{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:TNBFWS4IUY2VVGB6AJBNGQ5FSI","short_pith_number":"pith:TNBFWS4I","canonical_record":{"source":{"id":"1902.03793","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-02-11T09:53:13Z","cross_cats_sorted":[],"title_canon_sha256":"779749e97e7d5c5438972d053388b58f74fdf61de4956f6358e9417f898f4a2f","abstract_canon_sha256":"6da7d7eedc2b71f97fd82326bcf0c672fd433efaf6e0b07f0687561ea8362e97"},"schema_version":"1.0"},"canonical_sha256":"9b425b4b88a6355a983e0242d343a5920fccbc9d3e9ca2e8e453f7292ccde250","source":{"kind":"arxiv","id":"1902.03793","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.03793","created_at":"2026-05-17T23:54:19Z"},{"alias_kind":"arxiv_version","alias_value":"1902.03793v1","created_at":"2026-05-17T23:54:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.03793","created_at":"2026-05-17T23:54:19Z"},{"alias_kind":"pith_short_12","alias_value":"TNBFWS4IUY2V","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"TNBFWS4IUY2VVGB6","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"TNBFWS4I","created_at":"2026-05-18T12:33:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:TNBFWS4IUY2VVGB6AJBNGQ5FSI","target":"record","payload":{"canonical_record":{"source":{"id":"1902.03793","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-02-11T09:53:13Z","cross_cats_sorted":[],"title_canon_sha256":"779749e97e7d5c5438972d053388b58f74fdf61de4956f6358e9417f898f4a2f","abstract_canon_sha256":"6da7d7eedc2b71f97fd82326bcf0c672fd433efaf6e0b07f0687561ea8362e97"},"schema_version":"1.0"},"canonical_sha256":"9b425b4b88a6355a983e0242d343a5920fccbc9d3e9ca2e8e453f7292ccde250","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:19.555988Z","signature_b64":"4/DAoFennwQi2EZ1NfwXETdAk6wHsOaURC3cWIRiKKsREwHt+ClG8IwLA78rPfwcNXtPB3SuVz47oWbXOVYhCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b425b4b88a6355a983e0242d343a5920fccbc9d3e9ca2e8e453f7292ccde250","last_reissued_at":"2026-05-17T23:54:19.555442Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:19.555442Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1902.03793","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:54:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pQZh9Tx6VhokrFJtgHIL46DubY652diVO1fHnbOI9DkFPudwksGq1YzbxUykCElL5OJqjBJJslZKUFNeWw8tAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T18:10:01.238470Z"},"content_sha256":"af6b9b9c9aeec9d1ec9ddac12ee489b23899dd762f3bc555bd62feddcf76be72","schema_version":"1.0","event_id":"sha256:af6b9b9c9aeec9d1ec9ddac12ee489b23899dd762f3bc555bd62feddcf76be72"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:TNBFWS4IUY2VVGB6AJBNGQ5FSI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Understanding over-parameterized deep networks by geometrization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Ling Zhou, Xiao Dong","submitted_at":"2019-02-11T09:53:13Z","abstract_excerpt":"A complete understanding of the widely used over-parameterized deep networks is a key step for AI. In this work we try to give a geometric picture of over-parameterized deep networks using our geometrization scheme. We show that the Riemannian geometry of network complexity plays a key role in understanding the basic properties of over-parameterizaed deep networks, including the generalization, convergence and parameter sensitivity. We also point out deep networks share lots of similarities with quantum computation systems. This can be regarded as a strong support of our proposal that geometri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.03793","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-17T23:54:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qr9TIx8SMO/LERRqIXBLI8dVrQiMbwZckv4Z+6myIW4XnaqKQblFUEvW61Ko1r3ldJssq6QdNnRppcHMMDchBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T18:10:01.238810Z"},"content_sha256":"c04ec7f7fa831d9ce616d48ffb68146b94f10f0f94d3d04a0340d7ad3f3bc61c","schema_version":"1.0","event_id":"sha256:c04ec7f7fa831d9ce616d48ffb68146b94f10f0f94d3d04a0340d7ad3f3bc61c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TNBFWS4IUY2VVGB6AJBNGQ5FSI/bundle.json","state_url":"https://pith.science/pith/TNBFWS4IUY2VVGB6AJBNGQ5FSI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TNBFWS4IUY2VVGB6AJBNGQ5FSI/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":"2026-05-30T18:10:01Z","links":{"resolver":"https://pith.science/pith/TNBFWS4IUY2VVGB6AJBNGQ5FSI","bundle":"https://pith.science/pith/TNBFWS4IUY2VVGB6AJBNGQ5FSI/bundle.json","state":"https://pith.science/pith/TNBFWS4IUY2VVGB6AJBNGQ5FSI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TNBFWS4IUY2VVGB6AJBNGQ5FSI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:TNBFWS4IUY2VVGB6AJBNGQ5FSI","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":"6da7d7eedc2b71f97fd82326bcf0c672fd433efaf6e0b07f0687561ea8362e97","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-02-11T09:53:13Z","title_canon_sha256":"779749e97e7d5c5438972d053388b58f74fdf61de4956f6358e9417f898f4a2f"},"schema_version":"1.0","source":{"id":"1902.03793","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.03793","created_at":"2026-05-17T23:54:19Z"},{"alias_kind":"arxiv_version","alias_value":"1902.03793v1","created_at":"2026-05-17T23:54:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.03793","created_at":"2026-05-17T23:54:19Z"},{"alias_kind":"pith_short_12","alias_value":"TNBFWS4IUY2V","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"TNBFWS4IUY2VVGB6","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"TNBFWS4I","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:c04ec7f7fa831d9ce616d48ffb68146b94f10f0f94d3d04a0340d7ad3f3bc61c","target":"graph","created_at":"2026-05-17T23:54:19Z","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"},"paper":{"abstract_excerpt":"A complete understanding of the widely used over-parameterized deep networks is a key step for AI. In this work we try to give a geometric picture of over-parameterized deep networks using our geometrization scheme. We show that the Riemannian geometry of network complexity plays a key role in understanding the basic properties of over-parameterizaed deep networks, including the generalization, convergence and parameter sensitivity. We also point out deep networks share lots of similarities with quantum computation systems. This can be regarded as a strong support of our proposal that geometri","authors_text":"Ling Zhou, Xiao Dong","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-02-11T09:53:13Z","title":"Understanding over-parameterized deep networks by geometrization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.03793","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:af6b9b9c9aeec9d1ec9ddac12ee489b23899dd762f3bc555bd62feddcf76be72","target":"record","created_at":"2026-05-17T23:54:19Z","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":"6da7d7eedc2b71f97fd82326bcf0c672fd433efaf6e0b07f0687561ea8362e97","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-02-11T09:53:13Z","title_canon_sha256":"779749e97e7d5c5438972d053388b58f74fdf61de4956f6358e9417f898f4a2f"},"schema_version":"1.0","source":{"id":"1902.03793","kind":"arxiv","version":1}},"canonical_sha256":"9b425b4b88a6355a983e0242d343a5920fccbc9d3e9ca2e8e453f7292ccde250","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b425b4b88a6355a983e0242d343a5920fccbc9d3e9ca2e8e453f7292ccde250","first_computed_at":"2026-05-17T23:54:19.555442Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:19.555442Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4/DAoFennwQi2EZ1NfwXETdAk6wHsOaURC3cWIRiKKsREwHt+ClG8IwLA78rPfwcNXtPB3SuVz47oWbXOVYhCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:19.555988Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.03793","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:af6b9b9c9aeec9d1ec9ddac12ee489b23899dd762f3bc555bd62feddcf76be72","sha256:c04ec7f7fa831d9ce616d48ffb68146b94f10f0f94d3d04a0340d7ad3f3bc61c"],"state_sha256":"3a7d86ccd4f2819966746f86caa9faddf4739d670c65dd95c71080c6293de7c5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bcRLgyVUduZ/PRz8c244xSYJuK/Zf2JkjaN7CW4Aahb5nwxeX6Ml6fBHdSmQ0SKPEotOeT0f+7bxfOw31fMGDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T18:10:01.240721Z","bundle_sha256":"3ae292e34fd47f8c3f5d9583381976c65b49ceab99e7a90146c4001aede66e27"}}