{"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/gaussian-process-behaviour-in-wide-deep","title":"Gaussian Process Behaviour in Wide Deep Neural Networks","arxiv_id":"1804.11271","date":"2018-04-30","proceeding":"ICLR 2018 1","authors":["Alexander G. de G. Matthews","Mark Rowland","Jiri Hron","Richard E. Turner","Zoubin Ghahramani"],"abstract":"Whilst deep neural networks have shown great empirical success, there is\nstill much work to be done to understand their theoretical properties. In this\npaper, we study the relationship between random, wide, fully connected,\nfeedforward networks with more than one hidden layer and Gaussian processes\nwith a recursive kernel definition. We show that, under broad conditions, as we\nmake the architecture increasingly wide, the implied random function converges\nin distribution to a Gaussian process, formalising and extending existing\nresults by Neal (1996) to deep networks. To evaluate convergence rates\nempirically, we use maximum mean discrepancy. We then compare finite Bayesian\ndeep networks from the literature to Gaussian processes in terms of the key\npredictive quantities of interest, finding that in some cases the agreement can\nbe very close. We discuss the desirability of Gaussian process behaviour and\nreview non-Gaussian alternative models from the literature.","url_abs":"http://arxiv.org/abs/1804.11271v2","url_pdf":"http://arxiv.org/pdf/1804.11271v2.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":"gaussian-process-behaviour-in-wide-deep","repo_url":"https://github.com/widedeepnetworks/widedeepnetworks","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"Apache-2.0"}},{"paper_slug":"gaussian-process-behaviour-in-wide-deep","repo_url":"https://github.com/google/wide_bnn_sampling","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"jax","reach":null}],"tasks":[{"task_slug":"gaussian-processes","task_name":"Gaussian Processes"}],"methods":[{"method_slug":"gaussian-process","method_name":"Gaussian Process"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1804.11271","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1804.11271"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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