Incentivizing Strong Reasoning from Weak Supervision

TL;DR

The paper tackles the challenge of eliciting strong reasoning in large language models without costly reinforcement learning or high-quality chain-of-thought data. It introduces Weak-to-Strong Reasoning (W2SR), wherein a stronger student model is fine-tuned via supervised learning on long CoT traces produced by significantly weaker teacher models, and evaluates the extent to which such supervision recovers RL gains using the Reasoning Gap Recovered (RGR) metric. Across multiple benchmarks and model families, W2SR demonstrates substantial reasoning gains, with the surprising finding that the teacher’s explicit reasoning ability matters more than its size or end-task accuracy; moreover, even incorrect traces can effectively guide learning, and weaker teachers can offer strong efficiency advantages (e.g., 25× faster training for W2SR-P). Collectively, the results position weak-to-strong distillation as a practical, generalizable alternative to expensive methods for enabling inference-time reasoning in LLMs, with notable implications for domain-specific, privacy-preserving model refinement and future multi-modal extensions.

Abstract

Large language models (LLMs) have demonstrated impressive performance on reasoning-intensive tasks, but enhancing their reasoning abilities typically relies on either reinforcement learning (RL) with verifiable signals or supervised fine-tuning (SFT) with high-quality long chain-of-thought (CoT) demonstrations, both of which are expensive. In this paper, we study a novel problem of incentivizing the reasoning capacity of LLMs without expensive high-quality demonstrations and reinforcement learning. We investigate whether the reasoning capabilities of LLMs can be effectively incentivized via supervision from significantly weaker models. We further analyze when and why such weak supervision succeeds in eliciting reasoning abilities in stronger models. Our findings show that supervision from significantly weaker reasoners can substantially improve student reasoning performance, recovering close to 94% of the gains of expensive RL at a fraction of the cost. Experiments across diverse benchmarks and model architectures demonstrate that weak reasoners can effectively incentivize reasoning in stronger student models, consistently improving performance across a wide range of reasoning tasks. Our results suggest that this simple weak-to-strong paradigm is a promising and generalizable alternative to costly methods for incentivizing strong reasoning capabilities at inference-time in LLMs. The code is publicly available at https://github.com/yuanyige/w2sr.

Figures (8)

• Figure 2: Using W2SR with Qwen2.5-Math-7B as the strong student and Qwen2.5-1.5B-Reasoner as the weak teacher, the four bars represent: (1) teacher’s standalone performance, (2) student’s standalone performance, (3) student performance after W2SR, and (4) student performance after W2SR-P. More results are in \ref{['app:exp']}.
• Figure 3: Comparison of Weak-to-Strong Reasoning (W2SR) between Reasoner and Non-Reasoner Teachers using Qwen2.5-Math-7B as the student. Upper: The x-axis represents teacher model scale, with two lines indicating the W2SR student performance trained with Reasoner vs. Non-Reasoner teachers of corresponding scales. Lower: The first two bars show initial performance of Qwen2.5-1.5B-Reasoner and Qwen2.5-32B-Non-Reasoner teacher, while the last two bars show the resulting W2SR student performance. More results are in \ref{['app:exp']}.
• Figure 3: Cognitive Behavior of RL and W2SR
• Figure 4: Diminishing marginal returns from increasing reasoner-teacher scale on student performance. The x-axis represents scale of the reasoner teacher, while the y-axis shows Pass@1 performance of students trained under supervision from the corresponding teacher. The three lines correspond to student models of different sizes (7B-Math, 14B, and 32B). The results show that as teacher strength increases, student performance improves initially but eventually plateaus, indicating limited additional benefit from further increasing teacher scale.
• Figure 5: Comparison of efficiency (left bars) and performance (right bars) among GRPO, W2SR, and W2SR-P, evaluated with the Qwen2.5-Math-7B student and the Qwen2.5-1.5B-Reasoner teacher. W2SR-P achieves a 25× improvement in training efficiency and a 2.92% gain in performance. Further results are in \ref{['app:exp']}.