{"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/permutation-equivariant-neural-networks","title":"Permutation-equivariant neural networks applied to dynamics prediction","arxiv_id":"1612.04530","date":"2016-12-14","proceeding":null,"authors":["Nicholas Guttenberg","Nathaniel Virgo","Olaf Witkowski","Hidetoshi Aoki","Ryota Kanai"],"abstract":"The introduction of convolutional layers greatly advanced the performance of\nneural networks on image tasks due to innately capturing a way of encoding and\nlearning translation-invariant operations, matching one of the underlying\nsymmetries of the image domain. In comparison, there are a number of problems\nin which there are a number of different inputs which are all 'of the same\ntype' --- multiple particles, multiple agents, multiple stock prices, etc. The\ncorresponding symmetry to this is permutation symmetry, in that the algorithm\nshould not depend on the specific ordering of the input data. We discuss a\npermutation-invariant neural network layer in analogy to convolutional layers,\nand show the ability of this architecture to learn to predict the motion of a\nvariable number of interacting hard discs in 2D. In the same way that\nconvolutional layers can generalize to different image sizes, the permutation\nlayer we describe generalizes to different numbers of objects.","url_abs":"http://arxiv.org/abs/1612.04530v1","url_pdf":"http://arxiv.org/pdf/1612.04530v1.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":"permutation-equivariant-neural-networks","repo_url":"https://github.com/arayabrain/PermutationalNetworks","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok"}},{"paper_slug":"permutation-equivariant-neural-networks","repo_url":"https://github.com/phquanta/DeepPermInvFp","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"gone","observed_at":"2026-09-18","how":"tree_404+repo_404"}}],"tasks":[{"task_slug":"prediction","task_name":"Prediction"},{"task_slug":"translation","task_name":"Translation"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=1612.04530","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}