{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:2BCEDVT3WOXEMTBGIUJISANF5O","short_pith_number":"pith:2BCEDVT3","canonical_record":{"source":{"id":"2607.23333","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-25T19:11:15Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"09d90817ed083202552767db5bc27dc8d2e4a490db473d33796de30fd282e182","abstract_canon_sha256":"068d36beb51bccf7c74a4604f3ca05960c3dc87586c363eed29ad7ea31c1d221"},"schema_version":"1.0"},"canonical_sha256":"d04441d67bb3ae464c2645128901a5ebb2765e284491033927d1f50515748048","source":{"kind":"arxiv","id":"2607.23333","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.23333","created_at":"2026-07-28T01:22:48Z"},{"alias_kind":"arxiv_version","alias_value":"2607.23333v1","created_at":"2026-07-28T01:22:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.23333","created_at":"2026-07-28T01:22:48Z"},{"alias_kind":"pith_short_12","alias_value":"2BCEDVT3WOXE","created_at":"2026-07-28T01:22:48Z"},{"alias_kind":"pith_short_16","alias_value":"2BCEDVT3WOXEMTBG","created_at":"2026-07-28T01:22:48Z"},{"alias_kind":"pith_short_8","alias_value":"2BCEDVT3","created_at":"2026-07-28T01:22:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:2BCEDVT3WOXEMTBGIUJISANF5O","target":"record","payload":{"canonical_record":{"source":{"id":"2607.23333","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-25T19:11:15Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"09d90817ed083202552767db5bc27dc8d2e4a490db473d33796de30fd282e182","abstract_canon_sha256":"068d36beb51bccf7c74a4604f3ca05960c3dc87586c363eed29ad7ea31c1d221"},"schema_version":"1.0"},"canonical_sha256":"d04441d67bb3ae464c2645128901a5ebb2765e284491033927d1f50515748048","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-28T01:22:48.133467Z","signature_b64":"plG0SEmkgQxb1DQrGmYV1CfAJlYtRJeAsFvP51aaitMkdwH45W/vJFUDq6Y844zogvhl7C7VH1wmrmo4iRwZAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d04441d67bb3ae464c2645128901a5ebb2765e284491033927d1f50515748048","last_reissued_at":"2026-07-28T01:22:48.132727Z","signature_status":"signed_v1","first_computed_at":"2026-07-28T01:22:48.132727Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.23333","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":"2026-07-28T01:22:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Gmn1NdtYYb8SuGpKonAeA3qG2bFQMEt97/tSzEZJhz6pRyG301yw7qXHnJvcl37sVtTPPSI2MCzRcCWjoBQ1DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-01T15:12:49.923549Z"},"content_sha256":"62543c1c2a6d31b6e0c73d73fc6c1212f36f818b77d4eed2b4a4fbdaaee0b357","schema_version":"1.0","event_id":"sha256:62543c1c2a6d31b6e0c73d73fc6c1212f36f818b77d4eed2b4a4fbdaaee0b357"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:2BCEDVT3WOXEMTBGIUJISANF5O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Training with (Swap) Regret Loss in a Single-Layer Self-Attention Model: A Case Study on the Probability Simplex","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Asuman Ozdaglar, Chanwoo Park","submitted_at":"2026-07-25T19:11:15Z","abstract_excerpt":"We revisit the regret loss framework introduced in Park et al. (2025), which uses decision-theoretic regret as a direct loss function for training models to make better decisions, through the lens of probability-simplex policies. Our first result shows that a single-layer self-attention model trained with regret loss admits a stationary point whose forward-pass exactly matches smoothed fictitious play with the appropriate stepsize that ensures no-regret behavior-i.e., for any given policy input, the model outputs the same update that smoothed fictitious play would produce. In parallel, we also"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.23333","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/2607.23333/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":"2026-07-28T01:22:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qd0a5bmAzd5pqpoK2Omd2jhxTMupou7P+XZQDA4USBXcSKDuRoLj3U91MAted/Eqqi9WYHiQgxb6reUWwTGrCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-01T15:12:49.924129Z"},"content_sha256":"0dacf7e64f575340f1a9239981cc8a6b5af9b566cbd93df07d822d71a7a32b71","schema_version":"1.0","event_id":"sha256:0dacf7e64f575340f1a9239981cc8a6b5af9b566cbd93df07d822d71a7a32b71"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2BCEDVT3WOXEMTBGIUJISANF5O/bundle.json","state_url":"https://pith.science/pith/2BCEDVT3WOXEMTBGIUJISANF5O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2BCEDVT3WOXEMTBGIUJISANF5O/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":"2026-08-01T15:12:49Z","links":{"resolver":"https://pith.science/pith/2BCEDVT3WOXEMTBGIUJISANF5O","bundle":"https://pith.science/pith/2BCEDVT3WOXEMTBGIUJISANF5O/bundle.json","state":"https://pith.science/pith/2BCEDVT3WOXEMTBGIUJISANF5O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2BCEDVT3WOXEMTBGIUJISANF5O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:2BCEDVT3WOXEMTBGIUJISANF5O","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":"068d36beb51bccf7c74a4604f3ca05960c3dc87586c363eed29ad7ea31c1d221","cross_cats_sorted":["cs.AI"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-25T19:11:15Z","title_canon_sha256":"09d90817ed083202552767db5bc27dc8d2e4a490db473d33796de30fd282e182"},"schema_version":"1.0","source":{"id":"2607.23333","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.23333","created_at":"2026-07-28T01:22:48Z"},{"alias_kind":"arxiv_version","alias_value":"2607.23333v1","created_at":"2026-07-28T01:22:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.23333","created_at":"2026-07-28T01:22:48Z"},{"alias_kind":"pith_short_12","alias_value":"2BCEDVT3WOXE","created_at":"2026-07-28T01:22:48Z"},{"alias_kind":"pith_short_16","alias_value":"2BCEDVT3WOXEMTBG","created_at":"2026-07-28T01:22:48Z"},{"alias_kind":"pith_short_8","alias_value":"2BCEDVT3","created_at":"2026-07-28T01:22:48Z"}],"graph_snapshots":[{"event_id":"sha256:0dacf7e64f575340f1a9239981cc8a6b5af9b566cbd93df07d822d71a7a32b71","target":"graph","created_at":"2026-07-28T01:22:48Z","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/2607.23333/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We revisit the regret loss framework introduced in Park et al. (2025), which uses decision-theoretic regret as a direct loss function for training models to make better decisions, through the lens of probability-simplex policies. Our first result shows that a single-layer self-attention model trained with regret loss admits a stationary point whose forward-pass exactly matches smoothed fictitious play with the appropriate stepsize that ensures no-regret behavior-i.e., for any given policy input, the model outputs the same update that smoothed fictitious play would produce. In parallel, we also","authors_text":"Asuman Ozdaglar, Chanwoo Park","cross_cats":["cs.AI"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-25T19:11:15Z","title":"Training with (Swap) Regret Loss in a Single-Layer Self-Attention Model: A Case Study on the Probability Simplex"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.23333","kind":"arxiv","version":1},"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":"sha256:62543c1c2a6d31b6e0c73d73fc6c1212f36f818b77d4eed2b4a4fbdaaee0b357","target":"record","created_at":"2026-07-28T01:22:48Z","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":"068d36beb51bccf7c74a4604f3ca05960c3dc87586c363eed29ad7ea31c1d221","cross_cats_sorted":["cs.AI"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-25T19:11:15Z","title_canon_sha256":"09d90817ed083202552767db5bc27dc8d2e4a490db473d33796de30fd282e182"},"schema_version":"1.0","source":{"id":"2607.23333","kind":"arxiv","version":1}},"canonical_sha256":"d04441d67bb3ae464c2645128901a5ebb2765e284491033927d1f50515748048","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d04441d67bb3ae464c2645128901a5ebb2765e284491033927d1f50515748048","first_computed_at":"2026-07-28T01:22:48.132727Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-28T01:22:48.132727Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"plG0SEmkgQxb1DQrGmYV1CfAJlYtRJeAsFvP51aaitMkdwH45W/vJFUDq6Y844zogvhl7C7VH1wmrmo4iRwZAA==","signature_status":"signed_v1","signed_at":"2026-07-28T01:22:48.133467Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.23333","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:62543c1c2a6d31b6e0c73d73fc6c1212f36f818b77d4eed2b4a4fbdaaee0b357","sha256:0dacf7e64f575340f1a9239981cc8a6b5af9b566cbd93df07d822d71a7a32b71"],"state_sha256":"7d728f5e6f49811139f31b26d6bcfaf4f5df3d8c45e972e18551829da7b78451"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"82pH21MKZ/dkS9O7ql5sBYIE3o3uZ2XZD8C7G9Ez0FSIWID7pKey7XEj0BplP73/Vhz1RMrSer/lq06vQOv0Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-01T15:12:49.929856Z","bundle_sha256":"6d53f1a6b577b70b4f45ee6ff01b5040d4b2abb706bed25c8689d6ec4ef706cd"}}