{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:BXYYJXLKSZ2ZGAIRU35VJAIUGS","short_pith_number":"pith:BXYYJXLK","schema_version":"1.0","canonical_sha256":"0df184dd6a9675930111a6fb54811434ae880f9419ce6626c5267deaca06d513","source":{"kind":"arxiv","id":"2303.15477","version":5},"attestation_state":"computed","paper":{"title":"Adaptive Log-Euclidean Metrics for SPD Matrix Learning","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Nicu Sebe, Tianyang Xu, Xiao-Jun Wu, Yue Song, Zhiwu Huang, Ziheng Chen","submitted_at":"2023-03-26T18:31:52Z","abstract_excerpt":"Symmetric Positive Definite (SPD) matrices have received wide attention in machine learning due to their intrinsic capacity to encode underlying structural correlation in data. Many successful Riemannian metrics have been proposed to reflect the non-Euclidean geometry of SPD manifolds. However, most existing metric tensors are fixed, which might lead to sub-optimal performance for SPD matrix learning, especially for deep SPD neural networks. To remedy this limitation, we leverage the commonly encountered pullback techniques and propose Adaptive Log-Euclidean Metrics (ALEMs), which extend the w"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2303.15477","kind":"arxiv","version":5},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2023-03-26T18:31:52Z","cross_cats_sorted":[],"title_canon_sha256":"b138cbde6e99e7ca998ffaf68f3d105e2b1e0b2de552be13e6a893e29a37faab","abstract_canon_sha256":"011e16f52b2685f273fd5ac844d7b4408fbabeef6d1c4b9bcd27ff437650b985"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:00:34.580282Z","signature_b64":"UPpiPpLVax18InwwJ9BAGKn1HOapbxuh35ejJY1feMjpPhdQzLyzKnwgINbqsjO4XmodOaXrwohVzUm0tQA8CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0df184dd6a9675930111a6fb54811434ae880f9419ce6626c5267deaca06d513","last_reissued_at":"2026-07-05T09:00:34.579837Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:00:34.579837Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Adaptive Log-Euclidean Metrics for SPD Matrix Learning","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Nicu Sebe, Tianyang Xu, Xiao-Jun Wu, Yue Song, Zhiwu Huang, Ziheng Chen","submitted_at":"2023-03-26T18:31:52Z","abstract_excerpt":"Symmetric Positive Definite (SPD) matrices have received wide attention in machine learning due to their intrinsic capacity to encode underlying structural correlation in data. Many successful Riemannian metrics have been proposed to reflect the non-Euclidean geometry of SPD manifolds. However, most existing metric tensors are fixed, which might lead to sub-optimal performance for SPD matrix learning, especially for deep SPD neural networks. To remedy this limitation, we leverage the commonly encountered pullback techniques and propose Adaptive Log-Euclidean Metrics (ALEMs), which extend the w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.15477","kind":"arxiv","version":5},"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/2303.15477/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2303.15477","created_at":"2026-07-05T09:00:34.579891+00:00"},{"alias_kind":"arxiv_version","alias_value":"2303.15477v5","created_at":"2026-07-05T09:00:34.579891+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.15477","created_at":"2026-07-05T09:00:34.579891+00:00"},{"alias_kind":"pith_short_12","alias_value":"BXYYJXLKSZ2Z","created_at":"2026-07-05T09:00:34.579891+00:00"},{"alias_kind":"pith_short_16","alias_value":"BXYYJXLKSZ2ZGAIR","created_at":"2026-07-05T09:00:34.579891+00:00"},{"alias_kind":"pith_short_8","alias_value":"BXYYJXLK","created_at":"2026-07-05T09:00:34.579891+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BXYYJXLKSZ2ZGAIRU35VJAIUGS","json":"https://pith.science/pith/BXYYJXLKSZ2ZGAIRU35VJAIUGS.json","graph_json":"https://pith.science/api/pith-number/BXYYJXLKSZ2ZGAIRU35VJAIUGS/graph.json","events_json":"https://pith.science/api/pith-number/BXYYJXLKSZ2ZGAIRU35VJAIUGS/events.json","paper":"https://pith.science/paper/BXYYJXLK"},"agent_actions":{"view_html":"https://pith.science/pith/BXYYJXLKSZ2ZGAIRU35VJAIUGS","download_json":"https://pith.science/pith/BXYYJXLKSZ2ZGAIRU35VJAIUGS.json","view_paper":"https://pith.science/paper/BXYYJXLK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2303.15477&json=true","fetch_graph":"https://pith.science/api/pith-number/BXYYJXLKSZ2ZGAIRU35VJAIUGS/graph.json","fetch_events":"https://pith.science/api/pith-number/BXYYJXLKSZ2ZGAIRU35VJAIUGS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BXYYJXLKSZ2ZGAIRU35VJAIUGS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BXYYJXLKSZ2ZGAIRU35VJAIUGS/action/storage_attestation","attest_author":"https://pith.science/pith/BXYYJXLKSZ2ZGAIRU35VJAIUGS/action/author_attestation","sign_citation":"https://pith.science/pith/BXYYJXLKSZ2ZGAIRU35VJAIUGS/action/citation_signature","submit_replication":"https://pith.science/pith/BXYYJXLKSZ2ZGAIRU35VJAIUGS/action/replication_record"}},"created_at":"2026-07-05T09:00:34.579891+00:00","updated_at":"2026-07-05T09:00:34.579891+00:00"}