{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:FQLV235RQNYKTD2G3I6QCLDDC6","short_pith_number":"pith:FQLV235R","schema_version":"1.0","canonical_sha256":"2c175d6fb18370a98f46da3d012c63179dca4cd30a0c8f02106e1a782bd1d55d","source":{"kind":"arxiv","id":"2605.20988","version":1},"attestation_state":"computed","paper":{"title":"A Sharper Picture of Generalization in Transformers","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Paul Lintilhac, Sair Shaikh","submitted_at":"2026-05-20T10:23:03Z","abstract_excerpt":"We study transformers' generalization behavior on boolean domains from the perspective of the Fourier Spectra of their target functions. In contrast to prior work (Edelman et al., 2022; Trauger and Tewari, 2024), which derived generalization bounds from Rademacher complexity, we investigate the feasibility of obtaining generalization bounds via PAC-Bayes theory. We show that sparse spectra concentrated on low-degree components enable low-sharpness constructions with good generalization properties. Our idea is to show the existence of flat minima implementing any boolean function of sparsity no"},"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":"2605.20988","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-20T10:23:03Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"6866da49403a13ea9bd3056d2516326cd1c3fbf7aa0d5a5be49b72855eab6730","abstract_canon_sha256":"cb92a056490ea9453c2cf6560745f699c4ce2b0ce891347a59b67ca7ad0466cb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-21T01:05:31.236735Z","signature_b64":"uETBSLcEbAyRxhbJ3uJ2cH8/yG15PVCiGWjqIJxuaVAf44Ksigz2vfNA6keVgtmoNK1+RxF1bEbnAggHlwT0Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2c175d6fb18370a98f46da3d012c63179dca4cd30a0c8f02106e1a782bd1d55d","last_reissued_at":"2026-05-21T01:05:31.235933Z","signature_status":"signed_v1","first_computed_at":"2026-05-21T01:05:31.235933Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Sharper Picture of Generalization in Transformers","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Paul Lintilhac, Sair Shaikh","submitted_at":"2026-05-20T10:23:03Z","abstract_excerpt":"We study transformers' generalization behavior on boolean domains from the perspective of the Fourier Spectra of their target functions. In contrast to prior work (Edelman et al., 2022; Trauger and Tewari, 2024), which derived generalization bounds from Rademacher complexity, we investigate the feasibility of obtaining generalization bounds via PAC-Bayes theory. We show that sparse spectra concentrated on low-degree components enable low-sharpness constructions with good generalization properties. Our idea is to show the existence of flat minima implementing any boolean function of sparsity no"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.20988","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/2605.20988/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":"2605.20988","created_at":"2026-05-21T01:05:31.236075+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.20988v1","created_at":"2026-05-21T01:05:31.236075+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.20988","created_at":"2026-05-21T01:05:31.236075+00:00"},{"alias_kind":"pith_short_12","alias_value":"FQLV235RQNYK","created_at":"2026-05-21T01:05:31.236075+00:00"},{"alias_kind":"pith_short_16","alias_value":"FQLV235RQNYKTD2G","created_at":"2026-05-21T01:05:31.236075+00:00"},{"alias_kind":"pith_short_8","alias_value":"FQLV235R","created_at":"2026-05-21T01:05:31.236075+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/FQLV235RQNYKTD2G3I6QCLDDC6","json":"https://pith.science/pith/FQLV235RQNYKTD2G3I6QCLDDC6.json","graph_json":"https://pith.science/api/pith-number/FQLV235RQNYKTD2G3I6QCLDDC6/graph.json","events_json":"https://pith.science/api/pith-number/FQLV235RQNYKTD2G3I6QCLDDC6/events.json","paper":"https://pith.science/paper/FQLV235R"},"agent_actions":{"view_html":"https://pith.science/pith/FQLV235RQNYKTD2G3I6QCLDDC6","download_json":"https://pith.science/pith/FQLV235RQNYKTD2G3I6QCLDDC6.json","view_paper":"https://pith.science/paper/FQLV235R","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.20988&json=true","fetch_graph":"https://pith.science/api/pith-number/FQLV235RQNYKTD2G3I6QCLDDC6/graph.json","fetch_events":"https://pith.science/api/pith-number/FQLV235RQNYKTD2G3I6QCLDDC6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FQLV235RQNYKTD2G3I6QCLDDC6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FQLV235RQNYKTD2G3I6QCLDDC6/action/storage_attestation","attest_author":"https://pith.science/pith/FQLV235RQNYKTD2G3I6QCLDDC6/action/author_attestation","sign_citation":"https://pith.science/pith/FQLV235RQNYKTD2G3I6QCLDDC6/action/citation_signature","submit_replication":"https://pith.science/pith/FQLV235RQNYKTD2G3I6QCLDDC6/action/replication_record"}},"created_at":"2026-05-21T01:05:31.236075+00:00","updated_at":"2026-05-21T01:05:31.236075+00:00"}