Consistency-Constrained Self-Refinement for Multi-Step Mathematical Reasoning in Large Language Models
DOI:
https://doi.org/10.66238/ijrss.v6i2.135Keywords:
Large Language Models, Mathematical Reasoning, Self-Refinement, Consistency ConstraintsAbstract
Large language models have demonstrated remarkable capabilities in natural language understanding and generation, yet their performance on complex, multi-step mathematical reasoning remains sub-optimal due to compounding errors and logical inconsistencies. This paper introduces a novel framework, Consistency-Constrained Self-Refinement, designed to enhance the mathematical problem-solving proficiency of language models. By integrating an iterative self-correction mechanism grounded in strict mathematical consistency constraints, the proposed architecture significantly reduces intermediate reasoning deviations. We formalize the verification process using algebraic invariants and logical consistency checks, ensuring that each generated reasoning step adheres to global constraints before proceeding to the subsequent state. Comprehensive experiments conducted on standardized mathematical reasoning benchmarks reveal substantial improvements in both accuracy and reasoning robustness compared to traditional chain-of-thought prompting and unconstrained self-reflection methods. The findings underscore the critical role of hard constraints in guiding the self-refinement trajectory of autoregressive language models. This research contributes to the broader objective of developing reliable, interpretable, and mathematically sound artificial intelligence systems capable of autonomous logical deduction.
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