{"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/an-analytic-theory-of-shallow-networks","title":"An analytic theory of shallow networks dynamics for hinge loss classification","arxiv_id":"2006.11209","date":"2020-06-19","proceeding":"NeurIPS 2020 12","authors":["Franco Pellegrini","Giulio Biroli"],"abstract":"Neural networks have been shown to perform incredibly well in classification tasks over structured high-dimensional datasets. However, the learning dynamics of such networks is still poorly understood. In this paper we study in detail the training dynamics of a simple type of neural network: a single hidden layer trained to perform a classification task. We show that in a suitable mean-field limit this case maps to a single-node learning problem with a time-dependent dataset determined self-consistently from the average nodes population. We specialize our theory to the prototypical case of a linearly separable dataset and a linear hinge loss, for which the dynamics can be explicitly solved. This allow us to address in a simple setting several phenomena appearing in modern networks such as slowing down of training dynamics, crossover between rich and lazy learning, and overfitting. Finally, we asses the limitations of mean-field theory by studying the case of large but finite number of nodes and of training samples.","url_abs":"https://arxiv.org/abs/2006.11209v1","url_pdf":"https://arxiv.org/pdf/2006.11209v1.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":"an-analytic-theory-of-shallow-networks","repo_url":"https://github.com/phiandark/DynHingeLoss","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok"}}],"tasks":[{"task_slug":"classification","task_name":"General Classification"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=2006.11209","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}