{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:WD6JBCBPWNHIZDAOVCI3GXOW6X","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":"426226390bf74186bca83ecea61868a92ebf73520dd6002b7e52b1247faf8b40","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2017-11-05T12:17:35Z","title_canon_sha256":"0a83fa8ab943114df03d708b30da2fef489953b0ee16927412be7f8fb974e459"},"schema_version":"1.0","source":{"id":"1711.01573","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.01573","created_at":"2026-05-18T00:31:17Z"},{"alias_kind":"arxiv_version","alias_value":"1711.01573v1","created_at":"2026-05-18T00:31:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.01573","created_at":"2026-05-18T00:31:17Z"},{"alias_kind":"pith_short_12","alias_value":"WD6JBCBPWNHI","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"WD6JBCBPWNHIZDAO","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"WD6JBCBP","created_at":"2026-05-18T12:31:53Z"}],"graph_snapshots":[{"event_id":"sha256:d04eed469ddbc86eac887ae98e173940c43cced9dae1ed7c10bf53574d64adf1","target":"graph","created_at":"2026-05-18T00:31:17Z","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":"Based on our observation that there exists a dramatic drop for the singular values of the fully connected layers or a single feature map of the convolutional layer, and that the dimension of the concatenated feature vector almost equals the summation of the dimension on each feature map, we propose a singular value decomposition (SVD) based approach to estimate the dimension of the deep manifolds for a typical convolutional neural network VGG19. We choose three categories from the ImageNet, namely Persian Cat, Container Ship and Volcano, and determine the local dimension of the deep manifolds ","authors_text":"Huan Long, John E. Hopcroft, Kun He, Mengxiao Zhang, Tao Yu, Wangquan Wu, Yanren Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2017-11-05T12:17:35Z","title":"The Local Dimension of Deep Manifold"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.01573","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:a4625bd5da8843e3badcdb2a16d86290e1d38c1a52362cacdb9e9927ba79e9a0","target":"record","created_at":"2026-05-18T00:31:17Z","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":"426226390bf74186bca83ecea61868a92ebf73520dd6002b7e52b1247faf8b40","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2017-11-05T12:17:35Z","title_canon_sha256":"0a83fa8ab943114df03d708b30da2fef489953b0ee16927412be7f8fb974e459"},"schema_version":"1.0","source":{"id":"1711.01573","kind":"arxiv","version":1}},"canonical_sha256":"b0fc90882fb34e8c8c0ea891b35dd6f5e1271230ac77674f1facbb653f97ee29","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b0fc90882fb34e8c8c0ea891b35dd6f5e1271230ac77674f1facbb653f97ee29","first_computed_at":"2026-05-18T00:31:17.411191Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:17.411191Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vlUP1Ryb6QxOoctkvuenLe7KqUzCE6Z+raCDQTrR628PK+6MtKiM6nEKZvMGVfNNTWburlmuCcFou1AwxHzNCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:17.411738Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.01573","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a4625bd5da8843e3badcdb2a16d86290e1d38c1a52362cacdb9e9927ba79e9a0","sha256:d04eed469ddbc86eac887ae98e173940c43cced9dae1ed7c10bf53574d64adf1"],"state_sha256":"4d51d80fae9b9a6aa6586f5eeda16b2fb0444206fe148c3c965e5136957779ae"}