Ontology Neural Networks for Topologically Conditioned Constraint Satisfaction
This work addresses constraint satisfaction problems in neuro-symbolic AI, presenting an incremental enhancement to existing Ontology Neural Networks.
The paper tackles the challenge of maintaining semantic coherence while satisfying constraints in neuro-symbolic reasoning systems, achieving a mean energy reduction to 1.15 compared to baseline values of 11.68 with a 95% success rate in constraint satisfaction tasks.
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.