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Our approach, which we call\nJanossy pooling, expresses a permutation-invariant function as the average of a\npermutation-sensitive function applied to all reorderings of the input\nsequence. This allows us to leverage the rich and mature literature on\npermutation-sensitive functions to construct novel and flexible\npermutation-invariant functions. If carried out naively, Janossy pooling can be\ncomputationally prohibitive. To allow computational tractability, we consider\nthree kinds of approximations: canonical orderings of sequences, functions with\n$k$-order interactions, and stochastic optimization algorithms with random\npermutations. Our framework unifies a variety of existing work in the\nliterature, and suggests possible modeling and algorithmic extensions. We\nexplore a few in our experiments, which demonstrate improved performance over\ncurrent state-of-the-art methods.","url_abs":"http://arxiv.org/abs/1811.01900v3","url_pdf":"http://arxiv.org/pdf/1811.01900v3.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":"janossy-pooling-learning-deep-permutation","repo_url":"https://github.com/PurdueMINDS/JanossyPooling","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"Apache-2.0"}},{"paper_slug":"janossy-pooling-learning-deep-permutation","repo_url":"https://github.com/balasrini33/JanossyPooling","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"Apache-2.0"}}],"tasks":[{"task_slug":"stochastic-optimization","task_name":"Stochastic Optimization"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1811.01900","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1811.01900"}},"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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