Papers › CW-CNN & CW-AN: Convolutional Networks and Attention Networks for CW-Complexes
CW-CNN & CW-AN: Convolutional Networks and Attention Networks for CW-Complexes
Rahul Khorana
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.
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Tasks
Results from the paper archive 2025-07-28
| Task | Dataset | Model | Metric | Value | Rank at snapshot | Leaderboard | Report |
|---|---|---|---|---|---|---|---|
| Prediction | Synthetic | CW-AT | RMSE | 0.025331 | #1 of 2 | Archive leaderboard | report |
| Prediction | Synthetic | CW-CNN | RMSE | 1.148775 | #2 of 2 | Archive leaderboard | report |
Ranks are positions in the archive's leaderboards as they stood at the 2025-07-28 snapshot. Results published since then are not among these rows, so a rank here is not a current standing.
Methods
Introduced by this paper: CW-CNN & CW-AT
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