{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/cw-cnn-cw-an-convolutional-networks-and","title":"CW-CNN & CW-AN: Convolutional Networks and Attention Networks for CW-Complexes","arxiv_id":"2408.16686","date":"2024-08-29","proceeding":null,"authors":["Rahul Khorana"],"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.","url_abs":"https://arxiv.org/abs/2408.16686v2","url_pdf":"https://arxiv.org/pdf/2408.16686v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[],"tasks":[{"task_slug":"prediction","task_name":"Prediction"}],"methods":[{"method_slug":"attention","method_name":"Attention"},{"method_slug":"cw-cnn-cw-at","method_name":"CW-CNN & CW-AT"},{"method_slug":"convolution","method_name":"Convolution"},{"method_slug":"softmax","method_name":"Softmax"}],"datasets_introduced":[],"methods_introduced":[{"slug":"cw-cnn-cw-at","name":"CW-CNN & CW-AT","full_name":"CW-Complex Attention Mechanism"}],"results":[{"leaderboard":"/sota/prediction-on-synthetic","task":"Prediction","dataset":"Synthetic","model":"CW-AT","rank_in_archive_order":1,"of":2,"metrics":{"RMSE":"0.025331"},"uses_additional_data":false},{"leaderboard":"/sota/prediction-on-synthetic","task":"Prediction","dataset":"Synthetic","model":"CW-CNN","rank_in_archive_order":2,"of":2,"metrics":{"RMSE":"1.148775"},"uses_additional_data":false}],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}