让小模型像大模型一样高效解数学题
DenseSteer: Steering Small Language Models towards Dense Math Reasoning
- 通过调节内部表示，引导小模型采用高信息密度的推理方式
- 在不增加计算成本的前提下，显著提升30亿参数以下模型的解题准确率
- 适合希望低成本提升小模型推理能力的研究者和开发者
大型语言模型（LLMs）展现出强大的思维链（CoT）推理能力，而较小模型（≤3B参数）在多步推理任务中表现显著不足。通过对Qwen-2.5模型族在数学推理基准上的实证分析，我们发现更高效的推理与更少的推理步骤但更高的每步信息密度相关，这一特性被称为密集推理（Dense Reasoning）。受此启发，我们提出DenseSteer——一种无需训练的推理时调优框架，通过调节内部表示向密集推理模式对齐，增强小模型的推理能力。实验表明，该方法在不增加词元级负对数似然（Negative Log-Likelihood）的前提下，持续提升模型准确率，验证了密集推理作为数学问题求解有效结构路径的潜力。
原文摘要 · Abstract (English)
Large language models (LLMs) demonstrate strong chain-of-thought (CoT) reasoning abilities, while smaller models (<= 3B parameters) significantly underperform on multi-step reasoning tasks. Based on empirical analyses of the Qwen-2.5 model family on math reasoning benchmarks, we find that more proficient reasoning is associated with fewer reasoning steps but higher information density per step, a property we term Dense Reasoning. Motivated by this observation, we propose DenseSteer, a training-free inference-time steering framework that enhances small-model reasoning by modulating internal representations toward dense reasoning patterns. Experiments show that our method yields consistent accuracy improvements without increasing token-level Negative Log-Likelihood, highlighting dense reasoning as an effective structural approach to mathematical problem solving.
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