用模型自信心挑选最优解法，高效提升数学推理能力
Maximizing Prefix-Confidence at Test-Time Efficiently Improves Mathematical Reasoning
- 以模型生成前缀的自信度筛选最可能正确的解题路径
- 32词前缀即可超越多数投票法，在准确率与算力间更优
- 对长度偏差不敏感，适合追求效率的数学推理场景
近期研究表明，语言模型可通过最大化自身预测置信度实现自我改进，无需外部验证器或奖励信号。本文研究语言模型在数学推理任务中的测试时缩放方法，利用模型自身的置信度选择最具潜力的尝试路径。令人惊讶的是，仅继续由前缀置信度选出的最优尝试，便能显著提升性能。我们在五个数学推理数据集上系统评估：学校级的GSM8K和MATH500，以及竞赛级的AMC23、AIME24和AIME25。结果表明，仅使用32个词的前缀进行置信度缩放，其准确率-计算量权衡优于多数投票法；且相比BoN，对长度偏差更不敏感。此外，我们还评估了基于前缀置信度的测试时训练，发现虽优于基础模型，但未超越前缀置信度缩放效果。
原文摘要 · Abstract (English)
Recent work has shown that language models can self-improve by maximizing their own confidence in their predictions, without relying on external verifiers or reward signals. In this work, we study the test-time scaling of language models for mathematical reasoning tasks, where the model's own confidence is used to select the most promising attempts. Surprisingly, we find that we can achieve significant performance gains by continuing only the most promising attempt, selected by the model's prefix-confidence. We systematically evaluate prefix-confidence scaling on five mathematical reasoning datasets: the school-level GSM8K and MATH500, and the competition-level AMC23, AIME24, and AIME25. We find that prefix-confidence scaling with prefixes of only 32 tokens achieves a better accuracy-compute trade-off than majority voting. Moreover, prefix-confidence scaling appears less susceptible than BoN to length biases. Finally, we also evaluate test-time training with prefix-confidence and find that, while outperforming the base model, it does not improve over prefix-confidence scaling.
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