# Topological Data Analysis of Neural Network Layer Representations

arXiv: https://arxiv.org/abs/2208.06438 · HTML: https://mlsanity.com/paper/2208.06438/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 6 references that are in the map.
- First posted on arXiv 1 Jul 2022.

## Builds on (most cited first, 1 of 1)

- [Can neural networks learn persistent homology features?](https://mlsanity.com/paper/2011.14688/) (2020)

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

- [On the geometry and topology of representations: the manifolds of modular addition](https://mlsanity.com/paper/2512.25060/) (2025)

## Abstract (arXiv)

This paper is a cursory study on how topological features are preserved within the internal representations of neural network layers. Using techniques from topological data analysis, namely persistent homology, the topological features of a simple feedforward neural network's layer representations of a modified torus with a Klein bottle-like twist were computed. The network appeared to approximate homeomorphisms in early layers, before significantly changing the topology of the data in deeper layers. The resulting noise hampered the ability of persistent homology to compute these features, however similar topological features seemed to persist longer in a network with a bijective activation function.