{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:DJLO33U7VR44QUYGAPRDI2ENAD","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":"9e64080957648641c9674c081c8514447ef0403ed03fe57c5908b2b95c5865a0","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-03-03T15:36:01Z","title_canon_sha256":"4b8a62738a8d99781584007a281ee76551c52dc77d6872a9d49382a2512a8206"},"schema_version":"1.0","source":{"id":"2503.01660","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.01660","created_at":"2026-07-05T10:23:11Z"},{"alias_kind":"arxiv_version","alias_value":"2503.01660v1","created_at":"2026-07-05T10:23:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.01660","created_at":"2026-07-05T10:23:11Z"},{"alias_kind":"pith_short_12","alias_value":"DJLO33U7VR44","created_at":"2026-07-05T10:23:11Z"},{"alias_kind":"pith_short_16","alias_value":"DJLO33U7VR44QUYG","created_at":"2026-07-05T10:23:11Z"},{"alias_kind":"pith_short_8","alias_value":"DJLO33U7","created_at":"2026-07-05T10:23:11Z"}],"graph_snapshots":[{"event_id":"sha256:f553198fe02b07e9332ab8246211e3aa45dd80366c271b10a55674d393c707bb","target":"graph","created_at":"2026-07-05T10:23:11Z","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/2503.01660/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Despite the omnipresent use of stochastic gradient descent (SGD) optimization methods in the training of deep neural networks (DNNs), it remains, in basically all practically relevant scenarios, a fundamental open problem to provide a rigorous theoretical explanation for the success (and the limitations) of SGD optimization methods in deep learning. In particular, it remains an open question to prove or disprove convergence of the true risk of SGD optimization methods to the optimal true risk value in the training of DNNs. In one of the main results of this work we reveal for a general class o","authors_text":"Adrian Riekert, Arnulf Jentzen, Thang Do","cross_cats":["cs.NA","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-03-03T15:36:01Z","title":"Non-convergence to the optimal risk for Adam and stochastic gradient descent optimization in the training of deep neural networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.01660","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":"sha256:8c6b637ea8821f179ab4e51baad0d376125b5cd806c4a8d8e8ffaf68f80f6055","target":"record","created_at":"2026-07-05T10:23:11Z","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":"9e64080957648641c9674c081c8514447ef0403ed03fe57c5908b2b95c5865a0","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-03-03T15:36:01Z","title_canon_sha256":"4b8a62738a8d99781584007a281ee76551c52dc77d6872a9d49382a2512a8206"},"schema_version":"1.0","source":{"id":"2503.01660","kind":"arxiv","version":1}},"canonical_sha256":"1a56edee9fac79c8530603e234688d00c044156468615c9484bd33aa28de02a0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1a56edee9fac79c8530603e234688d00c044156468615c9484bd33aa28de02a0","first_computed_at":"2026-07-05T10:23:11.834056Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:23:11.834056Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iL1tFC0i5AIBpTUnyXKXM7xEHiAjQ7IJJEb16ZgTfECBeiUlBbMVpPSuc/45wQzgspTDb532meHwQ3b36HFPBg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:23:11.834690Z","signed_message":"canonical_sha256_bytes"},"source_id":"2503.01660","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8c6b637ea8821f179ab4e51baad0d376125b5cd806c4a8d8e8ffaf68f80f6055","sha256:f553198fe02b07e9332ab8246211e3aa45dd80366c271b10a55674d393c707bb"],"state_sha256":"a14fdf072a7f4d74bf6d23f209dbf9945e26397aec83ff479a87f8d61dcd08ec"}