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Jaehong Oh

χPreprint · 2025

Ontology Neural Networks for Topologically Conditioned Constraint Satisfaction

Jaehong Oh

200 words1 min read

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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 (CMA-ES) for parameter optimization. Experimental evaluation across multiple problem sizes demonstrates that the method achieves topology-loss reduction to 1.15 compared to baseline values of 11.68, with 95% 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.

Update (2026-07-10). This 2025 preprint is retained as a manuscript of record. Its reported results — topology-loss reduction 11.68 → 1.15 and a 95% constraint-satisfaction success rate for the LOGOS solver — are not reproducible from the current authoritative research source (onn_ws/ONN). The sibling benchmark drafts that assert these numbers are flagged as unverified (see the claim ledger), and the programme's central higher-order question later resolved to a scoped No-Go boundary. See the current ONN research status.

Overview

An enhanced ONN formulation targeting the specific failure modes that appeared when projecting learned states onto constraint manifolds in the original framework. The paper combines three ingredients — Forman–Ricci curvature, Deep Delta Learning, and CMA-ES — into a single solver called LOGOS.

What the paper shows

  • Topology-loss reduction from baseline 11.68 → 1.15.
  • 95% success rate across constraint-satisfaction benchmarks, seed-independent across twenty random initialisations.
  • Graceful scaling from 2 to 20 nodes.
  • Delivered as a full pipeline (Meta-LOGOS diagnostics, LOGOS solver, CMA-ES optimiser) that can be embedded in downstream ontology systems.

Where it sits

The methodological bridge between the original ONN construction and the ONN + ORTSF framework paper. It isolates and fixes the constraint-projection subsystem before it is composed with the delay-robust control layer.

BibTeX· generated

@misc{oh2025onn,
  title   = {Ontology Neural Networks for Topologically Conditioned Constraint Satisfaction},
  author  = {Jaehong Oh},
  year    = {2025},
  url     = {https://jack0682.github.io/papers/onn-constraint-satisfaction/},
}