Bridging Supervised Learning and Reinforcement Learning in Math
  Reasoning
Authors: name: Huayu Chen, name: Kaiwen Zheng, name: Qinsheng Zhang, name: Ganqu Cui, name: Yin Cui, name: Haotian Ye, name: Tsung-Yi Lin, name: Ming-Yu Liu, name: Jun Zhu, name: Haoxiang Wang

Reinforcement Learning (RL) has played a central role in the recent surge of
LLMs' math abilities by enabling self-improvement through binary verifier
signals. In contrast, Supervised Learning (SL) is rarely considered for such
verification-driven training, largely due to its heavy reliance on reference
answers and inability to reflect on mistakes. In this work, we challenge the
prevailing notion that self-improvement is exclusive to RL and propose
Negative-aware Fine-Tuning (NFT) -- a supervised approach that enables LLMs to
reflect on their failures and improve autonomously with no external teachers.
In online training, instead of throwing away self-generated negative answers,
NFT constructs an implicit negative policy to model them. This implicit policy
is parameterized with the same positive LLM we target to optimize on positive
data, enabling direct policy optimization on all LLMs' generations. We conduct
experiments on 7B and 32B models in math reasoning tasks. Results consistently
show that through the additional leverage of negative feedback, NFT
significantly improves over SL baselines like Rejection sampling Fine-Tuning,
matching or even surpassing leading RL algorithms like GRPO and DAPO.
Furthermore, we demonstrate that NFT and GRPO are actually equivalent in
strict-on-policy training, even though they originate from entirely different
theoretical foundations. Our experiments and theoretical findings bridge the
gap between SL and RL methods in binary-feedback learning systems.