Ontology Neural Networks

An Ontology Neural Network (ONN) is a neural model whose internal state is not a flat vector but a typed object carrying the structure of a target ontology: inference is a constraint-projection onto a topology-aware manifold. The companion ORTSF (Ontological Real-Time Semantic Fabric) framework turns the output of that inference into a closed-loop controller.

The programme's organising bet was that the topology of a representation space is itself a control-theoretic object — that the same higher-order/cohomological invariants which classify learned features would also certify the loop closed around them. That bet was put under a formal audit, and it did not survive in its strong form.

What survived the audit#

• A modest, non-higher-order positive. One signal held up under the audit: a small direction-channel effect (a Q-weak improvement of roughly +0.11–0.12 AUROC). It does not come from higher-order structure — it is the honest positive result of the programme.
• A scoped scalar control result. For the implemented recurrence $e[t+1] = \rho e[t] - K_c e[t-d]$ in one $H^\perp$ mode, $\rho + |K_c| < 1$ is sufficient for Schur stability for every integer delay $d \geq 1$ — decoupled from the ontology's cohomology. Coupled multimode dynamics, the $B$-operator bound, and PD-gain mapping remain open. See the certificate.
• The audit methodology. The pre-registered contract, the consistent/complete/finite scene conditions, and the falsification discipline that turned an appealing thesis into a checkable boundary.

Earlier manuscripts (superseded framing)#

These 2025 drafts state the original optimistic framing. Their headline empirical numbers (e.g. "99.75 % of predicted optimality", a constructive-Lyapunov "60-year gap" closure) are not reproducible from the current research source and are superseded by the audit above; they are retained as manuscripts of record with a status banner on each page.

• ONN for Topologically Conditioned Constraint Satisfaction — the Forman–Ricci / Deep-Delta projection line.
• Advanced Topology-Preserving Neural Networks — the empirical-optimality follow-up.
• Constructive Lyapunov Functions via Topology-Preserving Neural Networks — the Lyapunov-from-loss claim.
• An Axiomatic Framework for Understanding Relations via Gauge-Invariant Cohomology — the formal cohomology scaffolding.

Papers on this track#

• Ontology Neural Network and ORTSF — Int. J. Topol., accepted April 2026
• Ontology Neural Networks for Topologically Conditioned Constraint Satisfaction
• Advanced Topology-Preserving Neural Networks
• Constructive Lyapunov Functions via Topology-Preserving Neural Networks
• An Axiomatic Framework for Understanding Relations via Gauge-Invariant Cohomology

The archived working implementation included benchmarks against transformer baselines, ablation studies, and the ORTSF gate library. Audited results that survived are preserved here; active development now belongs to ULR.