KG -augmented executable CoT for mathematical coding.

In recent years, large language models (LLMs) have excelled in natural language processing tasks, but face significant challenges in complex reasoning tasks such as mathematical reasoning and code generation. To address these limitations, we introduce the Neuro-Symbolic paradigm into the field of mathematical reasoning and propose KGA-ECoT, a Knowledge Graph Augmented Executable Chain-of-Thought, which decomposes problems into a structured task graph, incorporates an adaptive on-demand GraphRAG mechanism for precise knowledge retrieval from Symbolic reasoning libraries, and generates verifiable code to ensure computational accuracy. This not only improves performance but also enhances the model's interpretability and verifiability, reducing its "black-box" nature. Evaluations on multiple mathematical reasoning benchmarks demonstrate that KGA-ECoT significantly outperforms existing prompting methods, achieving absolute accuracy improvements ranging from several to over ten percentage points. Further analysis confirms the critical roles of GraphRAG and external code execution, validating the efficacy of the Neuro-Symbolic paradigm for complex reasoning. Comprehensive implementation details and full prompt templates are provided in the appendix to ensure reproducibility.