# Homotopy Theoretic and Categorical Models of Neural Information Networks

arXiv: https://arxiv.org/abs/2006.15136 · HTML: https://mlsanity.com/paper/2006.15136/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jun 2020.

## Built on by (most cited first, 4 of 4)

- [Quiver neural networks](https://mlsanity.com/paper/2207.12773/) (2022)
- [Betti numbers of attention graphs is all you really need](https://mlsanity.com/paper/2207.01903/) (2022)
- [Higher Gauge Flow Models](https://mlsanity.com/paper/2507.16334/) (2025)
- [A homotopy-type-theoretic generalization of neurosymbolic inference](https://mlsanity.com/paper/2606.17851/) (2026)

## Abstract (arXiv)

In this paper we develop a novel mathematical formalism for the modeling of neural information networks endowed with additional structure in the form of assignments of resources, either computational or metabolic or informational. The starting point for this construction is the notion of summing functors and of Segal's Gamma-spaces in homotopy theory. The main results in this paper include functorial assignments of concurrent/distributed computing architectures and associated binary codes to networks and their subsystems, a categorical form of the Hopfield network dynamics, which recovers the usual Hopfield equations when applied to a suitable category of weighted codes, a functorial assignment to networks of corresponding information structures and information cohomology, and a cohomological version of integrated information.