# Ontology Neural Networks for Topologically Conditioned Constraint Satisfaction

arXiv: https://arxiv.org/abs/2601.05304 · HTML: https://mlsanity.com/paper/2601.05304/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 12 of its 24 references that are in the map.
- First posted on arXiv 8 Jan 2026.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 12 of 12)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Neural Architecture Search with Reinforcement Learning](https://mlsanity.com/paper/1611.01578/) (2016)
- [Knowledge Graphs](https://mlsanity.com/paper/2003.02320/) (2020)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Scene Graph Generation by Iterative Message Passing](https://mlsanity.com/paper/1701.02426/) (2017)
- [Neurosymbolic AI: The 3rd Wave](https://mlsanity.com/paper/2012.05876/) (2020)
- [Ricci Curvature of the Internet Topology](https://mlsanity.com/paper/1501.04138/) (2015)
- [Deep Delta Learning](https://mlsanity.com/paper/2601.00417/) (2026)
- [Ontology Neural Network and ORTSF: A Framework for Topological Reasoning and Delay-Robust Control](https://mlsanity.com/paper/2506.19277/) (2025)

## Abstract (arXiv)

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 for parameter optimization. Experimental evaluation across multiple problem sizes demonstrates that the method achieves mean energy reduction to 1.15 compared to baseline values of 11.68, with 95 percent 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.