{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:52Y2OBRO4DTXMSI2J426CI2TUL","short_pith_number":"pith:52Y2OBRO","schema_version":"1.0","canonical_sha256":"eeb1a7062ee0e776491a4f35e12353a2ca7eb8a0284165f147ac9853f1d7bf28","source":{"kind":"arxiv","id":"1804.08603","version":2},"attestation_state":"computed","paper":{"title":"Towards Learning Sparsely Used Dictionaries with Arbitrary Supports","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","stat.ML"],"primary_cat":"cs.LG","authors_text":"Aravindan Vijayaraghavan, Pranjal Awasthi","submitted_at":"2018-04-23T17:57:33Z","abstract_excerpt":"Dictionary learning is a popular approach for inferring a hidden basis or dictionary in which data has a sparse representation. Data generated from the dictionary A (an n by m matrix, with m > n in the over-complete setting) is given by Y = AX where X is a matrix whose columns have supports chosen from a distribution over k-sparse vectors, and the non-zero values chosen from a symmetric distribution. Given Y, the goal is to recover A and X in polynomial time. Existing algorithms give polytime guarantees for recovering incoherent dictionaries, under strong distributional assumptions both on the"},"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":"1804.08603","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-04-23T17:57:33Z","cross_cats_sorted":["cs.DS","stat.ML"],"title_canon_sha256":"74c8975cbb6f271aadbf0d3b62b66e979c4fc53996f5541b78f2b738bd3626e6","abstract_canon_sha256":"bac3c1b4b37152342e91e9bfd803f89b4e06bfc112ffbb79938fce796564f5b2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:36.211237Z","signature_b64":"BQrA7VntJV0cGjHdSs25wqpQbuwI3BBLg8W3RdfNoS3Z+86mJ5+DHdEtEmJFl9/FseOLPKBYtwc88nlwxuEDCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eeb1a7062ee0e776491a4f35e12353a2ca7eb8a0284165f147ac9853f1d7bf28","last_reissued_at":"2026-05-18T00:16:36.210804Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:36.210804Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Towards Learning Sparsely Used Dictionaries with Arbitrary Supports","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","stat.ML"],"primary_cat":"cs.LG","authors_text":"Aravindan Vijayaraghavan, Pranjal Awasthi","submitted_at":"2018-04-23T17:57:33Z","abstract_excerpt":"Dictionary learning is a popular approach for inferring a hidden basis or dictionary in which data has a sparse representation. Data generated from the dictionary A (an n by m matrix, with m > n in the over-complete setting) is given by Y = AX where X is a matrix whose columns have supports chosen from a distribution over k-sparse vectors, and the non-zero values chosen from a symmetric distribution. Given Y, the goal is to recover A and X in polynomial time. Existing algorithms give polytime guarantees for recovering incoherent dictionaries, under strong distributional assumptions both on the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.08603","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1804.08603","created_at":"2026-05-18T00:16:36.210872+00:00"},{"alias_kind":"arxiv_version","alias_value":"1804.08603v2","created_at":"2026-05-18T00:16:36.210872+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.08603","created_at":"2026-05-18T00:16:36.210872+00:00"},{"alias_kind":"pith_short_12","alias_value":"52Y2OBRO4DTX","created_at":"2026-05-18T12:32:05.422762+00:00"},{"alias_kind":"pith_short_16","alias_value":"52Y2OBRO4DTXMSI2","created_at":"2026-05-18T12:32:05.422762+00:00"},{"alias_kind":"pith_short_8","alias_value":"52Y2OBRO","created_at":"2026-05-18T12:32:05.422762+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/52Y2OBRO4DTXMSI2J426CI2TUL","json":"https://pith.science/pith/52Y2OBRO4DTXMSI2J426CI2TUL.json","graph_json":"https://pith.science/api/pith-number/52Y2OBRO4DTXMSI2J426CI2TUL/graph.json","events_json":"https://pith.science/api/pith-number/52Y2OBRO4DTXMSI2J426CI2TUL/events.json","paper":"https://pith.science/paper/52Y2OBRO"},"agent_actions":{"view_html":"https://pith.science/pith/52Y2OBRO4DTXMSI2J426CI2TUL","download_json":"https://pith.science/pith/52Y2OBRO4DTXMSI2J426CI2TUL.json","view_paper":"https://pith.science/paper/52Y2OBRO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1804.08603&json=true","fetch_graph":"https://pith.science/api/pith-number/52Y2OBRO4DTXMSI2J426CI2TUL/graph.json","fetch_events":"https://pith.science/api/pith-number/52Y2OBRO4DTXMSI2J426CI2TUL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/52Y2OBRO4DTXMSI2J426CI2TUL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/52Y2OBRO4DTXMSI2J426CI2TUL/action/storage_attestation","attest_author":"https://pith.science/pith/52Y2OBRO4DTXMSI2J426CI2TUL/action/author_attestation","sign_citation":"https://pith.science/pith/52Y2OBRO4DTXMSI2J426CI2TUL/action/citation_signature","submit_replication":"https://pith.science/pith/52Y2OBRO4DTXMSI2J426CI2TUL/action/replication_record"}},"created_at":"2026-05-18T00:16:36.210872+00:00","updated_at":"2026-05-18T00:16:36.210872+00:00"}