{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:S3XMBB7LCZP4W5VJF3L347DUZK","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":"eb63de7b62969381d8045b16a00af629ff9b2329a9d64f2bfdc14e5cc7541290","cross_cats_sorted":["cs.DS","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-12-03T22:31:47Z","title_canon_sha256":"243681310b0c6a00c4e4760fb5bfb837445ef487214d48766e8183b814671511"},"schema_version":"1.0","source":{"id":"1812.01115","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.01115","created_at":"2026-05-17T23:41:58Z"},{"alias_kind":"arxiv_version","alias_value":"1812.01115v2","created_at":"2026-05-17T23:41:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.01115","created_at":"2026-05-17T23:41:58Z"},{"alias_kind":"pith_short_12","alias_value":"S3XMBB7LCZP4","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"S3XMBB7LCZP4W5VJ","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"S3XMBB7L","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:6f11bf5918976cbbb0482ab616c09c803e5175fceef0daa2cc1187c4fbc3ca5c","target":"graph","created_at":"2026-05-17T23:41:58Z","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":"We describe new results and algorithms for two different, but related, problems which deal with circulant matrices: learning shift-invariant components from training data and calculating the shift (or alignment) between two given signals. In the first instance, we deal with the shift-invariant dictionary learning problem while the latter bears the name of (compressive) shift retrieval. We formulate these problems using circulant and convolutional matrices (including unions of such matrices), define optimization problems that describe our goals and propose efficient ways to solve them. Based on","authors_text":"Cristian Rusu","cross_cats":["cs.DS","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-12-03T22:31:47Z","title":"On learning with shift-invariant structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.01115","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:bdd4375e41d1024118ad3fb3e065534b0db7679c8f623518d7bcbc59e0ce75af","target":"record","created_at":"2026-05-17T23:41:58Z","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":"eb63de7b62969381d8045b16a00af629ff9b2329a9d64f2bfdc14e5cc7541290","cross_cats_sorted":["cs.DS","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-12-03T22:31:47Z","title_canon_sha256":"243681310b0c6a00c4e4760fb5bfb837445ef487214d48766e8183b814671511"},"schema_version":"1.0","source":{"id":"1812.01115","kind":"arxiv","version":2}},"canonical_sha256":"96eec087eb165fcb76a92ed7be7c74cab02a6e7e1d5e0f9c01c047bc00fb1b95","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"96eec087eb165fcb76a92ed7be7c74cab02a6e7e1d5e0f9c01c047bc00fb1b95","first_computed_at":"2026-05-17T23:41:58.067844Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:58.067844Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OAl0L2teOGatZaJ3nCp4Fy/IxSXUjgmaPoZd8b/wDMH0xQEpzgmFLLridHZXjv9p3N1XJdwHZlNG3L+nqcXgDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:58.068562Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.01115","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bdd4375e41d1024118ad3fb3e065534b0db7679c8f623518d7bcbc59e0ce75af","sha256:6f11bf5918976cbbb0482ab616c09c803e5175fceef0daa2cc1187c4fbc3ca5c"],"state_sha256":"c406751540593be2f7460a7b35a1178b25aa86919a16b6bd877d10ccc14d0241"}