# Topological Deep Learning

arXiv: https://arxiv.org/abs/2101.05778 · HTML: https://mlsanity.com/paper/2101.05778/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 30 references that are in the map.
- First posted on arXiv 14 Jan 2021.

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

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Quo Vadis, Action Recognition? A New Model and the Kinetics Dataset](https://mlsanity.com/paper/1705.07750/) (2017)
- [Learning Spatio-Temporal Representation with Local and Global Diffusion](https://mlsanity.com/paper/1906.05571/) (2019)
- [Topological Approaches to Deep Learning](https://mlsanity.com/paper/1811.01122/) (2018)
- [Robust Topological Inference: Distance To a Measure and Kernel Distance](https://mlsanity.com/paper/1412.7197/) (2014)

## Built on by (most cited first, 6 of 6)

- [Position: Topological Deep Learning is the New Frontier for Relational Learning](https://mlsanity.com/paper/2402.08871/) (2024)
- [Dist2Cycle: A Simplicial Neural Network for Homology Localization](https://mlsanity.com/paper/2110.15182/) (2021)
- [Topology-Aware Focal Loss for 3D Image Segmentation](https://mlsanity.com/paper/2304.12223/) (2023)
- [A Random Persistence Diagram Generator](https://mlsanity.com/paper/2104.07737/) (2021)
- [A Topological Deep Learning Framework for Neural Spike Decoding](https://mlsanity.com/paper/2212.05037/) (2022)
- [Topological structure of complex predictions](https://mlsanity.com/paper/2207.14358/) (2022)

## Abstract (arXiv)

This work introduces the Topological CNN (TCNN), which encompasses several topologically defined convolutional methods. Manifolds with important relationships to the natural image space are used to parameterize image filters which are used as convolutional weights in a TCNN. These manifolds also parameterize slices in layers of a TCNN across which the weights are localized. We show evidence that TCNNs learn faster, on less data, with fewer learned parameters, and with greater generalizability and interpretability than conventional CNNs. We introduce and explore TCNN layers for both image and video data. We propose extensions to 3D images and 3D video.