{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:MNXMNYVITLYCPS7ZVLSKIEMJJ6","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":"a337f254b9a9d004a99b2cc6c28d6e3a56998bf81d7dd044f9df202bcd88f0f9","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-04-01T20:48:21Z","title_canon_sha256":"7b9aeda7fe17cc95779239b007b58e3eacdf66c4eadb74ad6069aff8979c54cd"},"schema_version":"1.0","source":{"id":"1704.00227","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.00227","created_at":"2026-05-18T00:24:37Z"},{"alias_kind":"arxiv_version","alias_value":"1704.00227v2","created_at":"2026-05-18T00:24:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.00227","created_at":"2026-05-18T00:24:37Z"},{"alias_kind":"pith_short_12","alias_value":"MNXMNYVITLYC","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"MNXMNYVITLYCPS7Z","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"MNXMNYVI","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:e84d348d3e210c62fd2f3be8e782073605a1a638fcdd33a662c99f336fd8ef2d","target":"graph","created_at":"2026-05-18T00:24:37Z","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":"In this paper four iterative algorithms for learning analysis operators are presented. They are built upon the same optimisation principle underlying both Analysis K-SVD and Analysis SimCO. The Forward and Sequential Analysis Operator Learning (FAOL and SAOL) algorithms are based on projected gradient descent with optimally chosen step size. The Implicit AOL (IAOL) algorithm is inspired by the implicit Euler scheme for solving ordinary differential equations and does not require to choose a step size. The fourth algorithm, Singular Value AOL (SVAOL), uses a similar strategy as Analysis K-SVD w","authors_text":"Karin Schnass, Michael Sandbichler","cross_cats":["math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-04-01T20:48:21Z","title":"Online and Stable Learning of Analysis Operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.00227","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":"sha256:10df7556dc28db122fff99b8fcd35c8973dd0e9bc235d6618a535e886128831f","target":"record","created_at":"2026-05-18T00:24:37Z","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":"a337f254b9a9d004a99b2cc6c28d6e3a56998bf81d7dd044f9df202bcd88f0f9","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-04-01T20:48:21Z","title_canon_sha256":"7b9aeda7fe17cc95779239b007b58e3eacdf66c4eadb74ad6069aff8979c54cd"},"schema_version":"1.0","source":{"id":"1704.00227","kind":"arxiv","version":2}},"canonical_sha256":"636ec6e2a89af027cbf9aae4a411894f9c2f73fae1143ae7eb2d849b516c3e58","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"636ec6e2a89af027cbf9aae4a411894f9c2f73fae1143ae7eb2d849b516c3e58","first_computed_at":"2026-05-18T00:24:37.754599Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:37.754599Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GIb9hljJiuvl6aLPPeHIV+Hng7BAG16cWEha5Q1oUEL0vS366JDYLxbf9LPIPmgQFtFLHpebKoggW14wfT0+Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:37.755136Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.00227","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:10df7556dc28db122fff99b8fcd35c8973dd0e9bc235d6618a535e886128831f","sha256:e84d348d3e210c62fd2f3be8e782073605a1a638fcdd33a662c99f336fd8ef2d"],"state_sha256":"50bb413bdec4d75ad77ae667d499cdeb31c6ac8f4b0b7ae0212735b5ec2e3dc3"}