{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2000:C5KGNOKKSCK4AD565NCV7CDUVA","short_pith_number":"pith:C5KGNOKK","canonical_record":{"source":{"id":"physics/0004057","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"physics.data-an","submitted_at":"2000-04-24T15:22:30Z","cross_cats_sorted":["cond-mat.dis-nn","cs.LG","nlin.AO"],"title_canon_sha256":"b6b86581531d14c4a709055a43bdb23e259450d072b82c00da696a9f456ea64a","abstract_canon_sha256":"21faebfb4a2797cd3e9e920b1c58a9a676764a44e288113469512f98541a83af"},"schema_version":"1.0"},"canonical_sha256":"175466b94a9095c00fbeeb455f8874a822daaf87c76038dd73ef348c7d00abbf","source":{"kind":"arxiv","id":"physics/0004057","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"physics/0004057","created_at":"2026-07-04T14:43:14Z"},{"alias_kind":"arxiv_version","alias_value":"physics/0004057v1","created_at":"2026-07-04T14:43:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.physics/0004057","created_at":"2026-07-04T14:43:14Z"},{"alias_kind":"pith_short_12","alias_value":"C5KGNOKKSCK4","created_at":"2026-07-04T14:43:14Z"},{"alias_kind":"pith_short_16","alias_value":"C5KGNOKKSCK4AD56","created_at":"2026-07-04T14:43:14Z"},{"alias_kind":"pith_short_8","alias_value":"C5KGNOKK","created_at":"2026-07-04T14:43:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2000:C5KGNOKKSCK4AD565NCV7CDUVA","target":"record","payload":{"canonical_record":{"source":{"id":"physics/0004057","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"physics.data-an","submitted_at":"2000-04-24T15:22:30Z","cross_cats_sorted":["cond-mat.dis-nn","cs.LG","nlin.AO"],"title_canon_sha256":"b6b86581531d14c4a709055a43bdb23e259450d072b82c00da696a9f456ea64a","abstract_canon_sha256":"21faebfb4a2797cd3e9e920b1c58a9a676764a44e288113469512f98541a83af"},"schema_version":"1.0"},"canonical_sha256":"175466b94a9095c00fbeeb455f8874a822daaf87c76038dd73ef348c7d00abbf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:43:14.754874Z","signature_b64":"D4yJ9Hgra8H2ej5B0OsZOe4OB6HoakA3kwj9mRR/mErzP6Cl/kh716nQjBQLgaqTLslMYtsFa2PgjbagAi/gCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"175466b94a9095c00fbeeb455f8874a822daaf87c76038dd73ef348c7d00abbf","last_reissued_at":"2026-07-04T14:43:14.754516Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:43:14.754516Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"physics/0004057","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T14:43:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jZP+GuwP3ftanc/+6bC5/Nzn0aIaCpWXxmokfZvjwIlAJ/pazLgmdEsdPr/XoOZDoMIWWiuaybLJLcog/iF/Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T11:07:25.729230Z"},"content_sha256":"cd28187e51825c824ae02e7b0ef1ce84ce9265dd20457b581b956cdc205f9b46","schema_version":"1.0","event_id":"sha256:cd28187e51825c824ae02e7b0ef1ce84ce9265dd20457b581b956cdc205f9b46"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2000:C5KGNOKKSCK4AD565NCV7CDUVA","target":"graph","payload":{"graph_snapshot":{"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"},"verdict_id":"7a42c162-0a51-4ca6-b540-e8601ef108af"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T14:43:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hwstXJQh1wXXf5dSXbG07HObSrgFSHfCoEHF/mIqgZX9nlR687jtJSgJxfhy+9MWQrf0doyqyuuycJAYoEdfDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T11:07:25.730685Z"},"content_sha256":"3c6bf4f8307dca1473ff261532998d09cade8885aea342194bd51420021d60dc","schema_version":"1.0","event_id":"sha256:3c6bf4f8307dca1473ff261532998d09cade8885aea342194bd51420021d60dc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C5KGNOKKSCK4AD565NCV7CDUVA/bundle.json","state_url":"https://pith.science/pith/C5KGNOKKSCK4AD565NCV7CDUVA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C5KGNOKKSCK4AD565NCV7CDUVA/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-14T11:07:25Z","links":{"resolver":"https://pith.science/pith/C5KGNOKKSCK4AD565NCV7CDUVA","bundle":"https://pith.science/pith/C5KGNOKKSCK4AD565NCV7CDUVA/bundle.json","state":"https://pith.science/pith/C5KGNOKKSCK4AD565NCV7CDUVA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C5KGNOKKSCK4AD565NCV7CDUVA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2000:C5KGNOKKSCK4AD565NCV7CDUVA","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"21faebfb4a2797cd3e9e920b1c58a9a676764a44e288113469512f98541a83af","cross_cats_sorted":["cond-mat.dis-nn","cs.LG","nlin.AO"],"license":"","primary_cat":"physics.data-an","submitted_at":"2000-04-24T15:22:30Z","title_canon_sha256":"b6b86581531d14c4a709055a43bdb23e259450d072b82c00da696a9f456ea64a"},"schema_version":"1.0","source":{"id":"physics/0004057","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"physics/0004057","created_at":"2026-07-04T14:43:14Z"},{"alias_kind":"arxiv_version","alias_value":"physics/0004057v1","created_at":"2026-07-04T14:43:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.physics/0004057","created_at":"2026-07-04T14:43:14Z"},{"alias_kind":"pith_short_12","alias_value":"C5KGNOKKSCK4","created_at":"2026-07-04T14:43:14Z"},{"alias_kind":"pith_short_16","alias_value":"C5KGNOKKSCK4AD56","created_at":"2026-07-04T14:43:14Z"},{"alias_kind":"pith_short_8","alias_value":"C5KGNOKK","created_at":"2026-07-04T14:43:14Z"}],"graph_snapshots":[{"event_id":"sha256:3c6bf4f8307dca1473ff261532998d09cade8885aea342194bd51420021d60dc","target":"graph","created_at":"2026-07-04T14:43:14Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","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."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","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."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","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."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Compressing a signal X through limited codewords can preserve all the information it provides about another signal Y."}],"snapshot_sha256":"e7ea08004a2c4d3053f5dc81684fdbc9005bc3c843b7a6365190f9ab27257874"},"formal_canon":{"evidence_count":3,"snapshot_sha256":"d0d0f0d8242d395b77c52375aa203c456a780722daa8646dd59590f02cacd4ed"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/physics/0004057/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Fernando C. Pereira (ATT Shannon Laboratory), Naftali Tishby (Hebrew University, NEC Research Institute), William Bialek (NEC Research Institute)","cross_cats":["cond-mat.dis-nn","cs.LG","nlin.AO"],"headline":"Compressing a signal X through limited codewords can preserve all the information it provides about another signal Y.","license":"","primary_cat":"physics.data-an","submitted_at":"2000-04-24T15:22:30Z","title":"The information bottleneck method"},"references":{"count":6,"internal_anchors":0,"resolved_work":6,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":1,"title":"Extracting relevant informati on","work_id":"7285a58a-980d-4da6-9442-6706522b64a7","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":2,"title":"T. M. Cover and J. A. Thomas, Elements of Information Theory (Wiley, New York, 1991)","work_id":"29ddde8e-a28b-443a-9300-4d74b6d5d28f","year":1991},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":3,"title":"Information geometry and alternating mini- mization procedures","work_id":"3a0fb375-7d2d-4bc7-9ac2-057a1c88ed83","year":1984},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":4,"title":"Computation of channel capacity and rate d istortion func- tion","work_id":"736c0776-4b9f-4eee-be63-c7a408238c1e","year":1972},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"title":"Agglomerative information bot tleneck","work_id":"76079e41-5ad2-4500-9386-d554063b811c","year":1999}],"snapshot_sha256":"81ed3b039e82349e0606d851616e164d9b43d33f6f1cef13a99a158b6a8727ea"},"source":{"id":"physics/0004057","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-11T11:12:37.629353Z","id":"7a42c162-0a51-4ca6-b540-e8601ef108af","model_set":{"reader":"grok-4.3"},"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","pith_extraction_headline":"Compressing a signal X through limited codewords can preserve all the information it provides about another signal Y.","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.","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."}},"verdict_id":"7a42c162-0a51-4ca6-b540-e8601ef108af"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:cd28187e51825c824ae02e7b0ef1ce84ce9265dd20457b581b956cdc205f9b46","target":"record","created_at":"2026-07-04T14:43:14Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"21faebfb4a2797cd3e9e920b1c58a9a676764a44e288113469512f98541a83af","cross_cats_sorted":["cond-mat.dis-nn","cs.LG","nlin.AO"],"license":"","primary_cat":"physics.data-an","submitted_at":"2000-04-24T15:22:30Z","title_canon_sha256":"b6b86581531d14c4a709055a43bdb23e259450d072b82c00da696a9f456ea64a"},"schema_version":"1.0","source":{"id":"physics/0004057","kind":"arxiv","version":1}},"canonical_sha256":"175466b94a9095c00fbeeb455f8874a822daaf87c76038dd73ef348c7d00abbf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"175466b94a9095c00fbeeb455f8874a822daaf87c76038dd73ef348c7d00abbf","first_computed_at":"2026-07-04T14:43:14.754516Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:43:14.754516Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"D4yJ9Hgra8H2ej5B0OsZOe4OB6HoakA3kwj9mRR/mErzP6Cl/kh716nQjBQLgaqTLslMYtsFa2PgjbagAi/gCA==","signature_status":"signed_v1","signed_at":"2026-07-04T14:43:14.754874Z","signed_message":"canonical_sha256_bytes"},"source_id":"physics/0004057","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cd28187e51825c824ae02e7b0ef1ce84ce9265dd20457b581b956cdc205f9b46","sha256:3c6bf4f8307dca1473ff261532998d09cade8885aea342194bd51420021d60dc"],"state_sha256":"70bc65ca8e0281ad96723e6263b79c61b8897912c76e12a7af78b5deff813e85"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"813ktdDMHuIe/m7jdxwN2DLuhsM/PdEjN8FlY11WTVz0qfohpCK+c5du+cGEEcgMNmd8cVcpsP04Nk7gEB6NBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T11:07:25.738034Z","bundle_sha256":"bda763960ced44487d371cd61acb46581032bcb4a2b2d589d977d1fb6ea48f63"}}