{"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/manifold-tiling-localized-receptive-fields","title":"Manifold-tiling Localized Receptive Fields are Optimal in Similarity-preserving Neural Networks","arxiv_id":null,"date":"2018-12-01","proceeding":"NeurIPS 2018 12","authors":["Anirvan Sengupta","Cengiz Pehlevan","Mariano Tepper","Alexander Genkin","Dmitri Chklovskii"],"abstract":"Many neurons in the brain, such as place cells in the rodent hippocampus, have localized receptive fields, i.e., they respond to a small neighborhood of stimulus space. What is the functional significance of such representations and how can they arise? Here, we propose that localized receptive fields emerge in similarity-preserving networks of rectifying neurons that learn low-dimensional manifolds populated by sensory inputs.  Numerical simulations of such networks on standard datasets yield manifold-tiling localized receptive fields. More generally, we show analytically that, for data lying on symmetric manifolds, optimal solutions of objectives, from which similarity-preserving networks are derived, have localized receptive fields. Therefore, nonnegative similarity-preserving mapping (NSM) implemented by neural networks can model representations of continuous manifolds in the brain.","url_abs":"http://papers.nips.cc/paper/7939-manifold-tiling-localized-receptive-fields-are-optimal-in-similarity-preserving-neural-networks","url_pdf":"http://papers.nips.cc/paper/7939-manifold-tiling-localized-receptive-fields-are-optimal-in-similarity-preserving-neural-networks.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":"manifold-tiling-localized-receptive-fields","repo_url":"https://github.com/flatironinstitute/mantis","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":null,"task_name":"Hippocampus"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}