{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:YAM4G3A5YWNVTXM6KIDVRQJWVP","short_pith_number":"pith:YAM4G3A5","schema_version":"1.0","canonical_sha256":"c019c36c1dc59b59dd9e520758c136abc60d6866704e70251ad1097c7b17ca44","source":{"kind":"arxiv","id":"1709.09803","version":2},"attestation_state":"computed","paper":{"title":"Quantization for Low-Rank Matrix Recovery","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Eric Lybrand, Rayan Saab","submitted_at":"2017-09-28T05:02:20Z","abstract_excerpt":"We study Sigma-Delta quantization methods coupled with appropriate reconstruction algorithms for digitizing randomly sampled low-rank matrices. We show that the reconstruction error associated with our methods decays polynomially with the oversampling factor, and we leverage our results to obtain root-exponential accuracy by optimizing over the choice of quantization scheme. Additionally, we show that a random encoding scheme, applied to the quantized measurements, yields a near-optimal exponential bit-rate. As an added benefit, our schemes are robust both to noise and to deviations from the l"},"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":"1709.09803","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-09-28T05:02:20Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"7c33b7a2516bba6a022b886bdd80b411e5ddfcb3620f72aa8c5ba142a21fa949","abstract_canon_sha256":"e79f5b9175591448a6ef39297cd049f5f5d30710bd3eb4279574ee5946c70477"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:19.247807Z","signature_b64":"HfSj11b0bkl2i/wB1FDGBj0Bfu+ApamDIRCjGrcs03o3Ghgp0bXwG7zP7iEcPUO8zfkQ40rcYn7XjRBq/xWCDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c019c36c1dc59b59dd9e520758c136abc60d6866704e70251ad1097c7b17ca44","last_reissued_at":"2026-05-18T00:18:19.247357Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:19.247357Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quantization for Low-Rank Matrix Recovery","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Eric Lybrand, Rayan Saab","submitted_at":"2017-09-28T05:02:20Z","abstract_excerpt":"We study Sigma-Delta quantization methods coupled with appropriate reconstruction algorithms for digitizing randomly sampled low-rank matrices. We show that the reconstruction error associated with our methods decays polynomially with the oversampling factor, and we leverage our results to obtain root-exponential accuracy by optimizing over the choice of quantization scheme. Additionally, we show that a random encoding scheme, applied to the quantized measurements, yields a near-optimal exponential bit-rate. As an added benefit, our schemes are robust both to noise and to deviations from the l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.09803","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":"1709.09803","created_at":"2026-05-18T00:18:19.247422+00:00"},{"alias_kind":"arxiv_version","alias_value":"1709.09803v2","created_at":"2026-05-18T00:18:19.247422+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.09803","created_at":"2026-05-18T00:18:19.247422+00:00"},{"alias_kind":"pith_short_12","alias_value":"YAM4G3A5YWNV","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_16","alias_value":"YAM4G3A5YWNVTXM6","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_8","alias_value":"YAM4G3A5","created_at":"2026-05-18T12:31:56.362134+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/YAM4G3A5YWNVTXM6KIDVRQJWVP","json":"https://pith.science/pith/YAM4G3A5YWNVTXM6KIDVRQJWVP.json","graph_json":"https://pith.science/api/pith-number/YAM4G3A5YWNVTXM6KIDVRQJWVP/graph.json","events_json":"https://pith.science/api/pith-number/YAM4G3A5YWNVTXM6KIDVRQJWVP/events.json","paper":"https://pith.science/paper/YAM4G3A5"},"agent_actions":{"view_html":"https://pith.science/pith/YAM4G3A5YWNVTXM6KIDVRQJWVP","download_json":"https://pith.science/pith/YAM4G3A5YWNVTXM6KIDVRQJWVP.json","view_paper":"https://pith.science/paper/YAM4G3A5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1709.09803&json=true","fetch_graph":"https://pith.science/api/pith-number/YAM4G3A5YWNVTXM6KIDVRQJWVP/graph.json","fetch_events":"https://pith.science/api/pith-number/YAM4G3A5YWNVTXM6KIDVRQJWVP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YAM4G3A5YWNVTXM6KIDVRQJWVP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YAM4G3A5YWNVTXM6KIDVRQJWVP/action/storage_attestation","attest_author":"https://pith.science/pith/YAM4G3A5YWNVTXM6KIDVRQJWVP/action/author_attestation","sign_citation":"https://pith.science/pith/YAM4G3A5YWNVTXM6KIDVRQJWVP/action/citation_signature","submit_replication":"https://pith.science/pith/YAM4G3A5YWNVTXM6KIDVRQJWVP/action/replication_record"}},"created_at":"2026-05-18T00:18:19.247422+00:00","updated_at":"2026-05-18T00:18:19.247422+00:00"}