{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:2IKP3FYVU7HJY24HHHGDKOQXEL","short_pith_number":"pith:2IKP3FYV","canonical_record":{"source":{"id":"2012.10931","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-12-20T14:16:41Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"b547b4d0561bf64c7dc44d6eff0629f2ac61bcb4775c177ba7da3060547f2223","abstract_canon_sha256":"9f79858109683e5b665985115ba0bda1e0ffb2978a301043f21f9dcd950d9f82"},"schema_version":"1.0"},"canonical_sha256":"d214fd9715a7ce9c6b8739cc353a1722f8bccddb33fe241d353b2816796e45de","source":{"kind":"arxiv","id":"2012.10931","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2012.10931","created_at":"2026-07-05T02:22:06Z"},{"alias_kind":"arxiv_version","alias_value":"2012.10931v2","created_at":"2026-07-05T02:22:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2012.10931","created_at":"2026-07-05T02:22:06Z"},{"alias_kind":"pith_short_12","alias_value":"2IKP3FYVU7HJ","created_at":"2026-07-05T02:22:06Z"},{"alias_kind":"pith_short_16","alias_value":"2IKP3FYVU7HJY24H","created_at":"2026-07-05T02:22:06Z"},{"alias_kind":"pith_short_8","alias_value":"2IKP3FYV","created_at":"2026-07-05T02:22:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:2IKP3FYVU7HJY24HHHGDKOQXEL","target":"record","payload":{"canonical_record":{"source":{"id":"2012.10931","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-12-20T14:16:41Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"b547b4d0561bf64c7dc44d6eff0629f2ac61bcb4775c177ba7da3060547f2223","abstract_canon_sha256":"9f79858109683e5b665985115ba0bda1e0ffb2978a301043f21f9dcd950d9f82"},"schema_version":"1.0"},"canonical_sha256":"d214fd9715a7ce9c6b8739cc353a1722f8bccddb33fe241d353b2816796e45de","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:22:06.817691Z","signature_b64":"ga7+dUgfwlw2PXBJ8fdlkBWhvOvbGhbvsaIlckRp5bA/cCO6YFuPXu1EUhdkRmXSI2G8OqeGGp7GFVthLoivCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d214fd9715a7ce9c6b8739cc353a1722f8bccddb33fe241d353b2816796e45de","last_reissued_at":"2026-07-05T02:22:06.817227Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:22:06.817227Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2012.10931","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T02:22:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bm3TzE3xslYUXMKl05NqvQj+mmot7A5DwB8DUSiWCg6Segubsj1BY5yEXL6fI1U4Oa1qgMPJhJ/OQsGE2S2GAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T06:52:55.315960Z"},"content_sha256":"c50ea1cab34923b03a3fe4f1b205e2bdbb84cd6e9da2008ec476be2f9bc3d542","schema_version":"1.0","event_id":"sha256:c50ea1cab34923b03a3fe4f1b205e2bdbb84cd6e9da2008ec476be2f9bc3d542"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:2IKP3FYVU7HJY24HHHGDKOQXEL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Recent advances in deep learning theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Dacheng Tao, Fengxiang He","submitted_at":"2020-12-20T14:16:41Z","abstract_excerpt":"Deep learning is usually described as an experiment-driven field under continuous criticizes of lacking theoretical foundations. This problem has been partially fixed by a large volume of literature which has so far not been well organized. This paper reviews and organizes the recent advances in deep learning theory. The literature is categorized in six groups: (1) complexity and capacity-based approaches for analyzing the generalizability of deep learning; (2) stochastic differential equations and their dynamic systems for modelling stochastic gradient descent and its variants, which characte"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.10931","kind":"arxiv","version":2},"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/2012.10931/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T02:22:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CJtBA/uucRpU5FuusDsFHj6KMMgNFPKp9U1+BTZMT0faAVTS8THDVYf2VKTr0b8eToedtvjtgyLmaTVg7q3JAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T06:52:55.316456Z"},"content_sha256":"e6b21671c6a867d958d4678ba0293669f0df09b80270936c13c97609940db840","schema_version":"1.0","event_id":"sha256:e6b21671c6a867d958d4678ba0293669f0df09b80270936c13c97609940db840"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2IKP3FYVU7HJY24HHHGDKOQXEL/bundle.json","state_url":"https://pith.science/pith/2IKP3FYVU7HJY24HHHGDKOQXEL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2IKP3FYVU7HJY24HHHGDKOQXEL/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-10T06:52:55Z","links":{"resolver":"https://pith.science/pith/2IKP3FYVU7HJY24HHHGDKOQXEL","bundle":"https://pith.science/pith/2IKP3FYVU7HJY24HHHGDKOQXEL/bundle.json","state":"https://pith.science/pith/2IKP3FYVU7HJY24HHHGDKOQXEL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2IKP3FYVU7HJY24HHHGDKOQXEL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:2IKP3FYVU7HJY24HHHGDKOQXEL","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":"9f79858109683e5b665985115ba0bda1e0ffb2978a301043f21f9dcd950d9f82","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-12-20T14:16:41Z","title_canon_sha256":"b547b4d0561bf64c7dc44d6eff0629f2ac61bcb4775c177ba7da3060547f2223"},"schema_version":"1.0","source":{"id":"2012.10931","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2012.10931","created_at":"2026-07-05T02:22:06Z"},{"alias_kind":"arxiv_version","alias_value":"2012.10931v2","created_at":"2026-07-05T02:22:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2012.10931","created_at":"2026-07-05T02:22:06Z"},{"alias_kind":"pith_short_12","alias_value":"2IKP3FYVU7HJ","created_at":"2026-07-05T02:22:06Z"},{"alias_kind":"pith_short_16","alias_value":"2IKP3FYVU7HJY24H","created_at":"2026-07-05T02:22:06Z"},{"alias_kind":"pith_short_8","alias_value":"2IKP3FYV","created_at":"2026-07-05T02:22:06Z"}],"graph_snapshots":[{"event_id":"sha256:e6b21671c6a867d958d4678ba0293669f0df09b80270936c13c97609940db840","target":"graph","created_at":"2026-07-05T02:22:06Z","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/2012.10931/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Deep learning is usually described as an experiment-driven field under continuous criticizes of lacking theoretical foundations. This problem has been partially fixed by a large volume of literature which has so far not been well organized. This paper reviews and organizes the recent advances in deep learning theory. The literature is categorized in six groups: (1) complexity and capacity-based approaches for analyzing the generalizability of deep learning; (2) stochastic differential equations and their dynamic systems for modelling stochastic gradient descent and its variants, which characte","authors_text":"Dacheng Tao, Fengxiang He","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-12-20T14:16:41Z","title":"Recent advances in deep learning theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.10931","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:c50ea1cab34923b03a3fe4f1b205e2bdbb84cd6e9da2008ec476be2f9bc3d542","target":"record","created_at":"2026-07-05T02:22:06Z","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":"9f79858109683e5b665985115ba0bda1e0ffb2978a301043f21f9dcd950d9f82","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-12-20T14:16:41Z","title_canon_sha256":"b547b4d0561bf64c7dc44d6eff0629f2ac61bcb4775c177ba7da3060547f2223"},"schema_version":"1.0","source":{"id":"2012.10931","kind":"arxiv","version":2}},"canonical_sha256":"d214fd9715a7ce9c6b8739cc353a1722f8bccddb33fe241d353b2816796e45de","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d214fd9715a7ce9c6b8739cc353a1722f8bccddb33fe241d353b2816796e45de","first_computed_at":"2026-07-05T02:22:06.817227Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:22:06.817227Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ga7+dUgfwlw2PXBJ8fdlkBWhvOvbGhbvsaIlckRp5bA/cCO6YFuPXu1EUhdkRmXSI2G8OqeGGp7GFVthLoivCA==","signature_status":"signed_v1","signed_at":"2026-07-05T02:22:06.817691Z","signed_message":"canonical_sha256_bytes"},"source_id":"2012.10931","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c50ea1cab34923b03a3fe4f1b205e2bdbb84cd6e9da2008ec476be2f9bc3d542","sha256:e6b21671c6a867d958d4678ba0293669f0df09b80270936c13c97609940db840"],"state_sha256":"3fa8d46b5ddcedff30a1366527ebacf0d6bc72f7905443dc6ab3f456e3e437d1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MOonm58T5RDIXUfszWKcQocAYoQ/ICo4ri68+Rond1ZIONRTa+NMVdUB1DE9hNEK7YfYbNAKzCON0cSaVy5NAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T06:52:55.319884Z","bundle_sha256":"2329fc5a116d733e12bc3aca8a94f22503f642c1062a2e7fcd9828c066026d7d"}}