{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:DT52VDZD3TO4WPJSRWUW2B3JAM","short_pith_number":"pith:DT52VDZD","canonical_record":{"source":{"id":"2302.08210","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-02-16T10:50:15Z","cross_cats_sorted":[],"title_canon_sha256":"20a0d1d0d18bf090002b4c6ca4f15164ce2aa0901305d1707cadd1b8b99236a7","abstract_canon_sha256":"17d47e2bdd8d87f13e02897f482a197d76910c9dd829c464e9b260262b40eb41"},"schema_version":"1.0"},"canonical_sha256":"1cfbaa8f23dcddcb3d328da96d07690333cbf80e36fd72c406e30bf72f6f34ab","source":{"kind":"arxiv","id":"2302.08210","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2302.08210","created_at":"2026-07-05T05:42:35Z"},{"alias_kind":"arxiv_version","alias_value":"2302.08210v1","created_at":"2026-07-05T05:42:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.08210","created_at":"2026-07-05T05:42:35Z"},{"alias_kind":"pith_short_12","alias_value":"DT52VDZD3TO4","created_at":"2026-07-05T05:42:35Z"},{"alias_kind":"pith_short_16","alias_value":"DT52VDZD3TO4WPJS","created_at":"2026-07-05T05:42:35Z"},{"alias_kind":"pith_short_8","alias_value":"DT52VDZD","created_at":"2026-07-05T05:42:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:DT52VDZD3TO4WPJSRWUW2B3JAM","target":"record","payload":{"canonical_record":{"source":{"id":"2302.08210","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-02-16T10:50:15Z","cross_cats_sorted":[],"title_canon_sha256":"20a0d1d0d18bf090002b4c6ca4f15164ce2aa0901305d1707cadd1b8b99236a7","abstract_canon_sha256":"17d47e2bdd8d87f13e02897f482a197d76910c9dd829c464e9b260262b40eb41"},"schema_version":"1.0"},"canonical_sha256":"1cfbaa8f23dcddcb3d328da96d07690333cbf80e36fd72c406e30bf72f6f34ab","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:42:35.585697Z","signature_b64":"N+kKFItq6+jJeu7Fk8J3cOhmL8sNcpmsFFvu4Sb+z/f1Obanv9t1KcQWGiieNazYrgoIALTC4BIxNovfLFiLAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1cfbaa8f23dcddcb3d328da96d07690333cbf80e36fd72c406e30bf72f6f34ab","last_reissued_at":"2026-07-05T05:42:35.585222Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:42:35.585222Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2302.08210","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":"2026-07-05T05:42:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zuhMx35RSpcd9hTQIG4Jki3hHWphM69fNsORzTg0WVTHpWKI2XG3VtuvudOauQlrXJ5VsMy+x/C3GPja+zEhCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T05:53:09.586130Z"},"content_sha256":"b9c6ce7f3dd882930564f0d7c74548cd8946b1e589ea4f71c5e71433aac322c6","schema_version":"1.0","event_id":"sha256:b9c6ce7f3dd882930564f0d7c74548cd8946b1e589ea4f71c5e71433aac322c6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:DT52VDZD3TO4WPJSRWUW2B3JAM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Survey of Geometric Optimization for Deep Learning: From Euclidean Space to Riemannian Manifold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Mingsong Chen, Xian Wei, Yanhong Fei, Yingjie Liu, Zhengyu Li","submitted_at":"2023-02-16T10:50:15Z","abstract_excerpt":"Although Deep Learning (DL) has achieved success in complex Artificial Intelligence (AI) tasks, it suffers from various notorious problems (e.g., feature redundancy, and vanishing or exploding gradients), since updating parameters in Euclidean space cannot fully exploit the geometric structure of the solution space. As a promising alternative solution, Riemannian-based DL uses geometric optimization to update parameters on Riemannian manifolds and can leverage the underlying geometric information. Accordingly, this article presents a comprehensive survey of applying geometric optimization in D"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.08210","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2302.08210/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":"2026-07-05T05:42:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EUGIi5A8dLgztd5ijg6jP0ayPOgaDvuLBgXDcjhZt14G212hAG+CSKVWMeNWPGn9wVP4f9NSCGr7K5P53Jc+Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T05:53:09.586669Z"},"content_sha256":"1164a5b7914fc5b97f115dc7d5a58e7bf46a247a84ecc09b9b919186b1fb9429","schema_version":"1.0","event_id":"sha256:1164a5b7914fc5b97f115dc7d5a58e7bf46a247a84ecc09b9b919186b1fb9429"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DT52VDZD3TO4WPJSRWUW2B3JAM/bundle.json","state_url":"https://pith.science/pith/DT52VDZD3TO4WPJSRWUW2B3JAM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DT52VDZD3TO4WPJSRWUW2B3JAM/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":"2026-08-23T05:53:09Z","links":{"resolver":"https://pith.science/pith/DT52VDZD3TO4WPJSRWUW2B3JAM","bundle":"https://pith.science/pith/DT52VDZD3TO4WPJSRWUW2B3JAM/bundle.json","state":"https://pith.science/pith/DT52VDZD3TO4WPJSRWUW2B3JAM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DT52VDZD3TO4WPJSRWUW2B3JAM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:DT52VDZD3TO4WPJSRWUW2B3JAM","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":"17d47e2bdd8d87f13e02897f482a197d76910c9dd829c464e9b260262b40eb41","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-02-16T10:50:15Z","title_canon_sha256":"20a0d1d0d18bf090002b4c6ca4f15164ce2aa0901305d1707cadd1b8b99236a7"},"schema_version":"1.0","source":{"id":"2302.08210","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2302.08210","created_at":"2026-07-05T05:42:35Z"},{"alias_kind":"arxiv_version","alias_value":"2302.08210v1","created_at":"2026-07-05T05:42:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.08210","created_at":"2026-07-05T05:42:35Z"},{"alias_kind":"pith_short_12","alias_value":"DT52VDZD3TO4","created_at":"2026-07-05T05:42:35Z"},{"alias_kind":"pith_short_16","alias_value":"DT52VDZD3TO4WPJS","created_at":"2026-07-05T05:42:35Z"},{"alias_kind":"pith_short_8","alias_value":"DT52VDZD","created_at":"2026-07-05T05:42:35Z"}],"graph_snapshots":[{"event_id":"sha256:1164a5b7914fc5b97f115dc7d5a58e7bf46a247a84ecc09b9b919186b1fb9429","target":"graph","created_at":"2026-07-05T05:42:35Z","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/2302.08210/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Although Deep Learning (DL) has achieved success in complex Artificial Intelligence (AI) tasks, it suffers from various notorious problems (e.g., feature redundancy, and vanishing or exploding gradients), since updating parameters in Euclidean space cannot fully exploit the geometric structure of the solution space. As a promising alternative solution, Riemannian-based DL uses geometric optimization to update parameters on Riemannian manifolds and can leverage the underlying geometric information. Accordingly, this article presents a comprehensive survey of applying geometric optimization in D","authors_text":"Mingsong Chen, Xian Wei, Yanhong Fei, Yingjie Liu, Zhengyu Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-02-16T10:50:15Z","title":"A Survey of Geometric Optimization for Deep Learning: From Euclidean Space to Riemannian Manifold"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.08210","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:b9c6ce7f3dd882930564f0d7c74548cd8946b1e589ea4f71c5e71433aac322c6","target":"record","created_at":"2026-07-05T05:42:35Z","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":"17d47e2bdd8d87f13e02897f482a197d76910c9dd829c464e9b260262b40eb41","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-02-16T10:50:15Z","title_canon_sha256":"20a0d1d0d18bf090002b4c6ca4f15164ce2aa0901305d1707cadd1b8b99236a7"},"schema_version":"1.0","source":{"id":"2302.08210","kind":"arxiv","version":1}},"canonical_sha256":"1cfbaa8f23dcddcb3d328da96d07690333cbf80e36fd72c406e30bf72f6f34ab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1cfbaa8f23dcddcb3d328da96d07690333cbf80e36fd72c406e30bf72f6f34ab","first_computed_at":"2026-07-05T05:42:35.585222Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:42:35.585222Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N+kKFItq6+jJeu7Fk8J3cOhmL8sNcpmsFFvu4Sb+z/f1Obanv9t1KcQWGiieNazYrgoIALTC4BIxNovfLFiLAw==","signature_status":"signed_v1","signed_at":"2026-07-05T05:42:35.585697Z","signed_message":"canonical_sha256_bytes"},"source_id":"2302.08210","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b9c6ce7f3dd882930564f0d7c74548cd8946b1e589ea4f71c5e71433aac322c6","sha256:1164a5b7914fc5b97f115dc7d5a58e7bf46a247a84ecc09b9b919186b1fb9429"],"state_sha256":"1d7197c47942c99d82330669265a15a166868055abdeccd75472760c1be4fd1f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6IjK4f5I9S6n93grpTVc+/3MRPmW0qc9Zmpf5lF5p9H8UBw1Fq4wlITy23YJXZas0wu/6RM0z0k4E4RntxLTAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-23T05:53:09.591533Z","bundle_sha256":"3fbe8b9bdaf57e976e40040e91ea579e520e55016954eb8b52f0f09bc975966c"}}