{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:344VHTDU5JPRHZWBOLY2NM6CPN","short_pith_number":"pith:344VHTDU","schema_version":"1.0","canonical_sha256":"df3953cc74ea5f13e6c172f1a6b3c27b4d7c13f22b323f27e091a3a6e65d9478","source":{"kind":"arxiv","id":"2204.02489","version":2},"attestation_state":"computed","paper":{"title":"Pareto-optimal clustering with the primal deterministic information bottleneck","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","stat.ML"],"primary_cat":"cs.LG","authors_text":"Andrew K. Tan, Isaac L. Chuang, Max Tegmark","submitted_at":"2022-04-05T21:08:45Z","abstract_excerpt":"At the heart of both lossy compression and clustering is a trade-off between the fidelity and size of the learned representation. Our goal is to map out and study the Pareto frontier that quantifies this trade-off. We focus on the optimization of the Deterministic Information Bottleneck (DIB) objective over the space of hard clusterings. To this end, we introduce the primal DIB problem, which we show results in a much richer frontier than its previously studied Lagrangian relaxation when optimized over discrete search spaces. We present an algorithm for mapping out the Pareto frontier of the p"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2204.02489","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-04-05T21:08:45Z","cross_cats_sorted":["cs.IT","math.IT","stat.ML"],"title_canon_sha256":"30c40ce386a89e5ace3ad78fb4b4033c6ed9fe119a7ef64d482b79dd852e0dfd","abstract_canon_sha256":"1046181fce2a9af6843a99c2888f20f4e0db6fd99ef066cde97efe39f71f6b62"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:44:10.928199Z","signature_b64":"t8UwltgAUCULFTkQqjUyxoUAHkbfj4ZmV4UeKYMQg4m0n/PnQFRBPKIFep90daZqtvDOn82NwPIZByByvOkwBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"df3953cc74ea5f13e6c172f1a6b3c27b4d7c13f22b323f27e091a3a6e65d9478","last_reissued_at":"2026-07-05T04:44:10.927719Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:44:10.927719Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Pareto-optimal clustering with the primal deterministic information bottleneck","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","stat.ML"],"primary_cat":"cs.LG","authors_text":"Andrew K. Tan, Isaac L. Chuang, Max Tegmark","submitted_at":"2022-04-05T21:08:45Z","abstract_excerpt":"At the heart of both lossy compression and clustering is a trade-off between the fidelity and size of the learned representation. Our goal is to map out and study the Pareto frontier that quantifies this trade-off. We focus on the optimization of the Deterministic Information Bottleneck (DIB) objective over the space of hard clusterings. To this end, we introduce the primal DIB problem, which we show results in a much richer frontier than its previously studied Lagrangian relaxation when optimized over discrete search spaces. We present an algorithm for mapping out the Pareto frontier of the p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2204.02489","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2204.02489/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2204.02489","created_at":"2026-07-05T04:44:10.927777+00:00"},{"alias_kind":"arxiv_version","alias_value":"2204.02489v2","created_at":"2026-07-05T04:44:10.927777+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2204.02489","created_at":"2026-07-05T04:44:10.927777+00:00"},{"alias_kind":"pith_short_12","alias_value":"344VHTDU5JPR","created_at":"2026-07-05T04:44:10.927777+00:00"},{"alias_kind":"pith_short_16","alias_value":"344VHTDU5JPRHZWB","created_at":"2026-07-05T04:44:10.927777+00:00"},{"alias_kind":"pith_short_8","alias_value":"344VHTDU","created_at":"2026-07-05T04:44:10.927777+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/344VHTDU5JPRHZWBOLY2NM6CPN","json":"https://pith.science/pith/344VHTDU5JPRHZWBOLY2NM6CPN.json","graph_json":"https://pith.science/api/pith-number/344VHTDU5JPRHZWBOLY2NM6CPN/graph.json","events_json":"https://pith.science/api/pith-number/344VHTDU5JPRHZWBOLY2NM6CPN/events.json","paper":"https://pith.science/paper/344VHTDU"},"agent_actions":{"view_html":"https://pith.science/pith/344VHTDU5JPRHZWBOLY2NM6CPN","download_json":"https://pith.science/pith/344VHTDU5JPRHZWBOLY2NM6CPN.json","view_paper":"https://pith.science/paper/344VHTDU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2204.02489&json=true","fetch_graph":"https://pith.science/api/pith-number/344VHTDU5JPRHZWBOLY2NM6CPN/graph.json","fetch_events":"https://pith.science/api/pith-number/344VHTDU5JPRHZWBOLY2NM6CPN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/344VHTDU5JPRHZWBOLY2NM6CPN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/344VHTDU5JPRHZWBOLY2NM6CPN/action/storage_attestation","attest_author":"https://pith.science/pith/344VHTDU5JPRHZWBOLY2NM6CPN/action/author_attestation","sign_citation":"https://pith.science/pith/344VHTDU5JPRHZWBOLY2NM6CPN/action/citation_signature","submit_replication":"https://pith.science/pith/344VHTDU5JPRHZWBOLY2NM6CPN/action/replication_record"}},"created_at":"2026-07-05T04:44:10.927777+00:00","updated_at":"2026-07-05T04:44:10.927777+00:00"}