# CW-CNN & CW-AN: Convolutional Networks and Attention Networks for CW-Complexes

arXiv: https://arxiv.org/abs/2408.16686 · HTML: https://mlsanity.com/paper/2408.16686/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 20 references that are in the map.
- First posted on arXiv 29 Aug 2024.

## Builds on (most cited first, 15 of 15)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [How Attentive are Graph Attention Networks?](https://mlsanity.com/paper/2105.14491/) (2021)
- [An Introduction to Convolutional Neural Networks](https://mlsanity.com/paper/1511.08458/) (2015)
- [Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networks](https://mlsanity.com/paper/2103.03212/) (2021)
- [Inverse design of 3d molecular structures with conditional generative neural networks](https://mlsanity.com/paper/2109.04824/) (2021)
- [Cell Complex Neural Networks](https://mlsanity.com/paper/2010.00743/) (2020)
- [Structure-based drug design with geometric deep learning](https://mlsanity.com/paper/2210.11250/) (2022)
- [Cell Attention Networks](https://mlsanity.com/paper/2209.08179/) (2022)
- [Gaussian Processes on Cellular Complexes](https://mlsanity.com/paper/2311.01198/) (2023)
- [Topological Signal Processing over Generalized Cell Complexes](https://mlsanity.com/paper/2201.08993/) (2022)
- [3D-Mol: A Novel Contrastive Learning Framework for Molecular Property Prediction with 3D Information](https://mlsanity.com/paper/2309.17366/) (2023)

## Abstract (arXiv)

We present a novel framework for learning on CW-complex structured data points. Recent advances have discussed CW-complexes as ideal learning representations for problems in cheminformatics. However, there is a lack of available machine learning methods suitable for learning on CW-complexes. In this paper we develop notions of convolution and attention that are well defined for CW-complexes. These notions enable us to create the first Hodge informed neural network that can receive a CW-complex as input. We illustrate and interpret this framework in the context of supervised prediction.