Neuro-Symbolic Compliance: Integrating LLMs and SMT Solvers for Automated Financial Legal Analysis

Financial regulations are increasingly complex, hindering automated compliance-especially the maintenance of logical consistency with minimal human oversight. We introduce a Neuro-Symbolic Compliance Framework that integrates Large Language Models (LLMs) with Satisfiability Modulo Theories (SMT) solvers to enable formal verifiability and optimizationbased compliance correction. The LLM interprets statutes and enforcement cases to generate SMT constraints, while the solver enforces consistency and computes the minimal factual modification required to restore legality when penalties arise. Unlike transparency-oriented methods, our approach emphasizes logic-driven optimization, delivering verifiable, legally consistent reasoning rather than post-hoc explanation. Evaluated on 87 enforcement cases from Taiwan's Financial Supervisory Commission (FSC), the system attains 86.2 % correctness in SMT code generation, improves reasoning efficiency by over $100 \times$, and consistently corrects violations-establishing a preliminary foundation for optimization-based compliance applications.