{"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/caveats-for-information-bottleneck-in","title":"Caveats for information bottleneck in deterministic scenarios","arxiv_id":"1808.07593","date":"2018-08-23","proceeding":"ICLR 2019 5","authors":["Artemy Kolchinsky","Brendan D. Tracey","Steven Van Kuyk"],"abstract":"Information bottleneck (IB) is a method for extracting information from one\nrandom variable $X$ that is relevant for predicting another random variable\n$Y$. To do so, IB identifies an intermediate \"bottleneck\" variable $T$ that has\nlow mutual information $I(X;T)$ and high mutual information $I(Y;T)$. The \"IB\ncurve\" characterizes the set of bottleneck variables that achieve maximal\n$I(Y;T)$ for a given $I(X;T)$, and is typically explored by maximizing the \"IB\nLagrangian\", $I(Y;T) - \\beta I(X;T)$. In some cases, $Y$ is a deterministic\nfunction of $X$, including many classification problems in supervised learning\nwhere the output class $Y$ is a deterministic function of the input $X$. We\ndemonstrate three caveats when using IB in any situation where $Y$ is a\ndeterministic function of $X$: (1) the IB curve cannot be recovered by\nmaximizing the IB Lagrangian for different values of $\\beta$; (2) there are\n\"uninteresting\" trivial solutions at all points of the IB curve; and (3) for\nmulti-layer classifiers that achieve low prediction error, different layers\ncannot exhibit a strict trade-off between compression and prediction, contrary\nto a recent proposal. We also show that when $Y$ is a small perturbation away\nfrom being a deterministic function of $X$, these three caveats arise in an\napproximate way. To address problem (1), we propose a functional that, unlike\nthe IB Lagrangian, can recover the IB curve in all cases. We demonstrate the\nthree caveats on the MNIST dataset.","url_abs":"http://arxiv.org/abs/1808.07593v4","url_pdf":"http://arxiv.org/pdf/1808.07593v4.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":"caveats-for-information-bottleneck-in","repo_url":"https://github.com/artemyk/ibcurve","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1808.07593","atlas_url":"https://app.syntology.ai/?focus=1808.07593","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1808.07593"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-25T09:33:49+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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