{"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/inductive-bias-of-deep-convolutional-networks","title":"Inductive Bias of Deep Convolutional Networks through Pooling Geometry","arxiv_id":"1605.06743","date":"2016-05-22","proceeding":null,"authors":["Nadav Cohen","Amnon Shashua"],"abstract":"Our formal understanding of the inductive bias that drives the success of\nconvolutional networks on computer vision tasks is limited. In particular, it\nis unclear what makes hypotheses spaces born from convolution and pooling\noperations so suitable for natural images. In this paper we study the ability\nof convolutional networks to model correlations among regions of their input.\nWe theoretically analyze convolutional arithmetic circuits, and empirically\nvalidate our findings on other types of convolutional networks as well.\nCorrelations are formalized through the notion of separation rank, which for a\ngiven partition of the input, measures how far a function is from being\nseparable. We show that a polynomially sized deep network supports\nexponentially high separation ranks for certain input partitions, while being\nlimited to polynomial separation ranks for others. The network's pooling\ngeometry effectively determines which input partitions are favored, thus serves\nas a means for controlling the inductive bias. Contiguous pooling windows as\ncommonly employed in practice favor interleaved partitions over coarse ones,\norienting the inductive bias towards the statistics of natural images. Other\npooling schemes lead to different preferences, and this allows tailoring the\nnetwork to data that departs from the usual domain of natural imagery. In\naddition to analyzing deep networks, we show that shallow ones support only\nlinear separation ranks, and by this gain insight into the benefit of functions\nbrought forth by depth - they are able to efficiently model strong correlation\nunder favored partitions of the input.","url_abs":"http://arxiv.org/abs/1605.06743v4","url_pdf":"http://arxiv.org/pdf/1605.06743v4.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":"inductive-bias-of-deep-convolutional-networks","repo_url":"https://github.com/HUJI-Deep/inductive-pooling","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"inductive-bias","task_name":"Inductive Bias"}],"methods":[{"method_slug":"convolution","method_name":"Convolution"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1605.06743","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}