{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:V3ZUVYL4SZ3K5NJTLTPMLCII66","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":"1d21d0ff0ec5d4981241c58d617f18a9643f6cf8ddef72bf480238f179b19640","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-02-08T11:23:11Z","title_canon_sha256":"2219a57ced1ca304467d72744139ac436a93fd85059ee4147e985fd09970587f"},"schema_version":"1.0","source":{"id":"2402.05576","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2402.05576","created_at":"2026-05-18T03:09:47Z"},{"alias_kind":"arxiv_version","alias_value":"2402.05576v4","created_at":"2026-05-18T03:09:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.05576","created_at":"2026-05-18T03:09:47Z"},{"alias_kind":"pith_short_12","alias_value":"V3ZUVYL4SZ3K","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"V3ZUVYL4SZ3K5NJT","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"V3ZUVYL4","created_at":"2026-05-18T12:33:37Z"}],"graph_snapshots":[{"event_id":"sha256:c3a3edd062ea328826e59c10c22dff83858f2464b7187e4ebef0cd832ae5c4ab","target":"graph","created_at":"2026-05-18T03:09:47Z","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"},"paper":{"abstract_excerpt":"Machine learning models with inputs in a Euclidean space $\\mathbb{R}^d$, when implemented on digital computers, generalize, and their generalization gap converges to $0$ at a rate of $c/N^{1/2}$ concerning the sample size $N$. However, the constant $c>0$ obtained through classical methods can be large in terms of the ambient dimension $d$ and machine precision, posing a challenge when $N$ is small to realistically large. In this paper, we derive a family of generalization bounds $\\{c_m/N^{1/(2\\vee m)}\\}_{m=1}^{\\infty}$ tailored for learning models on digital computers, which adapt to both the ","authors_text":"A. Martina Neuman, Anastasis Kratsios, Gudmund Pammer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-02-08T11:23:11Z","title":"Tighter Learning Guarantees on Digital Computers via Concentration of Measure on Finite Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.05576","kind":"arxiv","version":4},"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":"sha256:9709ca304850328dd0197c8e17c502b14122686e853fa4642215d8fa75112200","target":"record","created_at":"2026-05-18T03:09:47Z","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":"1d21d0ff0ec5d4981241c58d617f18a9643f6cf8ddef72bf480238f179b19640","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-02-08T11:23:11Z","title_canon_sha256":"2219a57ced1ca304467d72744139ac436a93fd85059ee4147e985fd09970587f"},"schema_version":"1.0","source":{"id":"2402.05576","kind":"arxiv","version":4}},"canonical_sha256":"aef34ae17c9676aeb5335cdec58908f7a677bbb6d241bc0ef060f641b12c6409","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aef34ae17c9676aeb5335cdec58908f7a677bbb6d241bc0ef060f641b12c6409","first_computed_at":"2026-05-18T03:09:47.018745Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:09:47.018745Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IaiNRVoNrIabNOBVvwsedI9epKnQBEY2/8gEstOVJC0oLllXc/tnjfizrD1y6sHbMzNZWzQO8Ai5r4SbTGQHAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:09:47.019503Z","signed_message":"canonical_sha256_bytes"},"source_id":"2402.05576","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9709ca304850328dd0197c8e17c502b14122686e853fa4642215d8fa75112200","sha256:c3a3edd062ea328826e59c10c22dff83858f2464b7187e4ebef0cd832ae5c4ab"],"state_sha256":"56741865bdf18a8d100ab5f348a45ad8bf418f54d09978553d794a5920f719fd"}