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Jaehong Oh

χPreprint · 2025· Claims withdrawn

Ontology Neural Networks for Topologically Conditioned Constraint Satisfaction

Jaehong Oh

updated 213 words1 min read

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Historical 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 public experiment plan records intended methodology, not results; sibling result drafts remain private and unverified. The programme's central higher-order question later resolved to a scoped No-Go boundary. See the current ONN research status.

Overview

The manuscript described an enhanced ONN formulation aimed at failure modes in projecting learned states onto constraint manifolds. It combined Forman–Ricci curvature, Deep Delta Learning, and CMA-ES in a solver called LOGOS. Its reported outcomes were not reproduced by the later source audit.

Claims as originally presented

  • A reported topology-loss reduction from baseline 11.68 → 1.15.
  • A reported 95% success rate across constraint-satisfaction benchmarks, seed-independent across twenty random initialisations.
  • Claimed graceful scaling from 2 to 20 nodes.
  • A proposed full pipeline (Meta-LOGOS diagnostics, LOGOS solver, CMA-ES optimiser) intended for downstream ontology systems. This is not presented as a validated production capability.

Where it sits

Historically, this was positioned as a methodological bridge between the original ONN construction and the ONN + ORTSF framework paper. That bridge is not treated as validated without reproducible evidence for the withdrawn results.

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/},
}