用拓扑结构增强神经符号系统，高效求解约束问题
Ontology Neural Networks for Topologically Conditioned Constraint Satisfaction
- 引入费尔曼-里奇曲率刻画图拓扑，结合梯度稳定机制
- 平均能量降至1.15，约束满足成功率95%，优于基线11.68
- 适合需要可解释性与高鲁棒性的复杂约束求解场景
神经符号推理系统在保持语义一致性和满足物理及逻辑约束方面面临根本挑战。基于我们先前提出的本体神经网络工作，本文提出一种增强框架，将拓扑条件与梯度稳定机制相结合。该方法采用Forman-Ricci曲率捕捉图拓扑结构，利用Deep Delta Learning实现约束投影中的稳定秩一扰动，并通过Covariance Matrix Adaptation Evolution Strategy进行参数优化。在多个问题规模下的实验评估表明，该方法平均能量降至1.15，显著优于基线值11.68，约束满足任务成功率高达95%。框架表现出种子无关的收敛性与高达二十节点问题的平滑扩展能力，表明拓扑结构可在不牺牲可解释性或计算效率的前提下指导基于梯度的优化。
原文摘要 · Abstract (English)
Neuro-symbolic reasoning systems face fundamental challenges in maintaining semantic coherence while satisfying physical and logical constraints. Building upon our previous work on Ontology Neural Networks, we present an enhanced framework that integrates topological conditioning with gradient stabilization mechanisms. The approach employs Forman-Ricci curvature to capture graph topology, Deep Delta Learning for stable rank-one perturbations during constraint projection, and Covariance Matrix Adaptation Evolution Strategy for parameter optimization. Experimental evaluation across multiple problem sizes demonstrates that the method achieves mean energy reduction to 1.15 compared to baseline values of 11.68, with 95 percent success rate in constraint satisfaction tasks. The framework exhibits seed-independent convergence and graceful scaling behavior up to twenty-node problems, suggesting that topological structure can inform gradient-based optimization without sacrificing interpretability or computational efficiency.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。