Agent-Guided Process Verification for Mathematical Self-Correction

Large language models have made substantial progress in mathematical reasoning, yet in complex multi-step reasoning, an error at any step may propagate along an incorrect path, and the resulting solution may omit necessary branches. Existing natural-language reflection methods often struggle to locate critical errors precisely, while outcome verification typically checks only whether the available candidate answers satisfy the problem conditions and can therefore overlook necessary branches. To address these limitations, we propose Agent-Guided Process Verification (AGPV) for mathematical self-correction. AGPV decomposes the current solution into an ordered sequence of key claims, verifies them individually while invoking a shared mathematical toolbox when needed, and stops upon detecting the first error. A summarization agent converts the failure evidence into a diagnosis that guides a correction agent to re-derive the subsequent solution from that point; AGPV then adapts the next verification iteration to the revised solution. AGPV also verifies solution completeness. We further prove that AGPV guarantees solution correctness and completeness when key claims provide sufficient coverage and local verification is reliable, provided that all key claims pass verification. The implementation compresses long working contexts and reuses successful tool results within each problem. We evaluate AGPV on five challenging mathematical reasoning datasets with four models from DeepSeek, Qwen, and GPT. AGPV achieves an average accuracy of 63.8%, outperforming the strongest among the representative baselines evaluated (50.3%) by 13.5 percentage points, with higher repair coverage than the programmatic-verification baselines.