{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:TIOMBKC7DHGOSU4R6SMO5HFYK7","short_pith_number":"pith:TIOMBKC7","schema_version":"1.0","canonical_sha256":"9a1cc0a85f19cce95391f498ee9cb857d2ed08cd6f6b3ad6eceef14c7a4d5524","source":{"kind":"arxiv","id":"2204.00077","version":1},"attestation_state":"computed","paper":{"title":"Efficient Maximal Coding Rate Reduction by Variational Forms","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CV"],"primary_cat":"cs.LG","authors_text":"Benjamin D. Haeffele, Christina Baek, Kwan Ho Ryan Chan, Tianjiao Ding, Yi Ma, Ziyang Wu","submitted_at":"2022-03-31T20:39:53Z","abstract_excerpt":"The principle of Maximal Coding Rate Reduction (MCR$^2$) has recently been proposed as a training objective for learning discriminative low-dimensional structures intrinsic to high-dimensional data to allow for more robust training than standard approaches, such as cross-entropy minimization. However, despite the advantages that have been shown for MCR$^2$ training, MCR$^2$ suffers from a significant computational cost due to the need to evaluate and differentiate a significant number of log-determinant terms that grows linearly with the number of classes. By taking advantage of variational fo"},"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":"2204.00077","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2022-03-31T20:39:53Z","cross_cats_sorted":["cs.CV"],"title_canon_sha256":"eb0701d1bc3c384f6503c1c60ebd2b0e85319428c59dc4aee4bd787afc3a58e6","abstract_canon_sha256":"97f7d4509c354c56d8cc58a6bf21fdfc60cb22a61122dba6e388e4de1a443dd6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:10:42.477638Z","signature_b64":"i4mTevb3Es8BzQoqgZXPJi5JbatmpsNuzVpHq5H0xovWP18TfrXMEiD4Z51AzJsWBofPZjZM6DktkZrXfLNaAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9a1cc0a85f19cce95391f498ee9cb857d2ed08cd6f6b3ad6eceef14c7a4d5524","last_reissued_at":"2026-07-05T04:10:42.477228Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:10:42.477228Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Efficient Maximal Coding Rate Reduction by Variational Forms","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CV"],"primary_cat":"cs.LG","authors_text":"Benjamin D. Haeffele, Christina Baek, Kwan Ho Ryan Chan, Tianjiao Ding, Yi Ma, Ziyang Wu","submitted_at":"2022-03-31T20:39:53Z","abstract_excerpt":"The principle of Maximal Coding Rate Reduction (MCR$^2$) has recently been proposed as a training objective for learning discriminative low-dimensional structures intrinsic to high-dimensional data to allow for more robust training than standard approaches, such as cross-entropy minimization. However, despite the advantages that have been shown for MCR$^2$ training, MCR$^2$ suffers from a significant computational cost due to the need to evaluate and differentiate a significant number of log-determinant terms that grows linearly with the number of classes. By taking advantage of variational fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2204.00077","kind":"arxiv","version":1},"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/2204.00077/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":"2204.00077","created_at":"2026-07-05T04:10:42.477286+00:00"},{"alias_kind":"arxiv_version","alias_value":"2204.00077v1","created_at":"2026-07-05T04:10:42.477286+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2204.00077","created_at":"2026-07-05T04:10:42.477286+00:00"},{"alias_kind":"pith_short_12","alias_value":"TIOMBKC7DHGO","created_at":"2026-07-05T04:10:42.477286+00:00"},{"alias_kind":"pith_short_16","alias_value":"TIOMBKC7DHGOSU4R","created_at":"2026-07-05T04:10:42.477286+00:00"},{"alias_kind":"pith_short_8","alias_value":"TIOMBKC7","created_at":"2026-07-05T04:10:42.477286+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2412.17810","citing_title":"Token Statistics Transformer: Linear-Time Attention via Variational Rate Reduction","ref_index":52,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TIOMBKC7DHGOSU4R6SMO5HFYK7","json":"https://pith.science/pith/TIOMBKC7DHGOSU4R6SMO5HFYK7.json","graph_json":"https://pith.science/api/pith-number/TIOMBKC7DHGOSU4R6SMO5HFYK7/graph.json","events_json":"https://pith.science/api/pith-number/TIOMBKC7DHGOSU4R6SMO5HFYK7/events.json","paper":"https://pith.science/paper/TIOMBKC7"},"agent_actions":{"view_html":"https://pith.science/pith/TIOMBKC7DHGOSU4R6SMO5HFYK7","download_json":"https://pith.science/pith/TIOMBKC7DHGOSU4R6SMO5HFYK7.json","view_paper":"https://pith.science/paper/TIOMBKC7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2204.00077&json=true","fetch_graph":"https://pith.science/api/pith-number/TIOMBKC7DHGOSU4R6SMO5HFYK7/graph.json","fetch_events":"https://pith.science/api/pith-number/TIOMBKC7DHGOSU4R6SMO5HFYK7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TIOMBKC7DHGOSU4R6SMO5HFYK7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TIOMBKC7DHGOSU4R6SMO5HFYK7/action/storage_attestation","attest_author":"https://pith.science/pith/TIOMBKC7DHGOSU4R6SMO5HFYK7/action/author_attestation","sign_citation":"https://pith.science/pith/TIOMBKC7DHGOSU4R6SMO5HFYK7/action/citation_signature","submit_replication":"https://pith.science/pith/TIOMBKC7DHGOSU4R6SMO5HFYK7/action/replication_record"}},"created_at":"2026-07-05T04:10:42.477286+00:00","updated_at":"2026-07-05T04:10:42.477286+00:00"}