Achieving Multi-Hop Calculation and Safe Abstention in Financial Numerical Reasoning by Metric Graph Constrained LLMs

Financial numerical reasoning demands rigorous adherence to domain-specific logic and precise evidence foundation. However, large language models (LLMs) are prone to forced generation when confronting ambiguous evidence or complex recursive dependencies, often hallucinating values to bridge information gaps. To address this, we propose graph-bounded financial reasoning (GBFR), a neuro-symbolic framework that imposes semantic and structural constraints via a financial metric knowledge graph (FMKG). Unlike sequential generation paradigms, our approach employs a parallel graph-constrained reasoning algorithm that orchestrates specialized operators to simultaneously explore heterogeneous derivation paths of complex financial metrics. Through cross-path verification, the framework aggregates only semantically consistent results, ensuring reasoning is bounded by available context. Crucially, this approach enables safe abstention by distinguishing genuine data absence from retrieval failure, thereby preventing ungrounded fabrication. To evaluate this capability, we further construct counterfactual samples by perturbing entities, times, and metrics to synthesize unanswerable scenarios. Empirical evaluations on standard benchmarks demonstrate that GBFR significantly outperforms state-of-the-art baselines.