{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2004:7DSRXRC73RHKDNOG3Y5ACSBLOJ","short_pith_number":"pith:7DSRXRC7","schema_version":"1.0","canonical_sha256":"f8e51bc45fdc4ea1b5c6de3a01482b72603270236a8bea72324983aa7f9e3cb8","source":{"kind":"arxiv","id":"cs/0411099","version":1},"attestation_state":"computed","paper":{"title":"A Note on the PAC Bayesian Theorem","license":"","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Andreas Maurer","submitted_at":"2004-11-30T08:36:59Z","abstract_excerpt":"We prove general exponential moment inequalities for averages of [0,1]-valued iid random variables and use them to tighten the PAC Bayesian Theorem. The logarithmic dependence on the sample count in the enumerator of the PAC Bayesian bound is halved."},"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":"cs/0411099","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cs.LG","submitted_at":"2004-11-30T08:36:59Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"21061ad9cc3d6380ba088509482086e528c93ad1da212d32ab60151d0d192411","abstract_canon_sha256":"473a045919e3f4ae9258f5963a5f2eb15a3510def167a2324ceb442496ff73d0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:24:49.530918Z","signature_b64":"Kc8T41vhW4vRUz31QUYAiAFeJDDPlreWlGcV6irWbiayvUSTwJxpHaRJ4WtWHSCftr4H6/4BYgDCpFp5QInuDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f8e51bc45fdc4ea1b5c6de3a01482b72603270236a8bea72324983aa7f9e3cb8","last_reissued_at":"2026-07-04T14:24:49.530514Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:24:49.530514Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Note on the PAC Bayesian Theorem","license":"","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Andreas Maurer","submitted_at":"2004-11-30T08:36:59Z","abstract_excerpt":"We prove general exponential moment inequalities for averages of [0,1]-valued iid random variables and use them to tighten the PAC Bayesian Theorem. The logarithmic dependence on the sample count in the enumerator of the PAC Bayesian bound is halved."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cs/0411099","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/cs/0411099/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":"cs/0411099","created_at":"2026-07-04T14:24:49.530579+00:00"},{"alias_kind":"arxiv_version","alias_value":"cs/0411099v1","created_at":"2026-07-04T14:24:49.530579+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cs/0411099","created_at":"2026-07-04T14:24:49.530579+00:00"},{"alias_kind":"pith_short_12","alias_value":"7DSRXRC73RHK","created_at":"2026-07-04T14:24:49.530579+00:00"},{"alias_kind":"pith_short_16","alias_value":"7DSRXRC73RHKDNOG","created_at":"2026-07-04T14:24:49.530579+00:00"},{"alias_kind":"pith_short_8","alias_value":"7DSRXRC7","created_at":"2026-07-04T14:24:49.530579+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":6,"internal_anchor_count":6,"sample":[{"citing_arxiv_id":"2606.01340","citing_title":"Sample Complexity and Decision-Theoretic Guarantees for Bayesian Model Averaging over Decision Trees with Catalan-Exponential Priors","ref_index":26,"is_internal_anchor":true},{"citing_arxiv_id":"2606.28281","citing_title":"PAC-Bayesian Certificates for Quadratic Closed-Loop Control","ref_index":11,"is_internal_anchor":true},{"citing_arxiv_id":"2310.11203","citing_title":"Federated Learning with Nonvacuous Generalisation Bounds","ref_index":37,"is_internal_anchor":true},{"citing_arxiv_id":"2605.17118","citing_title":"Differentiable Optimization Layers for Guaranteed Fairness in Deep Learning","ref_index":104,"is_internal_anchor":true},{"citing_arxiv_id":"2605.18598","citing_title":"Pointwise Generalization in Deep Neural Networks","ref_index":16,"is_internal_anchor":true},{"citing_arxiv_id":"2605.15416","citing_title":"Margin-Adaptive Confidence Ranking for Reliable LLM Judgement","ref_index":229,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7DSRXRC73RHKDNOG3Y5ACSBLOJ","json":"https://pith.science/pith/7DSRXRC73RHKDNOG3Y5ACSBLOJ.json","graph_json":"https://pith.science/api/pith-number/7DSRXRC73RHKDNOG3Y5ACSBLOJ/graph.json","events_json":"https://pith.science/api/pith-number/7DSRXRC73RHKDNOG3Y5ACSBLOJ/events.json","paper":"https://pith.science/paper/7DSRXRC7"},"agent_actions":{"view_html":"https://pith.science/pith/7DSRXRC73RHKDNOG3Y5ACSBLOJ","download_json":"https://pith.science/pith/7DSRXRC73RHKDNOG3Y5ACSBLOJ.json","view_paper":"https://pith.science/paper/7DSRXRC7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=cs/0411099&json=true","fetch_graph":"https://pith.science/api/pith-number/7DSRXRC73RHKDNOG3Y5ACSBLOJ/graph.json","fetch_events":"https://pith.science/api/pith-number/7DSRXRC73RHKDNOG3Y5ACSBLOJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7DSRXRC73RHKDNOG3Y5ACSBLOJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7DSRXRC73RHKDNOG3Y5ACSBLOJ/action/storage_attestation","attest_author":"https://pith.science/pith/7DSRXRC73RHKDNOG3Y5ACSBLOJ/action/author_attestation","sign_citation":"https://pith.science/pith/7DSRXRC73RHKDNOG3Y5ACSBLOJ/action/citation_signature","submit_replication":"https://pith.science/pith/7DSRXRC73RHKDNOG3Y5ACSBLOJ/action/replication_record"}},"created_at":"2026-07-04T14:24:49.530579+00:00","updated_at":"2026-07-04T14:24:49.530579+00:00"}