{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:M335HHJR64CPZ7TB4WNGKRSQKC","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":"ade41adb710809e255ef537dc66989c5995b27a021ca208bf714594aa0593a4c","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-08-28T15:21:19Z","title_canon_sha256":"3c94d317025ec7e1d8e3711133a35c0bf0802927a714cc21f0a684d25b7fab35"},"schema_version":"1.0","source":{"id":"2008.12702","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2008.12702","created_at":"2026-07-05T02:18:55Z"},{"alias_kind":"arxiv_version","alias_value":"2008.12702v2","created_at":"2026-07-05T02:18:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2008.12702","created_at":"2026-07-05T02:18:55Z"},{"alias_kind":"pith_short_12","alias_value":"M335HHJR64CP","created_at":"2026-07-05T02:18:55Z"},{"alias_kind":"pith_short_16","alias_value":"M335HHJR64CPZ7TB","created_at":"2026-07-05T02:18:55Z"},{"alias_kind":"pith_short_8","alias_value":"M335HHJR","created_at":"2026-07-05T02:18:55Z"}],"graph_snapshots":[{"event_id":"sha256:b4c0c830b284290c2cb41b2396de62854b3462c68c16d48bac344a1fa7667b0e","target":"graph","created_at":"2026-07-05T02:18:55Z","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/2008.12702/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Deep learning of the Artificial Neural Networks (ANN) can be treated as a particular class of interpolation problems. The goal is to find a neural network whose input-output map approximates well the desired map on a finite or an infinite training set. Our idea consists of taking as an approximant the input-output map, which arises from a nonlinear continuous-time control system. In the limit such control system can be seen as a network with a continuum of layers, each one labelled by the time variable. The values of the controls at each instant of time are the parameters of the layer.","authors_text":"Andrei Agrachev, Andrey Sarychev","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-08-28T15:21:19Z","title":"Control on the Manifolds of Mappings with a View to the Deep Learning"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.12702","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:c092fd1b99eeeea32e8d320cb906f911e12f3338c3b008f4b5aa7731d6b23c97","target":"record","created_at":"2026-07-05T02:18:55Z","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":"ade41adb710809e255ef537dc66989c5995b27a021ca208bf714594aa0593a4c","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-08-28T15:21:19Z","title_canon_sha256":"3c94d317025ec7e1d8e3711133a35c0bf0802927a714cc21f0a684d25b7fab35"},"schema_version":"1.0","source":{"id":"2008.12702","kind":"arxiv","version":2}},"canonical_sha256":"66f7d39d31f704fcfe61e59a65465050b9ddec6acb1f5468f9d29ef49a568594","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"66f7d39d31f704fcfe61e59a65465050b9ddec6acb1f5468f9d29ef49a568594","first_computed_at":"2026-07-05T02:18:55.085173Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:18:55.085173Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TnP9LlpMBevFXYFHbFQlpBl3KA0HnI19NVPFKEdEEmOqN1w6goc/oR42QIvLBIQlnnYQA56Fd2XwKNXwY0mDAA==","signature_status":"signed_v1","signed_at":"2026-07-05T02:18:55.085650Z","signed_message":"canonical_sha256_bytes"},"source_id":"2008.12702","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c092fd1b99eeeea32e8d320cb906f911e12f3338c3b008f4b5aa7731d6b23c97","sha256:b4c0c830b284290c2cb41b2396de62854b3462c68c16d48bac344a1fa7667b0e"],"state_sha256":"4baf414b8a73ac4414be13b672fd0e589683e6730e0b7c17c7383a3fee14a3cf"}