{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:EY3VREIURTV627RMO4OS6M3KY2","short_pith_number":"pith:EY3VREIU","canonical_record":{"source":{"id":"2410.00690","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-10-01T13:45:55Z","cross_cats_sorted":["cs.AI","math.OC"],"title_canon_sha256":"05a67d307bb4497bb6fe4fd10b235724df1ca73033e26af92fec72b53d3e8fc4","abstract_canon_sha256":"6d7f053c8bdfb234abb112d95ecaa323519fb6239cb2b77a7c469f1b4f28945a"},"schema_version":"1.0"},"canonical_sha256":"26375891148cebed7e2c771d2f336ac6a5202a6c198435a64072822d03492844","source":{"kind":"arxiv","id":"2410.00690","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.00690","created_at":"2026-07-05T10:07:44Z"},{"alias_kind":"arxiv_version","alias_value":"2410.00690v2","created_at":"2026-07-05T10:07:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.00690","created_at":"2026-07-05T10:07:44Z"},{"alias_kind":"pith_short_12","alias_value":"EY3VREIURTV6","created_at":"2026-07-05T10:07:44Z"},{"alias_kind":"pith_short_16","alias_value":"EY3VREIURTV627RM","created_at":"2026-07-05T10:07:44Z"},{"alias_kind":"pith_short_8","alias_value":"EY3VREIU","created_at":"2026-07-05T10:07:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:EY3VREIURTV627RMO4OS6M3KY2","target":"record","payload":{"canonical_record":{"source":{"id":"2410.00690","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-10-01T13:45:55Z","cross_cats_sorted":["cs.AI","math.OC"],"title_canon_sha256":"05a67d307bb4497bb6fe4fd10b235724df1ca73033e26af92fec72b53d3e8fc4","abstract_canon_sha256":"6d7f053c8bdfb234abb112d95ecaa323519fb6239cb2b77a7c469f1b4f28945a"},"schema_version":"1.0"},"canonical_sha256":"26375891148cebed7e2c771d2f336ac6a5202a6c198435a64072822d03492844","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:07:44.949661Z","signature_b64":"abQJ7sThibdgbNCaM8gHKA/U4tScNy41XL8pYI3DbiI965TRm7VJhrHijnDhIQrVBCLnLrDNIXCgsr92Dy2wDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"26375891148cebed7e2c771d2f336ac6a5202a6c198435a64072822d03492844","last_reissued_at":"2026-07-05T10:07:44.949130Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:07:44.949130Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2410.00690","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:07:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W8ef3lI4f74irk//N48r1iJAMhYeqyV5kIWhpsH6wnHPH2irImopPsYL5+RgRViPhODNQ/vQtGvuNYxWvs9vAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T05:29:47.560140Z"},"content_sha256":"d333966e0344bc379da4bdb401aa3d84db23609cf96d4513e83ca774387311f8","schema_version":"1.0","event_id":"sha256:d333966e0344bc379da4bdb401aa3d84db23609cf96d4513e83ca774387311f8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:EY3VREIURTV627RMO4OS6M3KY2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Beyond Minimax Rates in Group Distributionally Robust Optimization via a Novel Notion of Sparsity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI","math.OC"],"primary_cat":"cs.LG","authors_text":"Crist\\'obal Guzm\\'an, Nishant A. Mehta, Quan Nguyen","submitted_at":"2024-10-01T13:45:55Z","abstract_excerpt":"The minimax sample complexity of group distributionally robust optimization (GDRO) has been determined up to a $\\log(K)$ factor, where $K$ is the number of groups. In this work, we venture beyond the minimax perspective via a novel notion of sparsity that we dub $(\\lambda, \\beta)$-sparsity. In short, this condition means that at any parameter $\\theta$, there is a set of at most $\\beta$ groups whose risks at $\\theta$ all are at least $\\lambda$ larger than the risks of the other groups. To find an $\\epsilon$-optimal $\\theta$, we show via a novel algorithm and analysis that the $\\epsilon$-depende"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.00690","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/2410.00690/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:07:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mmQ7UqIhBN0fR32yNfWZJHgu9HvzGC7mM0yBLXaS30zM7plp/MopevIuCx3/jWui/hAUNw10lEb/OJs/eG3AAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T05:29:47.560638Z"},"content_sha256":"1901e4aea447ad9334ab91ab4ca8eb930bcda299929bb05ccdafb8a3124d0a66","schema_version":"1.0","event_id":"sha256:1901e4aea447ad9334ab91ab4ca8eb930bcda299929bb05ccdafb8a3124d0a66"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EY3VREIURTV627RMO4OS6M3KY2/bundle.json","state_url":"https://pith.science/pith/EY3VREIURTV627RMO4OS6M3KY2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EY3VREIURTV627RMO4OS6M3KY2/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":"2026-08-11T05:29:47Z","links":{"resolver":"https://pith.science/pith/EY3VREIURTV627RMO4OS6M3KY2","bundle":"https://pith.science/pith/EY3VREIURTV627RMO4OS6M3KY2/bundle.json","state":"https://pith.science/pith/EY3VREIURTV627RMO4OS6M3KY2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EY3VREIURTV627RMO4OS6M3KY2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:EY3VREIURTV627RMO4OS6M3KY2","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":"6d7f053c8bdfb234abb112d95ecaa323519fb6239cb2b77a7c469f1b4f28945a","cross_cats_sorted":["cs.AI","math.OC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-10-01T13:45:55Z","title_canon_sha256":"05a67d307bb4497bb6fe4fd10b235724df1ca73033e26af92fec72b53d3e8fc4"},"schema_version":"1.0","source":{"id":"2410.00690","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.00690","created_at":"2026-07-05T10:07:44Z"},{"alias_kind":"arxiv_version","alias_value":"2410.00690v2","created_at":"2026-07-05T10:07:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.00690","created_at":"2026-07-05T10:07:44Z"},{"alias_kind":"pith_short_12","alias_value":"EY3VREIURTV6","created_at":"2026-07-05T10:07:44Z"},{"alias_kind":"pith_short_16","alias_value":"EY3VREIURTV627RM","created_at":"2026-07-05T10:07:44Z"},{"alias_kind":"pith_short_8","alias_value":"EY3VREIU","created_at":"2026-07-05T10:07:44Z"}],"graph_snapshots":[{"event_id":"sha256:1901e4aea447ad9334ab91ab4ca8eb930bcda299929bb05ccdafb8a3124d0a66","target":"graph","created_at":"2026-07-05T10:07:44Z","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":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2410.00690/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The minimax sample complexity of group distributionally robust optimization (GDRO) has been determined up to a $\\log(K)$ factor, where $K$ is the number of groups. In this work, we venture beyond the minimax perspective via a novel notion of sparsity that we dub $(\\lambda, \\beta)$-sparsity. In short, this condition means that at any parameter $\\theta$, there is a set of at most $\\beta$ groups whose risks at $\\theta$ all are at least $\\lambda$ larger than the risks of the other groups. To find an $\\epsilon$-optimal $\\theta$, we show via a novel algorithm and analysis that the $\\epsilon$-depende","authors_text":"Crist\\'obal Guzm\\'an, Nishant A. Mehta, Quan Nguyen","cross_cats":["cs.AI","math.OC"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-10-01T13:45:55Z","title":"Beyond Minimax Rates in Group Distributionally Robust Optimization via a Novel Notion of Sparsity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.00690","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:d333966e0344bc379da4bdb401aa3d84db23609cf96d4513e83ca774387311f8","target":"record","created_at":"2026-07-05T10:07:44Z","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":"6d7f053c8bdfb234abb112d95ecaa323519fb6239cb2b77a7c469f1b4f28945a","cross_cats_sorted":["cs.AI","math.OC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-10-01T13:45:55Z","title_canon_sha256":"05a67d307bb4497bb6fe4fd10b235724df1ca73033e26af92fec72b53d3e8fc4"},"schema_version":"1.0","source":{"id":"2410.00690","kind":"arxiv","version":2}},"canonical_sha256":"26375891148cebed7e2c771d2f336ac6a5202a6c198435a64072822d03492844","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"26375891148cebed7e2c771d2f336ac6a5202a6c198435a64072822d03492844","first_computed_at":"2026-07-05T10:07:44.949130Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:07:44.949130Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"abQJ7sThibdgbNCaM8gHKA/U4tScNy41XL8pYI3DbiI965TRm7VJhrHijnDhIQrVBCLnLrDNIXCgsr92Dy2wDw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:07:44.949661Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.00690","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d333966e0344bc379da4bdb401aa3d84db23609cf96d4513e83ca774387311f8","sha256:1901e4aea447ad9334ab91ab4ca8eb930bcda299929bb05ccdafb8a3124d0a66"],"state_sha256":"7a93c0edcc591f0c690b1d2e2a86940b1bc621565f3ac8cc64c22fbbe12fa1e9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"unxwQ66UQH8g0d678kyFAvq+oSco7/A8jrE1le2tKKg0mndFrg21qcIRE3riGZhOdI0IRNKP62FCBHForiZDAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T05:29:47.565101Z","bundle_sha256":"3721c2946928f8a6d8d9f34051caccb96a858c4fb0ce89a267ffecb80ab6296e"}}