仅用13个参数让大模型学会推理，性能接近全量微调。
Learning to Reason in 13 Parameters
- 提出极简适配器TinyLoRA，将推理参数压缩至1个（共13参数）
- 80亿参数模型在GSM8K上达91%准确率，仅需26字节存储
- 适用于需要高效推理的场景，尤其适合资源受限部署
近期研究显示语言模型可通过强化学习学会推理。部分工作尝试使用低秩参数化进行推理训练，但传统LoRA无法缩小至低于模型维度。我们质疑即使秩=1的LoRA是否必要，提出TinyLoRA，可将低秩适配器规模缩减至仅1个参数。在新参数化下，我们仅用13个可训练参数（bf16精度下总26字节），即可使80亿参数的Qwen2.5在GSM8K上达到91%准确率。该趋势具普遍性：在更难的推理基准如AIME、AMC和MATH500上，仅需训练原参数量1/1000即可恢复90%性能提升。值得注意的是，仅通过强化学习能实现此效果；使用SFT训练则需100-1000倍更大的参数更新才能达到同等性能。
原文摘要 · Abstract (English)
Recent research has shown that language models can learn to \textit{reason}, often via reinforcement learning. Some work even trains low-rank parameterizations for reasoning, but conventional LoRA cannot scale below the model dimension. We question whether even rank=1 LoRA is necessary for learning to reason and propose TinyLoRA, a method for scaling low-rank adapters to sizes as small as one parameter. Within our new parameterization, we are able to train the 8B parameter size of Qwen2.5 to 91\% accuracy on GSM8K with only 13 trained parameters in bf16 (26 total bytes). We find this trend holds in general: we are able to recover 90\% of performance improvements while training $1000x$ fewer parameters across a suite of more difficult learning-to-reason benchmarks such as AIME, AMC, and MATH500. Notably, we are only able to achieve such strong performance with RL: models trained using SFT require $100-1000x$ larger updates to reach the same performance.
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