Neuro-Symbolic Energy-Based Framework Using Weighted Partial MaxSAT for Smart Contract Optimization and Digital Financial Risk Management

Abstract
This paper introduces WPMAXSAT-HNN, a novel neuro-symbolic energy-based framework for optimizing smart contract efficiency and security in blockchain-based financial systems. The framework establishes a precise mathematical mapping from Weighted Partial Maximum Satisfiability (WPMaxSAT) formulations to Hopfield Neural Network (HNN) configurations, enabling simultaneous formal verification and gradient-based optimization. By distinguishing between hard constraints (essential contract semantics) and soft constraints (optimization objectives such as gas cost reduction), the method provides a unified approach for constraint satisfaction and performance enhancement. Experimental validation across 127 production smart contracts, including Automated Market Makers, Lending Protocols, Derivatives, Insurance, Payment Channels, Token Systems, and Governance, demonstrates significant and consistent advantages over existing MAXSAT-HNN and RANMAXSAT-HNN approaches. The proposed framework achieves an average of 18.0% ± 2.9% gas savings while maintaining a 99.0% ± 0.6% satisfaction rate for hard constraints and a 2.04× computational speedup. The model’s efficiency is reflected in the best aggregate Bayesian Information Criterion (-200.5) and the highest F1-Score (0.958 ± 0.014). Performance is particularly strong for Payment Channels (24.8% ± 2.1% gas savings, F1-Score 0.981) and Token Contracts (19.3% ± 2.5% savings, 2.32× speedup). Real-world Ethereum testnet deployments confirm its practical impact, with an average return on investment of 3,744 gas saved per second across major protocols such as Uniswap, Compound, and high-throughput payment networks. The neuro-symbolic architecture effectively integrates exact symbolic reasoning with approximate neural optimization, addressing critical challenges in FinTech: reducing transaction costs, enhancing security through formal verification, and mitigating operational and compliance risks. By combining optimization with provable correctness, WPMAXSAT-HNN offers a foundational technology for the next generation of efficient, secure, and scalable decentralized financial applications.