{"paper":{"title":"The information bottleneck method","license":"","headline":"Compressing a signal X through limited codewords can preserve all the information it provides about another signal Y.","cross_cats":["cond-mat.dis-nn","cs.LG","nlin.AO"],"primary_cat":"physics.data-an","authors_text":"Fernando C. Pereira (ATT Shannon Laboratory), Naftali Tishby (Hebrew University, NEC Research Institute), William Bialek (NEC Research Institute)","submitted_at":"2000-04-24T15:22:30Z","abstract_excerpt":"We define the relevant information in a signal $x\\in X$ as being the information that this signal provides about another signal $y\\in \\Y$. Examples include the information that face images provide about the names of the people portrayed, or the information that speech sounds provide about the words spoken. Understanding the signal $x$ requires more than just predicting $y$, it also requires specifying which features of $\\X$ play a role in the prediction. We formalize this problem as that of finding a short code for $\\X$ that preserves the maximum information about $\\Y$. That is, we squeeze the"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"This constrained optimization problem can be seen as a generalization of rate distortion theory in which the distortion measure d(x, x̃) emerges from the joint statistics of X and Y. This approach yields an exact set of self consistent equations for the coding rules X → X̃ and X̃ → Y.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The joint distribution p(x,y) is known or can be reliably estimated from data, allowing the mutual information terms and the iterative re-estimation procedure to be computed exactly.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The information bottleneck method finds a compressed representation T of X that preserves maximal mutual information with Y by solving a variational optimization problem that generalizes rate-distortion theory.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Compressing a signal X through limited codewords can preserve all the information it provides about another signal Y.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"e7ea08004a2c4d3053f5dc81684fdbc9005bc3c843b7a6365190f9ab27257874"},"source":{"id":"physics/0004057","kind":"arxiv","version":1},"verdict":{"id":"7a42c162-0a51-4ca6-b540-e8601ef108af","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-11T11:12:37.629353Z","strongest_claim":"This constrained optimization problem can be seen as a generalization of rate distortion theory in which the distortion measure d(x, x̃) emerges from the joint statistics of X and Y. This approach yields an exact set of self consistent equations for the coding rules X → X̃ and X̃ → Y.","one_line_summary":"The information bottleneck method finds a compressed representation T of X that preserves maximal mutual information with Y by solving a variational optimization problem that generalizes rate-distortion theory.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The joint distribution p(x,y) is known or can be reliably estimated from data, allowing the mutual information terms and the iterative re-estimation procedure to be computed exactly.","pith_extraction_headline":"Compressing a signal X through limited codewords can preserve all the information it provides about another signal Y."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/physics/0004057/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":6,"sample":[{"doi":"","year":null,"title":"Extracting relevant informati on","work_id":"7285a58a-980d-4da6-9442-6706522b64a7","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1991,"title":"T. M. Cover and J. A. Thomas, Elements of Information Theory (Wiley, New York, 1991)","work_id":"29ddde8e-a28b-443a-9300-4d74b6d5d28f","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1984,"title":"Information geometry and alternating mini- mization procedures","work_id":"3a0fb375-7d2d-4bc7-9ac2-057a1c88ed83","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1972,"title":"Computation of channel capacity and rate d istortion func- tion","work_id":"736c0776-4b9f-4eee-be63-c7a408238c1e","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1999,"title":"Agglomerative information bot tleneck","work_id":"76079e41-5ad2-4500-9386-d554063b811c","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":6,"snapshot_sha256":"81ed3b039e82349e0606d851616e164d9b43d33f6f1cef13a99a158b6a8727ea","internal_anchors":0},"formal_canon":{"evidence_count":3,"snapshot_sha256":"d0d0f0d8242d395b77c52375aa203c456a780722daa8646dd59590f02cacd4ed"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}