One-shot Entropy Minimization (2505.20282v3)

Abstract: We trained 13,440 LLMs and found that entropy minimization requires only a single unlabeled data and 10 steps optimization to achieve performance improvements comparable to or even greater than those obtained using thousands of data and carefully designed rewards in rule-based reinforcement learning. This striking result may prompt a rethinking of post-training paradigms for LLMs. Our code is avaliable at https://github.com/zitian-gao/one-shot-em.

One-shot Entropy Minimization: A Critical Examination

In this paper titled "One-shot Entropy Minimization," the authors propose a novel approach to enhancing the post-training performance of LLMs. The proposed method, Entropy Minimization (EM), is shown to potentially offer significant advantages over traditional reinforcement learning (RL) techniques by requiring minimal data and computational resources.

Methodology Overview

The paper details an unsupervised EM technique that contrasts explicitly with the complexities involved in RL. EM is based on two straightforward assumptions: the inherent stochastic nature of LLM sampling processes and the typically lower entropy associated with correct answers compared to incorrect ones. By focusing on minimizing the token-level entropy during generation, EM sidesteps the extensive data labeling and reward design required for RL. Remarkably, the authors leveraged EM to train 13,440 LLMs, emphasizing an unsupervised technique grounded in these assumptions.

Key Findings

The crux of the paper is an assertion that EM, with a single unlabeled data point and as few as ten training steps, can surpass the performance gains typically associated with RL. Specifically, the results indicate that EM achieves better performance compared to thousands of data and elaborate reward schemas inherent in RL.

1. Performance Metrics: The application of EM on Qwen2.5-Math-7B led to large improvements across various reasoning benchmarks, such as an average score increase of 24.7 points, with notable gains in individual benchmarks like AMC23 and Olympiad Bench.
2. Logits Distribution Analysis: The authors observed a rightward skew in the logits distribution post-EM, signaling increased model confidence by concentrating on semantically correct tokens. Contrarily, RL fostered a leftward shift, which the paper argues could hinder model generation.
3. Loss and Performance Dynamics: An intriguing observation was that post-10-step training, further reductions in EM loss did not translate into improved reasoning performance, suggesting EM functions as a distribution-shaping tool versus a learning strategy.

Implications and Speculations

Practically, the findings challenge contemporary paradigms in model training, suggesting EM as a viable, lightweight alternative to RL, especially efficient when computational resources are a constraint. Theoretically, it implies a reevaluation of entropy-centric optimization methods and their role in exploiting pretrained model latent potential.

Looking ahead, there are several avenues for future work. Stochastic variability in EM outputs could be mitigated by stabilizing training methodologies. Furthermore, extending EM to other domains beyond reasoning, such as dialogue or summarization, could reveal more about its utility and robustness. The interaction effects between EM and RL, particularly in the sequence of application, warrant deeper exploration to maximize synergistic benefits.

Conclusion

This paper stands as a substantial contribution to the post-training optimization of LLMs and opens discourse on entropy minimization as a potent strategy. The drastic reduction in data and computational requirements, coupled with reliable performance metrics, underscores EM's potential as a favored method in future AI research frameworks.