (OCRN). It leverages causal intervention and concept instantiation to infer the three levels following their causal relations. In experiments, OCRN effectively infers the object knowledge while following the causalities well. Our data and code are available at https://mvig-rhos.com/ocl.

Physical AI aims to develop models that can perceive and predict real-world dynamics; yet, the extent to which current multi-modal large language models and video generative models support these abilities is insufficiently understood. We introduce Physical AI Bench (PAI-Bench), a unified and comprehensive benchmark that evaluates perception and prediction capabilities across video generation, conditional video generation, and video understanding, comprising 2,808 real-world cases with task-aligned metrics designed to capture physical plausibility and domain-specific reasoning. Our study provides a systematic assessment of recent models and shows that video generative models, despite strong visual fidelity, often struggle to maintain physically coherent dynamics, while multi-modal large language models exhibit limited performance in forecasting and causal interpretation. These observations suggest that current systems are still at an early stage in handling the perceptual and predictive demands of Physical AI. In summary, PAI-Bench establishes a realistic foundation for evaluating Physical AI and highlights key gaps that future systems must address.

Touch is a crucial sensing modality that provides rich information about object properties and interactions with the physical environment. Humans and robots both benefit from using touch to perceive and interact with the surrounding environment (Johansson and Flanagan, 2009; Li et al., 2020; Calandra et al., 2017). However, no existing systems provide rich, multi-modal digital touch-sensing capabilities through a hemispherical compliant embodiment. Here, we describe several conceptual and technological innovations to improve the digitization of touch. These advances are embodied in an artificial finger-shaped sensor with advanced sensing capabilities. Significantly, this fingertip contains high-resolution sensors (~8.3 million taxels) that respond to omnidirectional touch, capture multi-modal signals, and use on-device artificial intelligence to process the data in real time. Evaluations show that the artificial fingertip can resolve spatial features as small as 7 um, sense normal and shear forces with a resolution of 1.01 mN and 1.27 mN, respectively, perceive vibrations up to 10 kHz, sense heat, and even sense odor. Furthermore, it embeds an on-device AI neural network accelerator that acts as a peripheral nervous system on a robot and mimics the reflex arc found in humans. These results demonstrate the possibility of digitizing touch with superhuman performance. The implications are profound, and we anticipate potential applications in robotics (industrial, medical, agricultural, and consumer-level), virtual reality and telepresence, prosthetics, and e-commerce. Toward digitizing touch at scale, we open-source a modular platform to facilitate future research on the nature of touch.

While interpretability research has shed light on some internal algorithms utilized by transformer-based LLMs, reasoning in natural language, with its deep contextuality and ambiguity, defies easy categorization. As a result, formulating clear and motivating questions for circuit analysis that rely on well-defined in-domain and out-of-domain examples required for causal interventions is challenging. Although significant work has investigated circuits for specific tasks, such as indirect object identification (IOI), deciphering natural language reasoning through circuits remains difficult due to its inherent complexity. In this work, we take initial steps to characterize causal reasoning in LLMs by analyzing clear-cut cause-and-effect sentences like "I opened an umbrella because it started raining," where causal interventions may be possible through carefully crafted scenarios using GPT-2 small. Our findings indicate that causal syntax is localized within the first 2-3 layers, while certain heads in later layers exhibit heightened sensitivity to nonsensical variations of causal sentences. This suggests that models may infer reasoning by (1) detecting syntactic cues and (2) isolating distinct heads in the final layers that focus on semantic relationships.

With the rapid development of MLLMs, evaluating their visual capabilities has become increasingly crucial. Current benchmarks primarily fall into two main types: basic perception benchmarks, which focus on local details but lack deep reasoning (e.g., "what is in the image?"), and mainstream reasoning benchmarks, which concentrate on prominent image elements but may fail to assess subtle clues requiring intricate analysis. However, profound visual understanding and complex reasoning depend more on interpreting subtle, inconspicuous local details than on perceiving salient, macro-level objects. These details, though occupying minimal image area, often contain richer, more critical information for robust analysis. To bridge this gap, we introduce the VER-Bench, a novel framework to evaluate MLLMs' ability to: 1) identify fine-grained visual clues, often occupying on average just 0.25% of the image area; 2) integrate these clues with world knowledge for complex reasoning. Comprising 374 carefully designed questions across Geospatial, Temporal, Situational, Intent, System State, and Symbolic reasoning, each question in VER-Bench is accompanied by structured evidence: visual clues and question-related reasoning derived from them. VER-Bench reveals current models' limitations in extracting subtle visual evidence and constructing evidence-based arguments, highlighting the need to enhance models's capabilities in fine-grained visual evidence extraction, integration, and reasoning for genuine visual understanding and human-like analysis. Dataset and additional materials are available https://github.com/verbta/ACMMM-25-Materials.

Diffusion models can generate realistic videos, but existing methods rely on implicitly learning physical reasoning from large-scale text-video datasets, which is costly, difficult to scale, and still prone to producing implausible motions that violate fundamental physical laws. We introduce a training-free framework that improves physical plausibility at inference time by explicitly reasoning about implausibility and guiding the generation away from it. Specifically, we employ a lightweight physics-aware reasoning pipeline to construct counterfactual prompts that deliberately encode physics-violating behaviors. Then, we propose a novel Synchronized Decoupled Guidance (SDG) strategy, which leverages these prompts through synchronized directional normalization to counteract lagged suppression and trajectory-decoupled denoising to mitigate cumulative trajectory bias, ensuring that implausible content is suppressed immediately and consistently throughout denoising. Experiments across different physical domains show that our approach substantially enhances physical fidelity while maintaining photorealism, despite requiring no additional training. Ablation studies confirm the complementary effectiveness of both the physics-aware reasoning component and SDG. In particular, the aforementioned two designs of SDG are also individually validated to contribute critically to the suppression of implausible content and the overall gains in physical plausibility. This establishes a new and plug-and-play physics-aware paradigm for video generation.

Deep sequence models are said to store atomic facts predominantly in the form of associative memory: a brute-force lookup of co-occurring entities. We identify a dramatically different form of storage of atomic facts that we term as geometric memory. Here, the model has synthesized embeddings encoding novel global relationships between all entities, including ones that do not co-occur in training. Such storage is powerful: for instance, we show how it transforms a hard reasoning task involving an ell-fold composition into an easy-to-learn 1-step navigation task. From this phenomenon, we extract fundamental aspects of neural embedding geometries that are hard to explain. We argue that the rise of such a geometry, as against a lookup of local associations, cannot be straightforwardly attributed to typical supervisory, architectural, or optimizational pressures. Counterintuitively, a geometry is learned even when it is more complex than the brute-force lookup. Then, by analyzing a connection to Node2Vec, we demonstrate how the geometry stems from a spectral bias that -- in contrast to prevailing theories -- indeed arises naturally despite the lack of various pressures. This analysis also points out to practitioners a visible headroom to make Transformer memory more strongly geometric. We hope the geometric view of parametric memory encourages revisiting the default intuitions that guide researchers in areas like knowledge acquisition, capacity, discovery, and unlearning.

There is an analogy that is often made between deep neural networks and actual brains, suggested by the nomenclature itself: the "neurons" in deep neural networks should correspond to neurons (or nerve cells, to avoid confusion) in the brain. We claim, however, that this analogy doesn't even type check: it is structurally flawed. In agreement with the slightly glib summary of Hebbian learning as "cells that fire together wire together", this article makes the case that the analogy should be different. Since the "neurons" in deep neural networks are managing the changing weights, they are more akin to the synapses in the brain; instead, it is the wires in deep neural networks that are more like nerve cells, in that they are what cause the information to flow. An intuition that nerve cells seem like more than mere wires is exactly right, and is justified by a precise category-theoretic analogy which we will explore in this article. Throughout, we will continue to highlight the error in equating artificial neurons with nerve cells by leaving "neuron" in quotes or by calling them artificial neurons. We will first explain how to view deep neural networks as nested dynamical systems with a very restricted sort of interaction pattern, and then explain a more general sort of interaction for dynamical systems that is useful throughout engineering, but which fails to adapt to changing circumstances. As mentioned, an analogy is then forced upon us by the mathematical formalism in which they are both embedded. We call the resulting encompassing generalization deeply interacting learning systems: they have complex interaction as in control theory, but adaptation to circumstances as in deep neural networks.

Modern artificial intelligence excels at statistical interpolation within seen manifolds but fundamentally fails at the exact reasoning required for theoretical physics and mathematics. We identify the "Float Wall" -- a catastrophic collapse of neural extrapolation at scales beyond 10^{16} -- caused by standard floating-point representation and linguistic tokenization (BPE). To resolve this, we introduce the Active Discoverer Framework, a digit-native neuro-symbolic architecture designed for invariant discovery. At its core is NumberNet, a Siamese Arithmetic Transformer that utilizes least-significant-bit (LSB) sequence encoding to achieve 0% precision loss and cosmic-scale extrapolation up to 10^{50}. To enforce physical grounding, we implement a Hamiltonian-based energy descent and Symmetry Grouping layer, ensuring the model respects Noether's theorem natively. The primary innovation is the Symbolic LaTeX Bottleneck: an active discovery loop where the model is forced to hypothesize unknown physical variables through an autoregressive LaTeX decoder. By reconciling numeric "hallucinations" with structurally valid mathematical expressions, the framework ensures that any discovered physics is parsimonious and human-interpretable. We evaluate this system against a 30-billion scale benchmark and the Universal Physics Pantheon, featuring 50 "Chaos Mode" systemic perturbations. Our results demonstrate that while traditional GBDT and LLM-based architectures collapse at cosmic scales, the Active Discoverer autonomously deduces universal constants such as the Gravitational Constant (G) with high fidelity. This framework establishes a path toward zero-hallucination artificial intelligence and truly autonomous scientific research agents.

In this paper I apply newly-proposed information-theoretic principles to thermodynamic work extraction. I show that if it is possible to extract work deterministically from a physical system prepared in any one of a set of states, then those states must be distinguishable from one another. This result is formulated independently of scale and of particular dynamical laws; it also provides a novel connection between thermodynamics and information theory, established via the law of conservation of energy (rather than the second law of thermodynamics). Albeit compatible with these conclusions, existing thermodynamics approaches cannot provide a result of such generality, because they are scale-dependent (relying on ensembles or coarse-graining) or tied to particular dynamical laws. This paper thus provides a broader foundation for thermodynamics, with implications for the theory of von Neumann's universal constructor

The integration of visual understanding and generation into unified multimodal models represents a significant stride toward general-purpose AI. However, a fundamental question remains unanswered by existing benchmarks: does this architectural unification actually enable synergetic interaction between the constituent capabilities? Existing evaluation paradigms, which primarily assess understanding and generation in isolation, are insufficient for determining whether a unified model can leverage its understanding to enhance its generation, or use generative simulation to facilitate deeper comprehension. To address this critical gap, we introduce RealUnify, a benchmark specifically designed to evaluate bidirectional capability synergy. RealUnify comprises 1,000 meticulously human-annotated instances spanning 10 categories and 32 subtasks. It is structured around two core axes: 1) Understanding Enhances Generation, which requires reasoning (e.g., commonsense, logic) to guide image generation, and 2) Generation Enhances Understanding, which necessitates mental simulation or reconstruction (e.g., of transformed or disordered visual inputs) to solve reasoning tasks. A key contribution is our dual-evaluation protocol, which combines direct end-to-end assessment with a diagnostic stepwise evaluation that decomposes tasks into distinct understanding and generation phases. This protocol allows us to precisely discern whether performance bottlenecks stem from deficiencies in core abilities or from a failure to integrate them. Through large-scale evaluations of 12 leading unified models and 6 specialized baselines, we find that current unified models still struggle to achieve effective synergy, indicating that architectural unification alone is insufficient. These results highlight the need for new training strategies and inductive biases to fully unlock the potential of unified modeling.

Vision-Language-Action (VLA) models have shown remarkable achievements, driven by the rich implicit knowledge of their vision-language components. However, achieving generalist robotic agents demands precise grounding into physical interactions, especially in contact-rich scenarios where fine-grained force control is essential. We advance VLAs' implicit knowledge beyond identifying what to do, towards guiding how to physically interact with real world. This paper introduces Tactile-VLA, a novel framework that deeply fuses vision, language, action, and tactile sensing. This framework incorporates a hybrid position-force controller to translate the model's intentions into precise physical actions and a reasoning module that allows the robot to adapt its strategy based on tactile feedback. Experiments demonstrate Tactile-VLA's effectiveness and generalizability in three key aspects: (1) enabling tactile-aware instruction following, (2) utilizing tactile-relevant commonsense, and (3) facilitating adaptive tactile-involved reasoning. A key finding is that the VLM's prior knowledge already contains semantic understanding of physical interaction; by connecting it to the robot's tactile sensors with only a few demonstrations, we can activate this prior knowledge to achieve zero-shot generalization in contact-rich tasks.

Large Language Models (LLMs) have shown remarkable capabilities in text and multimodal processing, yet they fundamentally lack physical awareness--understanding of real-world physical phenomena. In this work, we present ACORN, a framework that teaches LLMs physical awareness through sound, focusing on fundamental physical phenomena like the Doppler effect, multipath effect, and spatial relationships. To overcome data scarcity, ACORN introduce a physics-based simulator combining real-world sound sources with controlled physical channels to generate diverse training data. Using this simulator, we build AQA-PHY, a comprehensive Audio Question-Answer dataset, and propose an audio encoder that processes both magnitude and phase information. By connecting our audio encoder to state-of-the-art LLMs, we demonstrate reasonable results in both simulated and real-world tasks, such as line-of-sight detection, Doppler effect estimation, and Direction-of-Arrival estimation, paving the way for enabling LLMs to understand physical world.

Recent advances in scientific machine learning (SciML) have enabled neural operators (NOs) to serve as powerful surrogates for modeling the dynamic evolution of physical systems governed by partial differential equations (PDEs). While existing approaches focus primarily on learning simulations from the target PDE, they often overlook more fundamental physical principles underlying these equations. Inspired by how numerical solvers are compatible with simulations of different settings of PDEs, we propose a multiphysics training framework that jointly learns from both the original PDEs and their simplified basic forms. Our framework enhances data efficiency, reduces predictive errors, and improves out-of-distribution (OOD) generalization, particularly in scenarios involving shifts of physical parameters and synthetic-to-real transfer. Our method is architecture-agnostic and demonstrates consistent improvements in normalized root mean square error (nRMSE) across a wide range of 1D/2D/3D PDE problems. Through extensive experiments, we show that explicit incorporation of fundamental physics knowledge significantly strengthens the generalization ability of neural operators. We will release models and codes at https://sites.google.com/view/sciml-fundemental-pde.

The widespread use of neural networks across different scientific domains often involves constraining them to satisfy certain symmetries, conservation laws, or other domain knowledge. Such constraints are often imposed as soft penalties during model training and effectively act as domain-specific regularizers of the empirical risk loss. Physics-informed neural networks is an example of this philosophy in which the outputs of deep neural networks are constrained to approximately satisfy a given set of partial differential equations. In this work we review recent advances in scientific machine learning with a specific focus on the effectiveness of physics-informed neural networks in predicting outcomes of physical systems and discovering hidden physics from noisy data. We will also identify and analyze a fundamental mode of failure of such approaches that is related to numerical stiffness leading to unbalanced back-propagated gradients during model training. To address this limitation we present a learning rate annealing algorithm that utilizes gradient statistics during model training to balance the interplay between different terms in composite loss functions. We also propose a novel neural network architecture that is more resilient to such gradient pathologies. Taken together, our developments provide new insights into the training of constrained neural networks and consistently improve the predictive accuracy of physics-informed neural networks by a factor of 50-100x across a range of problems in computational physics. All code and data accompanying this manuscript are publicly available at https://github.com/PredictiveIntelligenceLab/GradientPathologiesPINNs.

We present TACIT (Transformation-Aware Capturing of Implicit Thought), a diffusion-based transformer for interpretable visual reasoning. Unlike language-based reasoning systems, TACIT operates entirely in pixel space using rectified flow, enabling direct visualization of the reasoning process at each inference step. We demonstrate the approach on maze-solving, where the model learns to transform images of unsolved mazes into solutions. Key results on 1 million synthetic maze pairs include: - 192x reduction in training loss over 100 epochs - 22.7x improvement in L2 distance to ground truth - Only 10 Euler steps required (vs. 100-1000 for typical diffusion models) Quantitative analysis reveals a striking phase transition phenomenon: the solution remains invisible for 68% of the transformation (zero recall), then emerges abruptly at t=0.70 within just 2% of the process. Most remarkably, 100% of samples exhibit simultaneous emergence across all spatial regions, ruling out sequential path construction and providing evidence for holistic rather than algorithmic reasoning. This "eureka moment" pattern -- long incubation followed by sudden crystallization -- parallels insight phenomena in human cognition. The pixel-space design with noise-free flow matching provides a foundation for understanding how neural networks develop implicit reasoning strategies that operate below and before language.

Visuo-tactile perception aims to understand an object's tactile properties, such as texture, softness, and rigidity. However, the field remains underexplored because collecting tactile data is costly and labor-intensive. We observe that visually distinct objects can exhibit similar surface textures or material properties. For example, a leather sofa and a leather jacket have different appearances but share similar tactile properties. This implies that tactile understanding can be guided by material cues in visual data, even without direct tactile supervision. In this paper, we introduce RA-Touch, a retrieval-augmented framework that improves visuo-tactile perception by leveraging visual data enriched with tactile semantics. We carefully recaption a large-scale visual dataset with tactile-focused descriptions, enabling the model to access tactile semantics typically absent from conventional visual datasets. A key challenge remains in effectively utilizing these tactile-aware external descriptions. RA-Touch addresses this by retrieving visual-textual representations aligned with tactile inputs and integrating them to focus on relevant textural and material properties. By outperforming prior methods on the TVL benchmark, our method demonstrates the potential of retrieval-based visual reuse for tactile understanding. Code is available at https://aim-skku.github.io/RA-Touch