专为印度理工科入学考设计的70亿参数数学推理模型
Aryabhata: An exam-focused language model for JEE Math
- 融合强开源推理模型，经课程化监督微调与验证链式思维训练
- 在JEE主考题上准确率达83.2%，优于现有同类模型
- 适合教育场景，提供可解释的分步解题过程
我们提出Aryabhata 1.0，一个70亿参数的紧凑型数学推理模型，专为印度国家级学术考试联合入学考试（JEE）优化。尽管大语言模型进展迅速，但多数仍不适用于教育场景。Aryabhata 1.0通过整合高性能开源推理模型，并采用课程学习策略对经最佳- n 拒绝采样验证的链式思维（CoT）轨迹进行监督微调（SFT）。为进一步提升性能，引入基于可验证奖励的强化学习（RLVR），使用A2C目标结合组相对优势估计，辅以自适应组大小调整和温度缩放等新型探索策略。在分布内（JEE Main 2025）和分布外（MATH、GSM8K）基准上评估，Aryabhata在准确率和效率方面均超越现有模型，同时提供具有教学价值的逐步推理过程。我们开放发布Aryabhata作为基础模型，推动面向考试的开源小型语言模型发展。这是首次向社区开放获取（https://huggingface.co/PhysicsWallahAI/Aryabhata-1.0）；PhysicsWallah正积极训练后续模型，以进一步提升学生学习成效。
原文摘要 · Abstract (English)
We present Aryabhata 1.0, a compact 7B parameter math reasoning model optimized for the Indian academic exam, the Joint Entrance Examination (JEE). Despite rapid progress in large language models (LLMs), current models often remain unsuitable for educational use. Aryabhata 1.0 is built by merging strong open-weight reasoning models, followed by supervised fine-tuning (SFT) with curriculum learning on verified chain-of-thought (CoT) traces curated through best-of-$n$ rejection sampling. To further boost performance, we apply reinforcement learning with verifiable rewards (RLVR) using A2C objective with group-relative advantage estimation along with novel exploration strategies such as Adaptive Group Resizing and Temperature Scaling. Evaluated on both in-distribution (JEE Main 2025) and out-of-distribution (MATH, GSM8K) benchmarks, Aryabhata outperforms existing models in accuracy and efficiency, while offering pedagogically useful step-by-step reasoning. We release Aryabhata as a foundation model to advance exam-centric, open-source small language models. This marks our first open release for community feedback (https://huggingface.co/PhysicsWallahAI/Aryabhata-1.0); PW is actively training future models to further improve learning outcomes for students.
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