# Ontology Neural Network and ORTSF: A Framework for Topological Reasoning and Delay-Robust Control

arXiv: https://arxiv.org/abs/2506.19277 · HTML: https://mlsanity.com/paper/2506.19277/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Spatial and embodied reasoning, one of 17 directions in LLM reasoning.
- Builds on 5 of its 48 references that are in the map.
- First posted on arXiv 24 Jun 2025.

## Placed in

- LLM reasoning / [Spatial and embodied reasoning](https://mlsanity.com/lr/spatial-and-embodied-reasoning/)

## Builds on (most cited first, 5 of 5)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Gated Graph Sequence Neural Networks](https://mlsanity.com/paper/1511.05493/) (2015)
- [An introduction to Topological Data Analysis: fundamental and practical aspects for data scientists](https://mlsanity.com/paper/1710.04019/) (2017)

## Built on by (most cited first, 1 of 1)

- [Ontology Neural Networks for Topologically Conditioned Constraint Satisfaction](https://mlsanity.com/paper/2601.05304/) (2026)

## Abstract (arXiv)

The advancement of autonomous robotic systems has led to impressive capabilities in perception, localization, mapping, and control. Yet, a fundamental gap remains: existing frameworks excel at geometric reasoning and dynamic stability but fall short in representing and preserving relational semantics, contextual reasoning, and cognitive transparency essential for collaboration in dynamic, human-centric environments. This paper introduces a unified architecture comprising the Ontology Neural Network (ONN) and the Ontological Real-Time Semantic Fabric (ORTSF) to address this gap. The ONN formalizes relational semantic reasoning as a dynamic topological process. By embedding Forman-Ricci curvature, persistent homology, and semantic tensor structures within a unified loss formulation, ONN ensures that relational integrity and topological coherence are preserved as scenes evolve over time. The ORTSF transforms reasoning traces into actionable control commands while compensating for system delays. It integrates predictive and delay-aware operators that ensure phase margin preservation and continuity of control signals, even under significant latency conditions. Empirical studies demonstrate the ONN + ORTSF framework's ability to unify semantic cognition and robust control, providing a mathematically principled and practically viable solution for cognitive robotics.