{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:PBY5RDORWPSAFRQ3P6OMYUK5YP","short_pith_number":"pith:PBY5RDOR","schema_version":"1.0","canonical_sha256":"7871d88dd1b3e402c61b7f9ccc515dc3d59fe4873dd931efffe053b136d4f281","source":{"kind":"arxiv","id":"2403.04234","version":1},"attestation_state":"computed","paper":{"title":"Fundamental limits of Non-Linear Low-Rank Matrix Estimation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Florent Krzakala, Justin Ko, Lenka Zdeborov\\'a, Pierre Mergny","submitted_at":"2024-03-07T05:26:52Z","abstract_excerpt":"We consider the task of estimating a low-rank matrix from non-linear and noisy observations. We prove a strong universality result showing that Bayes-optimal performances are characterized by an equivalent Gaussian model with an effective prior, whose parameters are entirely determined by an expansion of the non-linear function. In particular, we show that to reconstruct the signal accurately, one requires a signal-to-noise ratio growing as $N^{\\frac 12 (1-1/k_F)}$, where $k_F$ is the first non-zero Fisher information coefficient of the function. We provide asymptotic characterization for 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":"2403.04234","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2024-03-07T05:26:52Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"6987401e78949dd1323f8f8f81a93f95d9ac237eaf298f31e8e934640227690c","abstract_canon_sha256":"9424233082e6e95db976cfdc9d53a5042b574197356ae5f623f0940aa4082525"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:53:20.266909Z","signature_b64":"/TEZlgMV90LaNoW0kIDFDVKLnVzA9avQblXyafnM7Vt0200QctNwzHeFpHpMRPrnlVDG5NDHhoTpGEIub4rnCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7871d88dd1b3e402c61b7f9ccc515dc3d59fe4873dd931efffe053b136d4f281","last_reissued_at":"2026-07-05T07:53:20.266445Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:53:20.266445Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fundamental limits of Non-Linear Low-Rank Matrix Estimation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Florent Krzakala, Justin Ko, Lenka Zdeborov\\'a, Pierre Mergny","submitted_at":"2024-03-07T05:26:52Z","abstract_excerpt":"We consider the task of estimating a low-rank matrix from non-linear and noisy observations. We prove a strong universality result showing that Bayes-optimal performances are characterized by an equivalent Gaussian model with an effective prior, whose parameters are entirely determined by an expansion of the non-linear function. In particular, we show that to reconstruct the signal accurately, one requires a signal-to-noise ratio growing as $N^{\\frac 12 (1-1/k_F)}$, where $k_F$ is the first non-zero Fisher information coefficient of the function. We provide asymptotic characterization for the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.04234","kind":"arxiv","version":1},"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/2403.04234/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":"2403.04234","created_at":"2026-07-05T07:53:20.266505+00:00"},{"alias_kind":"arxiv_version","alias_value":"2403.04234v1","created_at":"2026-07-05T07:53:20.266505+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.04234","created_at":"2026-07-05T07:53:20.266505+00:00"},{"alias_kind":"pith_short_12","alias_value":"PBY5RDORWPSA","created_at":"2026-07-05T07:53:20.266505+00:00"},{"alias_kind":"pith_short_16","alias_value":"PBY5RDORWPSAFRQ3","created_at":"2026-07-05T07:53:20.266505+00:00"},{"alias_kind":"pith_short_8","alias_value":"PBY5RDOR","created_at":"2026-07-05T07:53:20.266505+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2506.06749","citing_title":"Statistical Limits for Finite-Rank Tensor Estimation","ref_index":49,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PBY5RDORWPSAFRQ3P6OMYUK5YP","json":"https://pith.science/pith/PBY5RDORWPSAFRQ3P6OMYUK5YP.json","graph_json":"https://pith.science/api/pith-number/PBY5RDORWPSAFRQ3P6OMYUK5YP/graph.json","events_json":"https://pith.science/api/pith-number/PBY5RDORWPSAFRQ3P6OMYUK5YP/events.json","paper":"https://pith.science/paper/PBY5RDOR"},"agent_actions":{"view_html":"https://pith.science/pith/PBY5RDORWPSAFRQ3P6OMYUK5YP","download_json":"https://pith.science/pith/PBY5RDORWPSAFRQ3P6OMYUK5YP.json","view_paper":"https://pith.science/paper/PBY5RDOR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2403.04234&json=true","fetch_graph":"https://pith.science/api/pith-number/PBY5RDORWPSAFRQ3P6OMYUK5YP/graph.json","fetch_events":"https://pith.science/api/pith-number/PBY5RDORWPSAFRQ3P6OMYUK5YP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PBY5RDORWPSAFRQ3P6OMYUK5YP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PBY5RDORWPSAFRQ3P6OMYUK5YP/action/storage_attestation","attest_author":"https://pith.science/pith/PBY5RDORWPSAFRQ3P6OMYUK5YP/action/author_attestation","sign_citation":"https://pith.science/pith/PBY5RDORWPSAFRQ3P6OMYUK5YP/action/citation_signature","submit_replication":"https://pith.science/pith/PBY5RDORWPSAFRQ3P6OMYUK5YP/action/replication_record"}},"created_at":"2026-07-05T07:53:20.266505+00:00","updated_at":"2026-07-05T07:53:20.266505+00:00"}