{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:HQY6WNFK4ABASDUKUEYTKG6TQ5","short_pith_number":"pith:HQY6WNFK","canonical_record":{"source":{"id":"1805.10451","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-05-26T09:15:53Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"c7e8c8641c4bd7f76c63d606553f89205cb5d0e08f0b6dd3a352e0ff14670f8f","abstract_canon_sha256":"6e7d7d200b0a021eea0fcb47e066f310cf7c4097ed91d9439d924730e5958cd0"},"schema_version":"1.0"},"canonical_sha256":"3c31eb34aae002090e8aa131351bd38773987a5225e4c5221cb0c6f7ef428f4f","source":{"kind":"arxiv","id":"1805.10451","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.10451","created_at":"2026-05-18T00:14:33Z"},{"alias_kind":"arxiv_version","alias_value":"1805.10451v2","created_at":"2026-05-18T00:14:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.10451","created_at":"2026-05-18T00:14:33Z"},{"alias_kind":"pith_short_12","alias_value":"HQY6WNFK4ABA","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"HQY6WNFK4ABASDUK","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"HQY6WNFK","created_at":"2026-05-18T12:32:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:HQY6WNFK4ABASDUKUEYTKG6TQ5","target":"record","payload":{"canonical_record":{"source":{"id":"1805.10451","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-05-26T09:15:53Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"c7e8c8641c4bd7f76c63d606553f89205cb5d0e08f0b6dd3a352e0ff14670f8f","abstract_canon_sha256":"6e7d7d200b0a021eea0fcb47e066f310cf7c4097ed91d9439d924730e5958cd0"},"schema_version":"1.0"},"canonical_sha256":"3c31eb34aae002090e8aa131351bd38773987a5225e4c5221cb0c6f7ef428f4f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:33.630690Z","signature_b64":"lpa/oPs3DnbEhKaHnJPES2nELM/ZAt4NtwyBoy4Wp01LaPj1axqc58/fmYRnONxio3W69O+h4OP1ZF1VtkGvBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3c31eb34aae002090e8aa131351bd38773987a5225e4c5221cb0c6f7ef428f4f","last_reissued_at":"2026-05-18T00:14:33.630057Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:33.630057Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.10451","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":"2026-05-18T00:14:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3w28cHRh6LHZNcSBdFroFbo5VGBvaoiNvgMm0aeXlH61TRrBhOmAyBku7QO9FLMB6WXC9qLVjDQTyK3EgCDYCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T17:54:08.522012Z"},"content_sha256":"c94495eff181aa68ca985942d16aed660f65cdf1e6023ed001c77f7a2d3209c5","schema_version":"1.0","event_id":"sha256:c94495eff181aa68ca985942d16aed660f65cdf1e6023ed001c77f7a2d3209c5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:HQY6WNFK4ABASDUKUEYTKG6TQ5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Geometric Understanding of Deep Learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"David Xianfeng Gu, Na Lei, Shing-Tung Yau, Zhongxuan Luo","submitted_at":"2018-05-26T09:15:53Z","abstract_excerpt":"Deep learning is the mainstream technique for many machine learning tasks, including image recognition, machine translation, speech recognition, and so on. It has outperformed conventional methods in various fields and achieved great successes. Unfortunately, the understanding on how it works remains unclear. It has the central importance to lay down the theoretic foundation for deep learning.\n  In this work, we give a geometric view to understand deep learning: we show that the fundamental principle attributing to the success is the manifold structure in data, namely natural high dimensional "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.10451","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":""},"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":"2026-05-18T00:14:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XCOw5ebf9DOBYtmmo6qJhX7fcgsWR+wN55WuBNfhCSBb6KgqJxW/pkDHCPzfgBkhS9QMHgmgIgoAK5Pc6EJEAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T17:54:08.522703Z"},"content_sha256":"05f8311462f3046505fd1524fc8652b6ce31ed7197fb9441eaf8bb2a46c23f9d","schema_version":"1.0","event_id":"sha256:05f8311462f3046505fd1524fc8652b6ce31ed7197fb9441eaf8bb2a46c23f9d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HQY6WNFK4ABASDUKUEYTKG6TQ5/bundle.json","state_url":"https://pith.science/pith/HQY6WNFK4ABASDUKUEYTKG6TQ5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HQY6WNFK4ABASDUKUEYTKG6TQ5/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":"2026-05-28T17:54:08Z","links":{"resolver":"https://pith.science/pith/HQY6WNFK4ABASDUKUEYTKG6TQ5","bundle":"https://pith.science/pith/HQY6WNFK4ABASDUKUEYTKG6TQ5/bundle.json","state":"https://pith.science/pith/HQY6WNFK4ABASDUKUEYTKG6TQ5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HQY6WNFK4ABASDUKUEYTKG6TQ5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:HQY6WNFK4ABASDUKUEYTKG6TQ5","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":"6e7d7d200b0a021eea0fcb47e066f310cf7c4097ed91d9439d924730e5958cd0","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-05-26T09:15:53Z","title_canon_sha256":"c7e8c8641c4bd7f76c63d606553f89205cb5d0e08f0b6dd3a352e0ff14670f8f"},"schema_version":"1.0","source":{"id":"1805.10451","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.10451","created_at":"2026-05-18T00:14:33Z"},{"alias_kind":"arxiv_version","alias_value":"1805.10451v2","created_at":"2026-05-18T00:14:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.10451","created_at":"2026-05-18T00:14:33Z"},{"alias_kind":"pith_short_12","alias_value":"HQY6WNFK4ABA","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"HQY6WNFK4ABASDUK","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"HQY6WNFK","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:05f8311462f3046505fd1524fc8652b6ce31ed7197fb9441eaf8bb2a46c23f9d","target":"graph","created_at":"2026-05-18T00:14:33Z","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":"Deep learning is the mainstream technique for many machine learning tasks, including image recognition, machine translation, speech recognition, and so on. It has outperformed conventional methods in various fields and achieved great successes. Unfortunately, the understanding on how it works remains unclear. It has the central importance to lay down the theoretic foundation for deep learning.\n  In this work, we give a geometric view to understand deep learning: we show that the fundamental principle attributing to the success is the manifold structure in data, namely natural high dimensional ","authors_text":"David Xianfeng Gu, Na Lei, Shing-Tung Yau, Zhongxuan Luo","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-05-26T09:15:53Z","title":"Geometric Understanding of Deep Learning"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.10451","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:c94495eff181aa68ca985942d16aed660f65cdf1e6023ed001c77f7a2d3209c5","target":"record","created_at":"2026-05-18T00:14:33Z","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":"6e7d7d200b0a021eea0fcb47e066f310cf7c4097ed91d9439d924730e5958cd0","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-05-26T09:15:53Z","title_canon_sha256":"c7e8c8641c4bd7f76c63d606553f89205cb5d0e08f0b6dd3a352e0ff14670f8f"},"schema_version":"1.0","source":{"id":"1805.10451","kind":"arxiv","version":2}},"canonical_sha256":"3c31eb34aae002090e8aa131351bd38773987a5225e4c5221cb0c6f7ef428f4f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3c31eb34aae002090e8aa131351bd38773987a5225e4c5221cb0c6f7ef428f4f","first_computed_at":"2026-05-18T00:14:33.630057Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:33.630057Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lpa/oPs3DnbEhKaHnJPES2nELM/ZAt4NtwyBoy4Wp01LaPj1axqc58/fmYRnONxio3W69O+h4OP1ZF1VtkGvBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:33.630690Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.10451","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c94495eff181aa68ca985942d16aed660f65cdf1e6023ed001c77f7a2d3209c5","sha256:05f8311462f3046505fd1524fc8652b6ce31ed7197fb9441eaf8bb2a46c23f9d"],"state_sha256":"c1918f33057cb867ad4349890fec129b4d2d3d6bbb33d2daaa64a316c6291314"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VGO8Zqy7HdCw7Ggt4Ojsb7F1MklTLtw1iyjJBbt4rf3XX486TKadpERvIDkAq0UKoeiY/ENeRklQPNffm1oZDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T17:54:08.527560Z","bundle_sha256":"df204f7431bf2a8adda0c4e840a44c26da5323c0d746d892410d35058d954380"}}