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.

翻译：神经符号推理系统在满足物理和逻辑约束的同时保持语义一致性面临根本性挑战。基于我们先前在本体神经网络上的研究工作，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在约束投影过程中实现稳定的秩一扰动，并通过协方差矩阵自适应进化策略进行参数优化。跨多个问题规模的实验评估表明，相较于基线值11.68，该方法将平均能量降低至1.15，在约束满足任务中达到95%的成功率。该框架展现出与随机种子无关的收敛特性，并在多达二十节点的问题规模上保持优雅的扩展行为，表明拓扑结构能够在保持可解释性与计算效率的前提下，为基于梯度的优化提供有效信息。