CW-CNN & CW-AN: Convolutional Networks and Attention Networks for CW-Complexes
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 a Hodge informed neural network that can receive a CW-complex as input. We illustrate and interpret this framework in the context of supervised prediction.
Submission Length: Regular submission (no more than 12 pages of main content)
Changes Since Last Submission: - We update the literature review in line with the suggestions from Reviewer HeyR.
- These changes are typeset in blue text and are contained to subsection 2.4. We include all updated citations and discussion of the methodologies of all articles mentioned by Reviewer HeyR.
- This round of changes includes a theoretical comparison and intuitive comparison with regard to point (1) raised by reviewer fyM9.
- Currently experiments are being expanded to encompass broader baselines
- This next round encompasses changes related to message passing comparisons suggested by reviewer fyM9.
Assigned Action Editor: ~Frederic_Sala1
Submission Number: 2964
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