CW-CNN & CW-AN: Convolutional Networks and Attention Networks for CW-Complexes
This addresses a gap in cheminformatics by enabling learning on CW-complex representations, though it appears incremental as it adapts existing neural network concepts to a new structure.
The paper tackled the lack of machine learning methods for CW-complex structured data by developing convolution and attention operations for CW-complexes, resulting in the first Hodge-informed neural network that can process CW-complex inputs.
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.