Yen-Ting Lin, Di Jin, Tengyu Xu, Tianhao Wu, Sainbayar Sukhbaatar, Chen Zhu, Yun He, Yun-Nung Chen, Jason Weston, Yuandong Tian, Arash Rahnama, Sinong Wang, Hao Ma, Han Fang

Step-KTO: Optimizing Mathematical Reasoning through Stepwise Binary Feedback

http://arxiv.org/abs/2501.10799v1

Large language models (LLMs) have recently demonstrated remarkable success in mathematical reasoning. Despite progress in methods like chain-of-thought prompting and self-consistency sampling, these advances often focus on final correctness without ensuring that the underlying reasoning process is coherent and reliable. This paper introduces Step-KTO, a training framework that combines process-level and outcome-level binary feedback to guide LLMs toward more trustworthy reasoning trajectories. By providing binary evaluations for both the intermediate reasoning steps and the final answer, Step-KTO encourages the model to adhere to logical progressions rather than relying on superficial shortcuts. Our experiments on challenging mathematical benchmarks show that Step-KTO significantly improves both final answer accuracy and the quality of intermediate reasoning steps. For example, on the MATH-500 dataset, Step-KTO achieves a notable improvement in Pass@1 accuracy over strong baselines. These results highlight the promise of integrating stepwise process feedback into LLM training, paving the way toward more interpretable and dependable reasoning capabilities.