Step-KTO: Optimizing Mathematical Reasoning through Stepwise Binary Feedback (2501.10799v1)

Abstract: 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.

Exploring the Step-KTO Framework for Mathematical Reasoning with LLMs

The paper entitled "Step-KTO: Optimizing Mathematical Reasoning through Stepwise Binary Feedback" introduces a novel framework designed to enhance mathematical reasoning in LLMs. The research addresses the limitations of current methods that focus on final correctness, often neglecting the coherence and reliability of the reasoning process. The presented framework, Step-KTO, integrates both process-level and outcome-level binary feedback, promoting adherence to logical progressions rather than reliance on superficial shortcuts.

Overview and Methodology

The Step-KTO framework builds upon existing LLM prompting strategies, such as chain-of-thought prompting and self-consistency sampling, but distinguishes itself by emphasizing logical coherence in reasoning trajectories. At its core, Step-KTO evaluates both intermediate reasoning steps and the final answer using binary feedback systems called the Process Reward Model (PRM) and the Outcome Reward Model (ORM), respectively. This dual feedback system is integrated into a unified training objective utilizing a Kahneman-Tversky-inspired value function, which reflects human-like risk aversion to guide the model toward error correction.

The training process involves multiple iterative refinement phases, during which the model generates potential solutions to mathematical problems. Each candidate solution is assessed using both the PRM and ORM, providing a composite feedback that aids in fine-tuning the LLM's reasoning capabilities. By this iterative method, the model progressively improves not only in final accuracy but also in maintaining logical consistency during problem-solving.

Experimental Evaluation and Results

The authors conduct extensive experiments using challenging mathematical benchmarks, including the MATH-500 dataset, AMC23, and AIME24. The Step-KTO framework yields significant improvements in Pass@1 accuracy over strong baselines. For instance, on the MATH-500 dataset, Step-KTO improves Pass@1 accuracy from 53.4% to 63.2%. These strong numerical results demonstrate the framework's effectiveness in enhancing both the accuracy of final answers and the interpretability of intermediate reasoning steps.

Implications and Future Directions

The implications of integrating stepwise process feedback as demonstrated by Step-KTO are multifaceted. Practically, this framework promises enhanced trustworthiness of LLMs when applied in high-stakes domains requiring rigorous reasoning, such as mathematics or scientific problem solving. Theoretically, Step-KTO advances the understanding of how complex reasoning processes can be scaffolded in machine learning models, aligning more closely with structured human thought processes.

Looking forward, this work paves the way for further developments in AI, particularly in enhancing the interpretability and reliability of model outputs. Future research might delve into broader applications of the Step-KTO framework, testing its effectiveness across varying types of reasoning tasks, or integrating it with other advanced model training methodologies to explore synergistic effects.

In conclusion, the Step-KTO framework presents a significant methodological advancement in optimizing mathematical reasoning within LLMs. By harmonizing process and outcome evaluations, it propels LLM training towards producing consistently accurate and logically sound reasoning outputs.