Distilling LLM Feedback for Lean Theorem Proving
This work provides an incremental improvement in post-training methods for complex reasoning tasks, specifically for developers working on theorem-proving with Lean4.
This paper addresses the limitations of GRPO in post-training for reasoning models by introducing Feedback Distillation, a method that trains the model to match its own distribution conditioned on privileged feedback from a language model. Applied to Lean4 theorem-proving, Feedback Distillation maintains greater diversity in generated trajectories and achieves better pass@k scaling compared to GRPO, with the best results obtained by initializing GRPO with a Feedback Distillation checkpoint.
Post-training for reasoning models typically combines supervised fine-tuning with reinforcement learning from verifiable rewards, most commonly with GRPO. However, this algorithm suffers from sparse rewards, limited exploration, and mode collapse. Building upon recent works on self-distillation, we propose Feedback Distillation, a training method where the model is trained to match, at the token level, its own distribution conditioned on privileged feedback produced by a language model. Feedback Distillation offers token-level supervision and can inject external knowledge. Evaluating our method for Lean4 theorem-proving, we find that Feedback Distillation maintains greater diversity in generated trajectories than GRPO, yielding higher policy entropy and better pass@k scaling. The two methods are complementary: initializing GRPO from a Feedback Distillation checkpoint outperforms either method alone. All in all, our results suggest a promising avenue to improve post-training for complex reasoning.