Critique-Guided Distillation for Efficient and Robust Language Model Reasoning

Supervised fine-tuning (SFT) with expert demonstrations often suffers from the imitation problem, where models reproduce correct responses without internalizing the underlying reasoning. We propose Critique-Guided Distillation (CGD), a multi-stage training framework that augments SFT with teacher-generated explanatory critiques and refined responses. Instead of directly imitating teacher outputs, a student learns to map the triplet of prompt, its own initial response, and teacher critique into the refined teacher response, thereby capturing both what to output and why. Our analyses show that CGD consistently reduces refinement uncertainty, improves alignment between critiques and responses, and enhances sample efficiency. On reasoning benchmarks, CGD achieves substantial gains across LLaMA and Qwen families, including +15.0% on AMC23 and +12.2% on MATH-500, while avoiding the format drift issues observed in prior critique-based fine-tuning. Importantly, on LLaMA-3.1-8B CGD approaches or exceeds the performance of SimpleRL-Zero, which is a DeepSeek-R1 replication, while requiring 60x less compute. Beyond reasoning, CGD maintains or improves general instruction-following and factual accuracy, matching baseline performance on IFEval, MUSR, TruthfulQA, and BBH. In contrast, prior critique-based methods degrade these capabilities (e.g., -21% on IFEval). Taken together, these results establish CGD} as a robust and generalizable alternative to both conventional SFT and RL-based methods, offering a more efficient path toward advancing the reasoning and safety of large language models.