{"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/expressive-power-of-recurrent-neural-networks","title":"Expressive power of recurrent neural networks","arxiv_id":"1711.00811","date":"2017-11-02","proceeding":"ICLR 2018 1","authors":["Valentin Khrulkov","Alexander Novikov","Ivan Oseledets"],"abstract":"Deep neural networks are surprisingly efficient at solving practical tasks,\nbut the theory behind this phenomenon is only starting to catch up with the\npractice. Numerous works show that depth is the key to this efficiency. A\ncertain class of deep convolutional networks -- namely those that correspond to\nthe Hierarchical Tucker (HT) tensor decomposition -- has been proven to have\nexponentially higher expressive power than shallow networks. I.e. a shallow\nnetwork of exponential width is required to realize the same score function as\ncomputed by the deep architecture. In this paper, we prove the expressive power\ntheorem (an exponential lower bound on the width of the equivalent shallow\nnetwork) for a class of recurrent neural networks -- ones that correspond to\nthe Tensor Train (TT) decomposition. This means that even processing an image\npatch by patch with an RNN can be exponentially more efficient than a (shallow)\nconvolutional network with one hidden layer. Using theoretical results on the\nrelation between the tensor decompositions we compare expressive powers of the\nHT- and TT-Networks. We also implement the recurrent TT-Networks and provide\nnumerical evidence of their expressivity.","url_abs":"http://arxiv.org/abs/1711.00811v2","url_pdf":"http://arxiv.org/pdf/1711.00811v2.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":"expressive-power-of-recurrent-neural-networks","repo_url":"https://github.com/rballester/tntorch","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"LGPL-3.0"}},{"paper_slug":"expressive-power-of-recurrent-neural-networks","repo_url":"https://github.com/vmml/tntorch","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"LGPL-3.0"}}],"tasks":[{"task_slug":"tensor-decomposition","task_name":"Tensor Decomposition"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1711.00811","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}