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. Training preserves the type algebra by construction; inference is a constraint-projection onto a topology-aware manifold. The companion ORTSF (Ontological Real-Time State Feedback) framework turns the output of that inference into a closed-loop controller whose stability margins are stated in cohomological terms.
The programme begins with the observation that the topology of a representation space is itself a control-theoretic object. Once recognised, the usual separation between representation learning and controller synthesis dissolves: the same invariants that classify learned features also certify that the loop closed around them is stable under delay.
Three active threads
- Representational cohomology. How the invariants of a learned ontology appear as cohomology classes, and what that implies about generalisation. The formal scaffolding lives in An Axiomatic Framework for Understanding Relations via Gauge-Invariant Cohomology.
- Constraint projection and topological conditioning. A series of papers sharpening the projection step with Forman–Ricci curvature and Deep Delta Learning. See ONN for Topologically Conditioned Constraint Satisfaction and the empirical follow-up Advanced Topology-Preserving Neural Networks, which reaches 99.75 % of the theoretically predicted optimality.
- Lyapunov functions that fall out of the loss. The ONN total loss 𝓛_total turns out to be a constructive Lyapunov function — closing a sixty-year gap left open by Massera and Kurzweil. Treated in full in Constructive Lyapunov Functions via Topology-Preserving Neural Networks.
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 working implementation — benchmarks against transformer baselines, ablation studies, and the ORTSF gate library — is maintained privately and results are surfaced here as they are cleaned for public reading.