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

Rahul Khorana

2024-08-29Prediction

Abstract

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.

Results

Task	Dataset	Metric	Value	Model
Prediction	Synthetic	RMSE	0.025331	CW-AT
Prediction	Synthetic	RMSE	1.148775	CW-CNN

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