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 optimization-based 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 100x, and consistently corrects violations-establishing a preliminary foundation for optimization-based compliance applications.

翻译：金融法规日益复杂，阻碍了自动化合规进程，尤其是在最小化人工监督下保持逻辑一致性方面。本文提出一种神经符号合规框架，该框架将大型语言模型（LLM）与可满足性模理论（SMT）求解器相结合，以实现形式化可验证性与基于优化的合规修正。LLM负责解释法规条文及执法案例以生成SMT约束条件，而求解器则强制执行逻辑一致性，并在出现违规时计算恢复合法状态所需的最小事实修正量。与侧重透明度的传统方法不同，本方法强调逻辑驱动的优化机制，提供可验证且法律层面一致的形式化推理，而非事后解释性分析。基于台湾金融监督管理委员会（FSC）87个执法案例的评估显示，本系统在SMT代码生成方面达到86.2%的正确率，推理效率提升超100倍，并能持续修正违规行为，为基于优化的合规应用奠定了初步基础。