New Training-Free Method Boosts LLM Reasoning with Depth-Entropy.

This paper presents Depth-Entropy Guided Sampling (DEGS), an innovative training-free method designed to enhance the reasoning capabilities of large language models (LLMs) at test time. Unlike traditional approaches that rely on expensive reinforcement learning (RL) or curated data, DEGS leverages an intrinsic quality signal: the layer-wise entropy collapse observed within the transformer's internal forward pass. The core observation is that stronger reasoners, including those post-trained with RL, exhibit a distinct "late collapse" where logit-lens decoded entropy remains high until deeper layers before converging. DEGS quantifies this as a per-sequence collapse depth and integrates it into a joint objective function, combining sequence likelihood with this depth-entropy structure within an MCMC power-sampling framework (DEGS-MCMC). Evaluated across three open-weight models and four reasoning benchmarks, DEGS-MCMC achieved state-of-the-art training-free accuracy. Notably, its gains were most significant in out-of-domain scenarios and on harder problem splits, precisely where methods relying solely on likelihood often fall short. The method demonstrated performance competitive with, and often surpassing, RL-trained models on out-of-domain tasks like GPQA, all with minimal computational overhead and without any additional training or labeled data.