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Such problems are widespread, ranging from\nestimation of population statistics \\cite{poczos13aistats}, to anomaly\ndetection in piezometer data of embankment dams \\cite{Jung15Exploration}, to\ncosmology \\cite{Ntampaka16Dynamical,Ravanbakhsh16ICML1}. Our main theorem\ncharacterizes the permutation invariant functions and provides a family of\nfunctions to which any permutation invariant objective function must belong.\nThis family of functions has a special structure which enables us to design a\ndeep network architecture that can operate on sets and which can be deployed on\na variety of scenarios including both unsupervised and supervised learning\ntasks. We also derive the necessary and sufficient conditions for permutation\nequivariance in deep models. We demonstrate the applicability of our method on\npopulation statistic estimation, point cloud classification, set expansion, and\noutlier detection.","url_abs":"http://arxiv.org/abs/1703.06114v3","url_pdf":"http://arxiv.org/pdf/1703.06114v3.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":"deep-sets","repo_url":"https://github.com/MathieuCarriere/perslay","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":null},{"paper_slug":"deep-sets","repo_url":"https://github.com/acciorocketships/setautoencoder","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null},{"paper_slug":"deep-sets","repo_url":"https://github.com/frgsimpson/kitt","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":null},{"paper_slug":"deep-sets","repo_url":"https://github.com/jmmartyn/neural-network-quantum-field-states","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null},{"paper_slug":"deep-sets","repo_url":"https://github.com/lwtnn/lwtnn","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"deep-sets","repo_url":"https://github.com/pluskal-lab/massspecgym","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"deep-sets","repo_url":"https://github.com/aai-institute/pyDVL","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"ok","spdx":"LGPL-3.0"}}],"tasks":[{"task_slug":"anomaly-detection","task_name":"Anomaly Detection"},{"task_slug":"outlier-detection","task_name":"Outlier Detection"},{"task_slug":"point-cloud-classification","task_name":"Point Cloud Classification"}],"methods":[{"method_slug":"deep-sets","method_name":"Deep Sets"}],"datasets_introduced":[],"methods_introduced":[{"slug":"deep-sets","name":"Deep Sets","full_name":"Deep Sets"}],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1703.06114","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1703.06114"}},"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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