{"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/wide-feedforward-or-recurrent-neural-networks","title":"Wide Feedforward or Recurrent Neural Networks of Any Architecture are Gaussian Processes","arxiv_id":null,"date":"2019-12-01","proceeding":"NeurIPS 2019 12","authors":["Greg Yang"],"abstract":"Wide neural networks with random weights and biases are Gaussian processes, as observed by Neal (1995) for shallow networks, and more recently by Lee et al.~(2018) and Matthews et al.~(2018) for deep fully-connected networks, as well as by Novak et al.~(2019) and Garriga-Alonso et al.~(2019) for deep convolutional networks.\nWe show that this Neural Network-Gaussian Process correspondence surprisingly extends to all modern feedforward or recurrent neural networks composed of multilayer perceptron, RNNs (e.g. LSTMs, GRUs), (nD or graph) convolution, pooling, skip connection, attention, batch normalization, and/or layer normalization.\nMore generally, we introduce a language for expressing neural network computations, and our result encompasses all such expressible neural networks.\nThis work serves as a tutorial on the \\emph{tensor programs} technique formulated in Yang (2019) and elucidates the Gaussian Process results obtained there.\nWe provide open-source implementations of the Gaussian Process kernels of simple RNN, GRU, transformer, and batchnorm+ReLU network at  github.com/thegregyang/GP4A.\nPlease see our arxiv version for the complete and up-to-date version of this paper.","url_abs":"http://papers.nips.cc/paper/9186-wide-feedforward-or-recurrent-neural-networks-of-any-architecture-are-gaussian-processes","url_pdf":"http://papers.nips.cc/paper/9186-wide-feedforward-or-recurrent-neural-networks-of-any-architecture-are-gaussian-processes.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":"wide-feedforward-or-recurrent-neural-networks","repo_url":"https://github.com/thegregyang/GP4A","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[{"task_slug":"gaussian-processes","task_name":"Gaussian Processes"}],"methods":[{"method_slug":"gru","method_name":"GRU"},{"method_slug":"gaussian-process","method_name":"Gaussian Process"}],"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}