Faithful Self-Refinement in Mathematical Reasoning via Progressive Back-Translation

Large language models (LLMs) can achieve superior results through iterative refinement based on internal or external signals, compared to the unstable outputs from a single pass. However, the reliability of existing internal signals is questionable due to their susceptibility to intrinsic hallucinations, while external signals are only useful in limited scenarios. In this paper, we introduce a novel framework called Progressive Back-Translation refinement (PBT). Specifically, PBT prompts LLMs to extract and reconstruct the question from the answer, avoiding unreliable inferences, critiques, or judgments on intermediate results. We then derive and provide accurate, fine-grained feedback by identifying discrepancies between the back-translated and original questions. Experiments across various large language models and challenging mathematical datasets demonstrate consistent improvements. We also provide a detailed analysis to confirm the effectiveness of the proposed method.