{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:V62ZN5TO23K3BM7BPLRP5LMFF4","short_pith_number":"pith:V62ZN5TO","canonical_record":{"source":{"id":"2002.02247","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2020-02-06T13:25:26Z","cross_cats_sorted":["cs.LG","math.PR"],"title_canon_sha256":"2407032127bc89a08031f4132adb3a9c6686bb87620ba6a5b0b959f68420b65a","abstract_canon_sha256":"15dd3726d59f05451b481c47b673f5851f2e7dbaa7b81dee906e6671aa10cdab"},"schema_version":"1.0"},"canonical_sha256":"afb596f66ed6d5b0b3e17ae2fead852f08585f470239e1558dc4bf3288a55c3f","source":{"kind":"arxiv","id":"2002.02247","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2002.02247","created_at":"2026-07-05T05:53:45Z"},{"alias_kind":"arxiv_version","alias_value":"2002.02247v2","created_at":"2026-07-05T05:53:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2002.02247","created_at":"2026-07-05T05:53:45Z"},{"alias_kind":"pith_short_12","alias_value":"V62ZN5TO23K3","created_at":"2026-07-05T05:53:45Z"},{"alias_kind":"pith_short_16","alias_value":"V62ZN5TO23K3BM7B","created_at":"2026-07-05T05:53:45Z"},{"alias_kind":"pith_short_8","alias_value":"V62ZN5TO","created_at":"2026-07-05T05:53:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:V62ZN5TO23K3BM7BPLRP5LMFF4","target":"record","payload":{"canonical_record":{"source":{"id":"2002.02247","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2020-02-06T13:25:26Z","cross_cats_sorted":["cs.LG","math.PR"],"title_canon_sha256":"2407032127bc89a08031f4132adb3a9c6686bb87620ba6a5b0b959f68420b65a","abstract_canon_sha256":"15dd3726d59f05451b481c47b673f5851f2e7dbaa7b81dee906e6671aa10cdab"},"schema_version":"1.0"},"canonical_sha256":"afb596f66ed6d5b0b3e17ae2fead852f08585f470239e1558dc4bf3288a55c3f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:53:45.603460Z","signature_b64":"Mdkiv23A27g1O/Zs41CEYHo5PoOcNvQQifbwcEC3sWmhIsWGWq9QGrkkhtNjHeBeGWNOXvm+ILvd50X8diPMDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"afb596f66ed6d5b0b3e17ae2fead852f08585f470239e1558dc4bf3288a55c3f","last_reissued_at":"2026-07-05T05:53:45.603110Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:53:45.603110Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2002.02247","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":"2026-07-05T05:53:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6zlU384IT7ssZrjyI93BpTrh9zqONBpYlEfbBqgdBtM0yMHujoZJNud32Ke7fxomFoQVvBmy6CC9h2LLx5sZCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T09:24:04.301475Z"},"content_sha256":"f153d0d64841351c6e58a055adefdfdd36f281775d547ee800c9a3fe05043bc9","schema_version":"1.0","event_id":"sha256:f153d0d64841351c6e58a055adefdfdd36f281775d547ee800c9a3fe05043bc9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:V62ZN5TO23K3BM7BPLRP5LMFF4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Almost Sure Convergence of Dropout Algorithms for Neural Networks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG","math.PR"],"primary_cat":"math.OC","authors_text":"Albert Senen-Cerda, Jaron Sanders","submitted_at":"2020-02-06T13:25:26Z","abstract_excerpt":"We investigate the convergence and convergence rate of stochastic training algorithms for Neural Networks (NNs) that have been inspired by Dropout (Hinton et al., 2012). With the goal of avoiding overfitting during training of NNs, dropout algorithms consist in practice of multiplying the weight matrices of a NN componentwise by independently drawn random matrices with $\\{0, 1 \\}$-valued entries during each iteration of Stochastic Gradient Descent (SGD). This paper presents a probability theoretical proof that for fully-connected NNs with differentiable, polynomially bounded activation functio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2002.02247","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/2002.02247/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":"2026-07-05T05:53:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NARUEKlD2nx5s3OeqbUcaZFoq5Chac81mppCOjKfrzLu7No7xVuB6Gq5sGZgItYOKPsVczNM2aIlEc4jyFzAAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T09:24:04.302578Z"},"content_sha256":"3fc24e2dbc5ca45aca0d081abd4a3bd3af5bdb65fc9ccbb91fac2c4ce917e77a","schema_version":"1.0","event_id":"sha256:3fc24e2dbc5ca45aca0d081abd4a3bd3af5bdb65fc9ccbb91fac2c4ce917e77a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V62ZN5TO23K3BM7BPLRP5LMFF4/bundle.json","state_url":"https://pith.science/pith/V62ZN5TO23K3BM7BPLRP5LMFF4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V62ZN5TO23K3BM7BPLRP5LMFF4/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":"2026-08-10T09:24:04Z","links":{"resolver":"https://pith.science/pith/V62ZN5TO23K3BM7BPLRP5LMFF4","bundle":"https://pith.science/pith/V62ZN5TO23K3BM7BPLRP5LMFF4/bundle.json","state":"https://pith.science/pith/V62ZN5TO23K3BM7BPLRP5LMFF4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V62ZN5TO23K3BM7BPLRP5LMFF4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:V62ZN5TO23K3BM7BPLRP5LMFF4","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":"15dd3726d59f05451b481c47b673f5851f2e7dbaa7b81dee906e6671aa10cdab","cross_cats_sorted":["cs.LG","math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2020-02-06T13:25:26Z","title_canon_sha256":"2407032127bc89a08031f4132adb3a9c6686bb87620ba6a5b0b959f68420b65a"},"schema_version":"1.0","source":{"id":"2002.02247","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2002.02247","created_at":"2026-07-05T05:53:45Z"},{"alias_kind":"arxiv_version","alias_value":"2002.02247v2","created_at":"2026-07-05T05:53:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2002.02247","created_at":"2026-07-05T05:53:45Z"},{"alias_kind":"pith_short_12","alias_value":"V62ZN5TO23K3","created_at":"2026-07-05T05:53:45Z"},{"alias_kind":"pith_short_16","alias_value":"V62ZN5TO23K3BM7B","created_at":"2026-07-05T05:53:45Z"},{"alias_kind":"pith_short_8","alias_value":"V62ZN5TO","created_at":"2026-07-05T05:53:45Z"}],"graph_snapshots":[{"event_id":"sha256:3fc24e2dbc5ca45aca0d081abd4a3bd3af5bdb65fc9ccbb91fac2c4ce917e77a","target":"graph","created_at":"2026-07-05T05:53:45Z","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/2002.02247/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate the convergence and convergence rate of stochastic training algorithms for Neural Networks (NNs) that have been inspired by Dropout (Hinton et al., 2012). With the goal of avoiding overfitting during training of NNs, dropout algorithms consist in practice of multiplying the weight matrices of a NN componentwise by independently drawn random matrices with $\\{0, 1 \\}$-valued entries during each iteration of Stochastic Gradient Descent (SGD). This paper presents a probability theoretical proof that for fully-connected NNs with differentiable, polynomially bounded activation functio","authors_text":"Albert Senen-Cerda, Jaron Sanders","cross_cats":["cs.LG","math.PR"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2020-02-06T13:25:26Z","title":"Almost Sure Convergence of Dropout Algorithms for Neural Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2002.02247","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:f153d0d64841351c6e58a055adefdfdd36f281775d547ee800c9a3fe05043bc9","target":"record","created_at":"2026-07-05T05:53:45Z","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":"15dd3726d59f05451b481c47b673f5851f2e7dbaa7b81dee906e6671aa10cdab","cross_cats_sorted":["cs.LG","math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2020-02-06T13:25:26Z","title_canon_sha256":"2407032127bc89a08031f4132adb3a9c6686bb87620ba6a5b0b959f68420b65a"},"schema_version":"1.0","source":{"id":"2002.02247","kind":"arxiv","version":2}},"canonical_sha256":"afb596f66ed6d5b0b3e17ae2fead852f08585f470239e1558dc4bf3288a55c3f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"afb596f66ed6d5b0b3e17ae2fead852f08585f470239e1558dc4bf3288a55c3f","first_computed_at":"2026-07-05T05:53:45.603110Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:53:45.603110Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Mdkiv23A27g1O/Zs41CEYHo5PoOcNvQQifbwcEC3sWmhIsWGWq9QGrkkhtNjHeBeGWNOXvm+ILvd50X8diPMDA==","signature_status":"signed_v1","signed_at":"2026-07-05T05:53:45.603460Z","signed_message":"canonical_sha256_bytes"},"source_id":"2002.02247","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f153d0d64841351c6e58a055adefdfdd36f281775d547ee800c9a3fe05043bc9","sha256:3fc24e2dbc5ca45aca0d081abd4a3bd3af5bdb65fc9ccbb91fac2c4ce917e77a"],"state_sha256":"ace307bbf9d2f3d71910510c68f5b058bcbf8b996ae378bf54df42dca91cbc52"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UduXV+iTlZ2EHqrMVXNA5RLub384lpO9GltnkykCOiycjAEF39/Tmed5rMAjTfz+8Vj6Q8tED/zWXq8O1+QaDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T09:24:04.309171Z","bundle_sha256":"45037e8bdf328834228a3eeed7d0394ebf1fa6d981ce5aa450e63c188191b454"}}