{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:3JNLGQBZNTTPZZARRSBLEXXGGQ","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":"c220bc74e99062bb8896016fb0591632addc43a3998af6614741cbf3131b370b","cross_cats_sorted":["cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2023-05-29T14:40:56Z","title_canon_sha256":"c3422caa45f25052b14d26b31d1f854e13d3ab785aad226add5befaf4caa1dfa"},"schema_version":"1.0","source":{"id":"2305.18502","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2305.18502","created_at":"2026-07-05T07:50:50Z"},{"alias_kind":"arxiv_version","alias_value":"2305.18502v2","created_at":"2026-07-05T07:50:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2305.18502","created_at":"2026-07-05T07:50:50Z"},{"alias_kind":"pith_short_12","alias_value":"3JNLGQBZNTTP","created_at":"2026-07-05T07:50:50Z"},{"alias_kind":"pith_short_16","alias_value":"3JNLGQBZNTTPZZAR","created_at":"2026-07-05T07:50:50Z"},{"alias_kind":"pith_short_8","alias_value":"3JNLGQBZ","created_at":"2026-07-05T07:50:50Z"}],"graph_snapshots":[{"event_id":"sha256:e586362d8a802217a1ed7b2f6710cdca846577b2f7c8c636dd415891c4c814ab","target":"graph","created_at":"2026-07-05T07:50:50Z","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/2305.18502/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This study explores the sample complexity for two-layer neural networks to learn a generalized linear target function under Stochastic Gradient Descent (SGD), focusing on the challenging regime where many flat directions are present at initialization. It is well-established that in this scenario $n=O(d \\log d)$ samples are typically needed. However, we provide precise results concerning the pre-factors in high-dimensional contexts and for varying widths. Notably, our findings suggest that overparameterization can only enhance convergence by a constant factor within this problem class. These in","authors_text":"Bruno Loureiro, Florent Krzakala, Luca Arnaboldi, Ludovic Stephan","cross_cats":["cs.LG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2023-05-29T14:40:56Z","title":"Escaping mediocrity: how two-layer networks learn hard generalized linear models with SGD"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.18502","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":"sha256:432f9a999a3e02a644c2f76bb5ef09dd12a55db00baba3c4c44f64e405057e70","target":"record","created_at":"2026-07-05T07:50:50Z","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":"c220bc74e99062bb8896016fb0591632addc43a3998af6614741cbf3131b370b","cross_cats_sorted":["cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2023-05-29T14:40:56Z","title_canon_sha256":"c3422caa45f25052b14d26b31d1f854e13d3ab785aad226add5befaf4caa1dfa"},"schema_version":"1.0","source":{"id":"2305.18502","kind":"arxiv","version":2}},"canonical_sha256":"da5ab340396ce6fce4118c82b25ee6342eb3eae9837668258ced95ef19687268","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"da5ab340396ce6fce4118c82b25ee6342eb3eae9837668258ced95ef19687268","first_computed_at":"2026-07-05T07:50:50.084721Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:50:50.084721Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gihol9NlVEVMT9mhN8U+JuvxTYNSziHjbHuwT1iE/EcA+t4GEq1Kc0MKbV718MAFEJYTgdhFPWZC25YeYu/0AA==","signature_status":"signed_v1","signed_at":"2026-07-05T07:50:50.085229Z","signed_message":"canonical_sha256_bytes"},"source_id":"2305.18502","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:432f9a999a3e02a644c2f76bb5ef09dd12a55db00baba3c4c44f64e405057e70","sha256:e586362d8a802217a1ed7b2f6710cdca846577b2f7c8c636dd415891c4c814ab"],"state_sha256":"874a9a233b099346ec7aa04debba8ea75397a910d8ecabdcd095bb2a85578c93"}