{"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-capacity-scaling-law-for-artificial-neural","title":"A Capacity Scaling Law for Artificial Neural Networks","arxiv_id":"1708.06019","date":"2017-08-20","proceeding":null,"authors":["Gerald Friedland","Mario Krell"],"abstract":"We derive the calculation of two critical numbers predicting the behavior of\nperceptron networks. First, we derive the calculation of what we call the\nlossless memory (LM) dimension. The LM dimension is a generalization of the\nVapnik--Chervonenkis (VC) dimension that avoids structured data and therefore\nprovides an upper bound for perfectly fitting almost any training data. Second,\nwe derive what we call the MacKay (MK) dimension. This limit indicates a 50%\nchance of not being able to train a given function. Our derivations are\nperformed by embedding a neural network into Shannon's communication model\nwhich allows to interpret the two points as capacities measured in bits. We\npresent a proof and practical experiments that validate our upper bounds with\nrepeatable experiments using different network configurations, diverse\nimplementations, varying activation functions, and several learning algorithms.\nThe bottom line is that the two capacity points scale strictly linear with the\nnumber of weights. Among other practical applications, our result allows to\ncompare and benchmark different neural network implementations independent of a\nconcrete learning task. Our results provide insight into the capabilities and\nlimits of neural networks and generate valuable know how for experimental\ndesign decisions.","url_abs":"http://arxiv.org/abs/1708.06019v3","url_pdf":"http://arxiv.org/pdf/1708.06019v3.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-capacity-scaling-law-for-artificial-neural","repo_url":"https://github.com/multimedia-berkeley/deep_thoughts","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"experimental-design","task_name":"Experimental Design"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}