Self-rewarding correction for mathematical reasoning
Authors: name: Wei Xiong, name: Hanning Zhang, name: Chenlu Ye, name: Lichang Chen, name: Nan Jiang, name: Tong Zhang

We study self-rewarding reasoning large language models (LLMs), which can
simultaneously generate step-by-step reasoning and evaluate the correctness of
their outputs during the inference time-without external feedback. This
integrated approach allows a single model to independently guide its reasoning
process, offering computational advantages for model deployment. We
particularly focus on the representative task of self-correction, where models
autonomously detect errors in their responses, revise outputs, and decide when
to terminate iterative refinement loops. To enable this, we propose a
two-staged algorithmic framework for constructing self-rewarding reasoning
models using only self-generated data. In the first stage, we employ sequential
rejection sampling to synthesize long chain-of-thought trajectories that
incorporate both self-rewarding and self-correction mechanisms. Fine-tuning
models on these curated data allows them to learn the patterns of
self-rewarding and self-correction. In the second stage, we further enhance the
models' ability to assess response accuracy and refine outputs through
reinforcement learning with rule-based signals. Experiments with Llama-3 and
Qwen-2.5 demonstrate that our approach surpasses intrinsic self-correction
capabilities and achieves performance comparable to systems that rely on
external reward models.