amd
/

SAND-Math-Qwen2.5-32B

@@ -1,304 +1,304 @@
-SAND-MATH [Open RAIL-MSD]
-Licensed Artifact(s):
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-Attachment A
-AMD Responsible AI Use Policy
-AMD is committed to the responsible use of its Artificial Intelligence
-(AI) products and technologies (“AMD AI”).  AMD AI may include
-artificial intelligence or machine learning technologies that use
-algorithms to analyze data and generate output using predictions based
-on patterns in data.  This policy explains the uses that AMD
-specifically prohibits.
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-with applicable laws and not for any of the following prohibited uses.
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-national, state, local, or other jurisdictional law, rule, regulation,
-or sanction.
-2) No Explicit Content.  Do not use AMD AI to submit (as input),
-generate, or disseminate content depicting violent or sexually explicit
-content or to create sexual chatbots.
-3) No Harm.  Do not use AMD AI for any potentially harmful uses,
-   including fraud, deception, discrimination, abuse, or harassment,
-   including the following:
-   a) Harm or abuse of a minor, including grooming and child sexual
-      exploitation.
-   b) Impersonation of human beings for purposes of deception.
-   c) Generation or dissemination of information you know to be false
-      for the purpose of harming others.
-   d) Intentionally defame, disparage, or otherwise harass others.
-   e) Intentionally attempting to materially distort the behavior of a
-      person in a manner that causes or is likely to cause that person
-      or another person physical or psychological harm.
-   f) Providing medical advice or interpretation of medical results that
-      is intended to be a substitute for professional medical advice,
-      diagnosis, or treatment.
-   g) Engaging in the unlawful or unauthorized practice of any
-      profession, including financial, legal, medical, health, or
-      related professional practices.
-   h) Judgment of, discrimination against, or harm to individuals or
-      groups based on legally protected characteristics or categories,
-      online or offline social behavior, or known or predicted personal
-      or personality characteristics, including any of the foregoing
-      uses in social credit systems.
-4) No High-Risk Activity.  Do not use AMD AI in any high-risk activities
- or applications that create a risk of personal injury, death, or
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+SAND-MATH [Open RAIL-MSD]
+Licensed Artifact(s):
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+Section I: PREAMBLE
+BY ACCESSING, DOWNLOADING, INSTALLING, OR USING THE ARTIFACT, YOU AGREE
+TO BE BOUND BY THIS LICENSE. IF YOU DO NOT AGREE TO ALL OF THE TERMS AND
+CONDITIONS OF THIS LICENSE, DO NOT ACCESS, DOWNLOAD, INSTALL, OR USE THE
+ARTIFACT.
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+(a) �Application� refers to a sequence of instructions or statements
+    written in machine code language, including object code (that is the
+    product of a compiler), binary code (data using a two-symbol system)
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+    term �Source Code� as used in this License includes any and all
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+    distributing an Artifact; in connection with a Model as Artifact,
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+(p) �You� (or �Your�) means an individual or legal entity receiving and
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+    the Artifact for permitted purposes and in any permitted field of
+    use, including usage of the Artifact in an end-use application -
+    e.g. chatbot, translator, image generator, etc.
+Section II: INTELLECTUAL PROPERTY RIGHTS
+Both copyright and patent grants may apply to the Artifact. The Artifact
+is subject to additional terms and conditions as described in Section III
+below.
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+III below and subject to the terms and conditions of this License, each
+Contributor hereby grants to You a worldwide, non-exclusive, royalty-free copyright license to
+reproduce, use, publicly display, publicly perform, sublicense, and
+distribute the Artifact and Derivatives thereof.
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+royalty-free, irrevocable (except as stated in this paragraph) patent
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+submitted. If You institute patent litigation against any entity
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+Artifact and/or a Contribution incorporated within the Artifact
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+licenses granted to You under this License in connection with the
+Artifact shall terminate as of the date such litigation is asserted or
+filed.
+Licensor and Contributor each have the right to grant the licenses
+above.
+Section III: CONDITIONS OF USAGE, DISTRIBUTION AND REDISTRIBUTION
+4. Use-based restrictions. The restrictions set forth in Attachment A
+are mandatory Use-based restrictions. Therefore You may not Use the
+Artifact in violation of such restrictions. You may Use the Artifact
+only subject to this License. You shall require all of Your users who
+use the Artifact or its Derivative to comply with the terms of this
+paragraph.
+5. The Output You Generate with a Model (as Artifact). Except as set
+forth herein, Licensor claims no rights in the Output You generate. You
+are accountable for the Output You generate and its subsequent uses. No
+use of the Output may contravene any provision as stated in this
+License.
+6. Distribution and Redistribution. You may host for Third Party remote
+access purposes (e.g. software-as-a-service), reproduce and distribute
+copies of the Artifact or its Derivatives in any medium, with or without
+modifications, provided that You meet the following conditions:
+6.1.  Use-based restrictions in paragraph 4 MUST be included as a
+      condition precedent to effect any type of legal agreement (e.g. a
+      license) governing the use and/or distribution of the Artifact or
+      its Derivatives, and You shall give such notice to any subsequent
+      Third Party recipients;
+6.2.  You shall give any Third Party recipients of the Artifact or its
+      Derivatives a copy of this License;
+6.3.  You shall cause any modified files to carry prominent notices
+      stating that You changed the files;
+6.4.  You shall retain all copyright, patent, trademark, and attribution
+      notices excluding those notices that do not pertain to any part of
+      the Artifact or its Derivatives.
+You may add Your own copyright statement to Your modifications and may
+provide additional or different license terms and conditions with
+respect to paragraph 6.1., to govern the use, reproduction, or
+Distribution of Your modifications, or for any Derivative, provided that
+Your use, reproduction, and Distribution of the Artifact or its
+Derivative otherwise complies with the conditions stated in this
+License. In other words, the Use-based restrictions in Attachment A form
+the minimum set of terms for You to license to Third Parties any
+Artifact or its Derivative, but You may add more restrictive terms if
+You deem it necessary.
+Section IV: OTHER PROVISIONS
+7. Updates and Runtime Restrictions. To the maximum extent permitted by
+law, Licensor reserves the right to restrict (remotely or otherwise)
+usage of the Artifact in violation of this License or update the
+Artifact through electronic means.
+8. Trademarks and Related. Nothing in this License permits You to make
+use of Licensors� trademarks, trade names, logos or to otherwise suggest
+endorsement or misrepresent the relationship between the parties; and
+any rights not expressly granted herein are reserved by the Licensors.
+9. Disclaimer of Warranty. Unless required by applicable law or agreed
+to in writing, Licensor provides the Artifact (and each Contributor
+provides its Contributions) on an �AS IS� BASIS, WITHOUT WARRANTIES OR
+CONDITIONS OF ANY KIND, either express or implied, including, without
+limitation, any warranties or conditions of TITLE, NON-INFRINGEMENT,
+MERCHANTABILITY, or FITNESS FOR A PARTICULAR PURPOSE. You are solely
+responsible for determining the appropriateness of using the Artifact,
+and assume any risks associated with Your exercise of permissions under
+this License.
+10. Limitation of Liability. In no event and under no legal theory,
+whether in tort (including negligence), contract, or otherwise, unless
+required by applicable law (such as deliberate and grossly negligent
+acts) or agreed to in writing, shall any Contributor be liable to You
+for damages, including any direct, indirect, special, incidental, or
+consequential damages of any character arising as a result of this
+License or out of the use or inability to use the Artifact (including
+but not limited to damages for loss of goodwill, work stoppage, computer
+failure or malfunction, or any and all other commercial damages or
+losses), even if such Contributor has been advised of the possibility of
+such damages.
+11. If any provision of this License is held to be invalid, illegal or
+unenforceable, the remaining provisions shall be unaffected thereby and
+remain valid as if such provision had not been set forth herein.
+12. Term and Termination. The term of this License will commence upon
+the earlier of Your (a) acceptance of this License or (b) accessing the
+Artifact; and will continue in full force and effect until terminated in
+accordance with the terms and conditions herein. Licensor may terminate
+this License if You are in breach of any term or condition of this
+License. Upon termination of this License, all licenses granted to You
+will terminate and You must promptly delete and cease use of the
+Artifact. Sections 1, 7, 8, 9, 10, 11, and 12 survive termination of
+this License.
+END OF TERMS AND CONDITIONS
+Attachment A
+AMD Responsible AI Use Policy
+AMD is committed to the responsible use of its Artificial Intelligence
+(AI) products and technologies (�AMD AI�).  AMD AI may include
+artificial intelligence or machine learning technologies that use
+algorithms to analyze data and generate output using predictions based
+on patterns in data.  This policy explains the uses that AMD
+specifically prohibits.
+If you use any AMD AI, you are agreeing to use the AMD AI in compliance
+with applicable laws and not for any of the following prohibited uses.
+Prohibited Uses:
+1) No Illegal Acts.  Do not use AMD AI in violation of any applicable
+national, state, local, or other jurisdictional law, rule, regulation,
+or sanction.
+2) No Explicit Content.  Do not use AMD AI to submit (as input),
+generate, or disseminate content depicting violent or sexually explicit
+content or to create sexual chatbots.
+3) No Harm.  Do not use AMD AI for any potentially harmful uses,
+   including fraud, deception, discrimination, abuse, or harassment,
+   including the following:
+   a) Harm or abuse of a minor, including grooming and child sexual
+      exploitation.
+   b) Impersonation of human beings for purposes of deception.
+   c) Generation or dissemination of information you know to be false
+      for the purpose of harming others.
+   d) Intentionally defame, disparage, or otherwise harass others.
+   e) Intentionally attempting to materially distort the behavior of a
+      person in a manner that causes or is likely to cause that person
+      or another person physical or psychological harm.
+   f) Providing medical advice or interpretation of medical results that
+      is intended to be a substitute for professional medical advice,
+      diagnosis, or treatment.
+   g) Engaging in the unlawful or unauthorized practice of any
+      profession, including financial, legal, medical, health, or
+      related professional practices.
+   h) Judgment of, discrimination against, or harm to individuals or
+      groups based on legally protected characteristics or categories,
+      online or offline social behavior, or known or predicted personal
+      or personality characteristics, including any of the foregoing
+      uses in social credit systems.
+4) No High-Risk Activity.  Do not use AMD AI in any high-risk activities
+ or applications that create a risk of personal injury, death, or
+severe property or environmental damage, including in weapons or
+military applications.
+5) No Personal Information.  Do not use AMD AI to collect, process, or
+disclose personal data, including heath or sensitive personal
+information, without the necessary rights or consents.
+6) No Infringement.  Do not use AMD AI to generate or disseminate any
+information that infringes upon or misappropriates the intellectual
+property rights of others, including copyright, trademark, patent, and
+trade secret rights, rights to privacy, and publicity rights.
+7) No Malware.  Do not use AMD AI to generate or disseminate malware or
+any other content to be used for the purpose of facilitating unpermitted
+access to, or use of, computer systems or data.
+8) No Obfuscation.  Do not inappropriately obfuscate or fail to disclose
+to end users the presence of AI in any application in which AMD AI is
+deployed, along with any known risks or dangers of using AI without
+appropriate safeguards, oversight and human control.
+9) No Reliance.  Do not rely on any information generated using AMD AI
+without assessing it for accuracy, potential for harm, or other specific
+risks applicable to the use case.

README.md CHANGED Viewed

@@ -1,181 +1,178 @@
----
-license: other
-license_link: LICENSE
-library_name: transformers
-pipeline_tag: text-generation
-datasets:
-  - amd/SAND-Post-Training-Dataset
-language:
-  - en
-base_model:
-  - Qwen/Qwen2.5-32B-Instruct
----
-# SAND-Reasoning: Best-in-class Large Reasoning Model Built with Synthetic Data only using AMD GPUs
-<div align="center">
-| [**📄 Technical Report**](https://arxiv.org/pdf/2507.20527) | [**💾 Synthetic Datasets**](https://huggingface.co/datasets/amd/SAND-Post-Training-Dataset) | [**💻 GitHub Repository**](https://huggingface.co/datasets/amd/SAND-Post-Training-Dataset) | [**📝 Blog Post**](https://rocm.blogs.amd.com/artificial-intelligence/sand-math/README.html) |
-| :---: | :---: | :---: | :---: |
-</div>
----
-## Model Summary
-We introduce **SAND-Math-Qwen2.5-32B** and **SAND-MathScience-DeepSeek-Qwen32B**, reasoning models built entirely using a synthetic data pipeline running on the **AMD ROCm™ stack** and **AMD Instinct™ MI325 GPUs**.
-By prioritizing data difficulty along with quantity, we demonstrate that high-difficulty synthetic data can elevate prior-generation models to match or exceed modern proprietary models. `SAND-Math-Qwen2.5-32B` is fine-tuned from **Qwen2.5-32B-Instruct** on just **14k synthetic math samples**, achieving strong reasoning capabilities with minimal data outperforming other data distillation and post training approaches. `SAND-MathScience-DeepSeek-Qwen32B` is fine-tuned from **DeepSeek-R1-Distill-Qwen-32B** on a compact dataset of **27k samples** (15k Math + 12k Science), achieving a generational leap in performance that rivals **Qwen3-32B**.
-We are releasing the models, datasets, and code to empower the community to build their own state-of-the-art reasoning models using AMD hardware.
-## 📊 Benchmark Results
-We conducted extensive experiments to validate that our pipeline yields superior results compared to models trained on significantly larger datasets.
-### 1. Bridging the Generational Gap
-Fine-tuning the Qwen2.5-based **DeepSeek-R1-Distill-Qwen-32B** on our mixed Math/Science dataset allows it to rival and even surpass the next-generation **Qwen3-32B** on key benchmarks.
-| Model | AIME24 | AIME25 | MATH500 | GPQA |
-| :--- | :---: | :---: | :---: | :---: |
-| DeepSeek-Distilled-Qwen32B (Base) | 72.6 | 54.9 | 94.3 | 62.1 |
-| EXAONE Deep 32B | 72.1 | 65.8 | 95.8 | 66.1 |
-| Qwen3-32B (Thinking mode) | 81.4 | 72.9 | **97.0** | 68.4 |
-| **SAND-MathScience-DeepSeek-Qwen32B (Ours)** | **83.85** | **78.33** | 93.85 | **68.72** |
-### 2. Efficiency: Unlocking Reasoning with Less Data
-Using only **14k synthetic math samples** and standard SFT (no RL), our approach outperforms models trained on datasets 5x to 50x larger.
-| Model | Data Size | AIME24 | AIME25 | MATH500 | GPQA |
-| :--- | :--- | :---: | :---: | :---: | :---: |
-| Qwen2.5-32B-Instruct (Base) | - | 16.7 | 13.3 | 83.4 | 53.5 |
-| DeepSeek-R1-Distill-Qwen-32B | 800k | 72.6 | 54.9 | 94.3 | 62.1 |
-| Light-R1-32B | 79k | 73.0 | 64.3 | 93.3 | 60.6 |
-| OpenThinker-32B | 114k | 66.0 | 53.3 | 89.4 | 57.6 |
-| **SAND-Math-Qwen2.5-32B (Ours)** | **14k** | **74.01** | **68.18** | **92.05** | **60.8** |
----
-## ⚙️ The Synthetic Data Pipeline
-Our results are powered by a 4-stage automated pipeline running on AMD hardware that prioritizes **difficulty and novelty** over volume. Unlike datasets that recycle easy problems, our pipeline leverages a Teacher Model (`GPT-OSS120b`) to generate, validate, and systematically "hike" the difficulty of reasoning problems.
-![Pipeline Overview](PipelineSimple.png)
-### Pipeline Stages
-1. **Stage 1: QA Generation & Consistency** 🛠️
-   - Generates novel problems from scratch
-   - Enforces correctness by requiring the teacher to generate multiple independent solution paths
-   - Only questions where all answers align are kept
-2. **Stage 2: De-duplication & Decontamination** 🧹
-   - Removes internal duplicates via embedding similarity
-   - **Crucial Step:** Scans against known test sets (AIME, MATH, GPQA) to ensure zero contamination
-3. **Stage 3: Difficulty Hiking** 🏔️
-   - Moderately challenging questions are rewritten by the teacher model
-   - Introduces deeper reasoning chains, added constraints, or cross-domain logic
-   - Systematically elevates complexity
-   - Configurable step primarily used when initial generation yields insufficient volume of high-difficulty samples
----
-## 🚀 Quick Start
-### Python Inference (Transformers)
-```python
-from transformers import AutoModelForCausalLM, AutoTokenizer
-model_name = "amd/SAND-Math-Qwen2.5-32B"
-model = AutoModelForCausalLM.from_pretrained(
-    model_name,
-    torch_dtype="auto",
-    device_map="auto"
-)
-tokenizer = AutoTokenizer.from_pretrained(model_name)
-# Example prompt
-prompt = "Find the number of pairs of positive integers $(m, n)$ such that $m^2 + n < 22$ and $n^2 + m < 22$."
-messages = [
-    {"role": "user", "content": prompt}
-]
-text = tokenizer.apply_chat_template(
-    messages,
-    tokenize=False,
-    add_generation_prompt=True
-)
-model_inputs = tokenizer([text], return_tensors="pt").to(model.device)
-generated_ids = model.generate(
-    **model_inputs,
-    max_new_tokens=4096,
-    temperature=0.7, # Recommended temperature
-    do_sample=True
-)
-generated_ids = [
-    output_ids[len(input_ids):] for input_ids, output_ids in zip(model_inputs.input_ids, generated_ids)
-]
-response = tokenizer.batch_decode(generated_ids, skip_special_tokens=True)[0]
-print("Response:", response)
-```
-### Serving (vLLM & SGLang)
-You can easily serve this model as an OpenAI-compatible API endpoint.
-**Using SGLang:**
-```bash
-python -m sglang.launch_server --model-path amd/SAND-Math-Qwen2.5-32B --max-model-len 32768
-```
-**Using vLLM:**
-```bash
-vllm serve amd/SAND-Math-Qwen2.5-32B --max-model-len 32768
-```
----
-## 💡 Usage Recommendations
-To replicate our performance benchmarks and achieve the best reasoning results, we strongly recommend the following configurations:
-*   **Temperature:** Set `temperature=0.7`. **DO NOT use greedy decoding**, as it can lead to performance degradation and repetitive loops.
-*   **Prompting:** For mathematical problems, include a directive to enforce structure:
-    > "Please reason step by step, and put your final answer within \boxed{}."
-*   **Context Length:** We recommend allowing an output length of **32,768 tokens**. This ensures the model has sufficient space for long Chain-of-Thought (CoT) generation.
-*   **Thinking Token:** It is recommended to enforce the model to initiate its response with the `<think>\n` token to trigger the reasoning mode effectively.
-*   **Evaluation:** When benchmarking, conduct multiple passes (Pass@K) and average the results for stability.
----
-## 📜 License
-This project is licensed under the **Open RAIL-MSD** license. This is an open, royalty-free license that permits commercial use, modification, and distribution of the dataset, models, and source code.
-The license includes standard use-based restrictions to prevent harmful applications (e.g., illegal activities, generating harmful content, high-risk applications). These restrictions are designed to promote responsible AI development while keeping the license permissive for legitimate use cases.
-For full license terms and conditions, please see the [LICENSE](https://github.com/AMD-AGI/sand-pipeline/blob/main/LICENSE.txt) file.
----
-## Citation
-If you use this model, dataset, or pipeline in your research, please cite our work:
-```bibtex
-@misc{manem025sandmathusingllmsgenerate,
-      title={SAND-Math: Using LLMs to Generate Novel, Difficult and Useful Mathematics Questions and Answers},
-      author={Chaitanya Manem and Pratik Prabhanjan Brahma and Prakamya Mishra and Zicheng Liu and Emad Barsoum},
-      year={2025},
-      eprint={2507.20527},
-      archivePrefix={arXiv},
-      primaryClass={cs.CL},
-      url={https://arxiv.org/abs/2507.20527},
-}
-```

+---
+license: other
+license_link: LICENSE
+library_name: transformers
+pipeline_tag: text-generation
+datasets:
+  - amd/SAND-Post-Training-Dataset
+language:
+  - en
+base_model:
+  - Qwen/Qwen2.5-32B-Instruct
+---
+# SAND-Reasoning: Best-in-class Large Reasoning Model Built with Synthetic Data only using AMD GPUs
+<div align="center">
+| [![Paper](https://img.shields.io/badge/ArXiv-2507.20527-B31B1B.svg)](https://arxiv.org/pdf/2507.20527) | [![Hugging Face Dataset](https://img.shields.io/badge/🤗%20Hugging%20Face-Dataset-green)](https://huggingface.co/datasets/amd/SAND-Post-Training-Dataset) | [![GitHub](https://img.shields.io/badge/GitHub-Repository-black)](https://github.com/AMD-AGI/sand-pipeline) | [![Blog Post](https://img.shields.io/badge/Blog%20Post-Read%20More-blue)](https://rocm.blogs.amd.com/artificial-intelligence/sand-math/README.html) |
+| :---: | :---: | :---: | :---: |
+</div>
+## Model Summary
+We introduce **SAND-Math-Qwen2.5-32B** and **SAND-MathScience-DeepSeek-Qwen32B**, reasoning models built entirely using a synthetic data pipeline running on the **AMD ROCm™ stack** and **AMD Instinct™ MI325 GPUs**.
+By prioritizing data difficulty along with quantity, we demonstrate that high-difficulty synthetic data can elevate prior-generation models to match or exceed modern proprietary models. `SAND-Math-Qwen2.5-32B` is fine-tuned from **Qwen2.5-32B-Instruct** on just **14k synthetic math samples**, achieving strong reasoning capabilities with minimal data outperforming other data distillation and post training approaches. `SAND-MathScience-DeepSeek-Qwen32B` is fine-tuned from **DeepSeek-R1-Distill-Qwen-32B** on a compact dataset of **27k samples** (15k Math + 12k Science), achieving a generational leap in performance that rivals **Qwen3-32B**.
+We are releasing the models, datasets, and code to empower the community to build their own state-of-the-art reasoning models using AMD hardware.
+## 📊 Benchmark Results
+We conducted extensive experiments to validate that our pipeline yields superior results compared to models trained on significantly larger datasets.
+### 1. Bridging the Generational Gap
+Fine-tuning the Qwen2.5-based **DeepSeek-R1-Distill-Qwen-32B** on our mixed Math/Science dataset allows it to rival and even surpass the next-generation **Qwen3-32B** on key benchmarks.
+| Model | AIME24 | AIME25 | MATH500 | GPQA |
+| :--- | :---: | :---: | :---: | :---: |
+| DeepSeek-Distilled-Qwen32B (Base) | 72.6 | 54.9 | 94.3 | 62.1 |
+| EXAONE Deep 32B | 72.1 | 65.8 | 95.8 | 66.1 |
+| Qwen3-32B (Thinking mode) | 81.4 | 72.9 | **97.0** | 68.4 |
+| **SAND-MathScience-DeepSeek-Qwen32B (Ours)** | **83.85** | **78.33** | 93.85 | **68.72** |
+### 2. Efficiency: Unlocking Reasoning with Less Data
+Using only **14k synthetic math samples** and standard SFT (no RL), our approach outperforms models trained on datasets 5x to 50x larger.
+| Model | Data Size | AIME24 | AIME25 | MATH500 | GPQA |
+| :--- | :--- | :---: | :---: | :---: | :---: |
+| Qwen2.5-32B-Instruct (Base) | - | 16.7 | 13.3 | 83.4 | 53.5 |
+| DeepSeek-R1-Distill-Qwen-32B | 800k | 72.6 | 54.9 | 94.3 | 62.1 |
+| Light-R1-32B | 79k | 73.0 | 64.3 | 93.3 | 60.6 |
+| OpenThinker-32B | 114k | 66.0 | 53.3 | 89.4 | 57.6 |
+| **SAND-Math-Qwen2.5-32B (Ours)** | **14k** | **74.01** | **68.18** | **92.05** | **60.8** |
+---
+## ⚙️ The Synthetic Data Pipeline
+Our results are powered by a 4-stage automated pipeline running on AMD hardware that prioritizes **difficulty and novelty** over volume. Unlike datasets that recycle easy problems, our pipeline leverages a Teacher Model (`GPT-OSS120b`) to generate, validate, and systematically "hike" the difficulty of reasoning problems.
+![Pipeline Overview](PipelineSimple.png)
+### Pipeline Stages
+1. **Stage 1: QA Generation & Consistency** 🛠️
+   - Generates novel problems from scratch
+   - Enforces correctness by requiring the teacher to generate multiple independent solution paths
+   - Only questions where all answers align are kept
+2. **Stage 2: De-duplication & Decontamination** 🧹
+   - Removes internal duplicates via embedding similarity
+   - **Crucial Step:** Scans against known test sets (AIME, MATH, GPQA) to ensure zero contamination
+3. **Stage 3: Difficulty Hiking** 🏔️
+   - Moderately challenging questions are rewritten by the teacher model
+   - Introduces deeper reasoning chains, added constraints, or cross-domain logic
+   - Systematically elevates complexity
+   - Configurable step primarily used when initial generation yields insufficient volume of high-difficulty samples
+---
+## 🚀 Quick Start
+### Python Inference (Transformers)
+```python
+from transformers import AutoModelForCausalLM, AutoTokenizer
+model_name = "amd/SAND-Math-Qwen2.5-32B"
+model = AutoModelForCausalLM.from_pretrained(
+    model_name,
+    torch_dtype="auto",
+    device_map="auto"
+)
+tokenizer = AutoTokenizer.from_pretrained(model_name)
+# Example prompt
+prompt = "Find the number of pairs of positive integers $(m, n)$ such that $m^2 + n < 22$ and $n^2 + m < 22$."
+messages = [
+    {"role": "user", "content": prompt}
+]
+text = tokenizer.apply_chat_template(
+    messages,
+    tokenize=False,
+    add_generation_prompt=True
+)
+model_inputs = tokenizer([text], return_tensors="pt").to(model.device)
+generated_ids = model.generate(
+    **model_inputs,
+    max_new_tokens=4096,
+    temperature=0.7, # Recommended temperature
+    do_sample=True
+)
+generated_ids = [
+    output_ids[len(input_ids):] for input_ids, output_ids in zip(model_inputs.input_ids, generated_ids)
+]
+response = tokenizer.batch_decode(generated_ids, skip_special_tokens=True)[0]
+print("Response:", response)
+```
+### Serving (vLLM & SGLang)
+You can easily serve this model as an OpenAI-compatible API endpoint.
+**Using SGLang:**
+```bash
+python -m sglang.launch_server --model-path amd/SAND-Math-Qwen2.5-32B --max-model-len 32768
+```
+**Using vLLM:**
+```bash
+vllm serve amd/SAND-Math-Qwen2.5-32B --max-model-len 32768
+```
+---
+## 💡 Usage Recommendations
+To replicate our performance benchmarks and achieve the best reasoning results, we strongly recommend the following configurations:
+*   **Temperature:** Set `temperature=0.7`. **DO NOT use greedy decoding**, as it can lead to performance degradation and repetitive loops.
+*   **Prompting:** For mathematical problems, include a directive to enforce structure:
+    > "Please reason step by step, and put your final answer within \boxed{}."
+*   **Context Length:** We recommend allowing an output length of **32,768 tokens**. This ensures the model has sufficient space for long Chain-of-Thought (CoT) generation.
+*   **Thinking Token:** It is recommended to enforce the model to initiate its response with the `<think>\n` token to trigger the reasoning mode effectively.
+*   **Evaluation:** When benchmarking, conduct multiple passes (Pass@K) and average the results for stability.
+---
+## 📜 License
+This project is licensed under the **Open RAIL-MSD** license. This is an open, royalty-free license that permits commercial use, modification, and distribution of the dataset, models, and source code.
+The license includes standard use-based restrictions to prevent harmful applications (e.g., illegal activities, generating harmful content, high-risk applications). These restrictions are designed to promote responsible AI development while keeping the license permissive for legitimate use cases.
+For full license terms and conditions, please see the [LICENSE](./LICENSE) file.
+---
+## Citation
+If you use this model, dataset, or pipeline in your research, please cite our work:
+```bibtex
+@misc{manem025sandmathusingllmsgenerate,
+      title={SAND-Math: Using LLMs to Generate Novel, Difficult and Useful Mathematics Questions and Answers},
+      author={Chaitanya Manem and Pratik Prabhanjan Brahma and Prakamya Mishra and Zicheng Liu and Emad Barsoum},
+      year={2025},
+      eprint={2507.20527},
+      archivePrefix={arXiv},
+      primaryClass={cs.CL},
+      url={https://arxiv.org/abs/2507.20527},
+}
+```