# Dimensionality reduction and width of deep neural networks based on topological degree theory

arXiv: https://arxiv.org/abs/2511.06821 · HTML: https://mlsanity.com/paper/2511.06821/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 11 references that are in the map.
- First posted on arXiv 10 Nov 2025.

## Builds on (most cited first, 3 of 3)

- [Approximating Continuous Functions by ReLU Nets of Minimal Width](https://mlsanity.com/paper/1710.11278/) (2017)
- [Architectures of Topological Deep Learning: A Survey of Message-Passing Topological Neural Networks](https://mlsanity.com/paper/2304.10031/) (2023)
- [Autoencoding topology](https://mlsanity.com/paper/1803.00156/) (2018)

## Abstract (arXiv)

In this paper we present a mathematical framework on linking of embeddings of compact topological spaces into Euclidean spaces and separability of linked embeddings under a specific class of dimension reduction maps. As applications of the established theory, we provide some fascinating insights into classification and approximation problems in deep learning theory in the setting of deep neural networks.