AMTFV Enhances LLM Mathematical Self-Correction with Tool-Flow Verification

Large language models (LLMs) have demonstrated impressive mathematical problem-solving abilities, but reliably verifying their answers remains a significant challenge. Existing methods often rely on natural-language reflection, which may lack computational precision, or directly generate verification programs, which prematurely couples mathematical modeling with low-level implementation details. AMTFV (Agentic Mathematical Tool-Flow Verification) addresses these limitations by introducing a Mathematical Tool Flow (MTF) as an interrupt-execute-resume interface. This decouples the verification modeling process from concrete execution, allowing for exact computation through a specialized mathematical toolbox. The verification agent constructs a workflow, encodes mathematical objects and computational intent into an MTF request, and sends it to a mathematical toolbox agent. This toolbox parses the request, generates executable calls, and dispatches them for exact computation. The precise tool outputs then facilitate candidate-answer adjudication, answer revision, and even verification-workflow revision, leading to significant accuracy improvements on challenging mathematical reasoning datasets across various LLM configurations.