Exécution de notre outil de synthèse sur un nouvel article

Résumé : Despite the remarkable advancements of Large Language Models (LLMs), their application in the mathematical domain is frequently hindered by “hallucinations,” characterized by logical inconsistencies, numerical fabrication, and the inability to handle under-constrained problems. This paper presents a robust mathematical reasoning framework that integrates Retrieval-Augmented Generation (RAG) with a symbolic verification engine to mitigate these issues. Our system addresses the limitations of purely probabilistic generation by implementing a proximity-based filtering mechanism and Maximal Marginal Relevance (MMR) reranking, ensuring high-fidelity knowledge retrieval. The core of our approach lies in a “Step-tree” reasoning architecture, where natural language derivations are structurally decomposed and cross-verified against a SymPy-driven symbolic engine. We introduce a recursive back-filling verification mechanism that ensures consistency between linguistic steps and deterministic computational results. Furthermore, a robust rejection gate is implemented to detect and refuse under-constrained queries, preventing the model from improvising non-existent conditions. Experimental evaluations were conducted on a curated dataset of 300 problems across primary, junior, and senior high school levels. The results demonstrate that the proposed system significantly outperforms vanilla LLM baselines, achieving a substantial reduction in the Hallucination Rate (HR) for insufficient queries. This research provides a verifiable and interpretable pathway for deploying large language models in high-precision educational and scientific applications.