{"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/a-law-of-data-separation-in-deep-learning","title":"A Law of Data Separation in Deep Learning","arxiv_id":"2210.17020","date":"2022-10-31","proceeding":null,"authors":["Hangfeng He","Weijie J. Su"],"abstract":"While deep learning has enabled significant advances in many areas of science, its black-box nature hinders architecture design for future artificial intelligence applications and interpretation for high-stakes decision makings. We addressed this issue by studying the fundamental question of how deep neural networks process data in the intermediate layers. Our finding is a simple and quantitative law that governs how deep neural networks separate data according to class membership throughout all layers for classification. This law shows that each layer improves data separation at a constant geometric rate, and its emergence is observed in a collection of network architectures and datasets during training. This law offers practical guidelines for designing architectures, improving model robustness and out-of-sample performance, as well as interpreting the predictions.","url_abs":"https://arxiv.org/abs/2210.17020v2","url_pdf":"https://arxiv.org/pdf/2210.17020v2.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":[{"paper_slug":"a-law-of-data-separation-in-deep-learning","repo_url":"https://github.com/dadacheng/re-equi-sepa","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}},{"paper_slug":"a-law-of-data-separation-in-deep-learning","repo_url":"https://github.com/hornhehhf/equi-separation","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[{"task_slug":"deep-learning","task_name":"Deep Learning"}],"methods":[{"method_slug":"1x1-convolution","method_name":"1x1 Convolution"},{"method_slug":"average-pooling","method_name":"Average Pooling"},{"method_slug":"batch-normalization","method_name":"Batch Normalization"},{"method_slug":"bottleneck-residual-block","method_name":"Bottleneck Residual Block"},{"method_slug":"convolution","method_name":"Convolution"},{"method_slug":"global-average-pooling","method_name":"Global Average Pooling"},{"method_slug":"kaiming-initialization","method_name":"Kaiming Initialization"},{"method_slug":"max-pooling","method_name":"Max Pooling"},{"method_slug":"relu","method_name":"ReLU"},{"method_slug":"residual-block","method_name":"Residual Block"},{"method_slug":"residual-connection","method_name":"Residual Connection"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2210.17020","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}