Ontology Neural Networks for Topologically Conditioned Constraint Satisfaction

TL;DR

This paper introduces an advanced neuro-symbolic reasoning framework that leverages topological graph features and novel optimization techniques to improve constraint satisfaction and semantic coherence in complex systems.

Contribution

It integrates topological conditioning with gradient stabilization, employing Forman-Ricci curvature, Deep Delta Learning, and CMA-ES for enhanced neuro-symbolic reasoning.

Findings

Achieves mean energy reduction to 1.15 from 11.68 baseline

95% success rate in constraint satisfaction tasks

Scales effectively up to twenty-node problems

Abstract

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.