{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:B5ON3FQ7WPS3OWKZ3R7I5YEZ6O","short_pith_number":"pith:B5ON3FQ7","schema_version":"1.0","canonical_sha256":"0f5cdd961fb3e5b75959dc7e8ee099f3bcf36ab6d69c0b2ccd50740c4002df64","source":{"kind":"arxiv","id":"2502.02545","version":2},"attestation_state":"computed","paper":{"title":"Optimal Spectral Transitions in High-Dimensional Multi-Index Models","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.dis-nn"],"primary_cat":"cs.LG","authors_text":"Bruno Loureiro, Florent Krzakala, Leonardo Defilippis, Pierre Mergny, Yatin Dandi","submitted_at":"2025-02-04T18:15:51Z","abstract_excerpt":"We consider the problem of how many samples from a Gaussian multi-index model are required to weakly reconstruct the relevant index subspace. Despite its increasing popularity as a testbed for investigating the computational complexity of neural networks, results beyond the single-index setting remain elusive. In this work, we introduce spectral algorithms based on the linearization of a message passing scheme tailored to this problem. Our main contribution is to show that the proposed methods achieve the optimal reconstruction threshold. Leveraging a high-dimensional characterization of the a"},"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":"2502.02545","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-02-04T18:15:51Z","cross_cats_sorted":["cond-mat.dis-nn"],"title_canon_sha256":"42985cdc83600cc89515ea2fb40b6be627dd164089e9be7c49cee7aaa25d2abc","abstract_canon_sha256":"04ae4ec7395da9f8c8c3a516eca23ccad57b3db87c956c655484f7b0dfcd4dda"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:19:03.305379Z","signature_b64":"F8G71Q+voAzYS+F/j6KTT3DIIxypM6FWsy8uQ3chxjUQsVb84GyeR7JyjSNJ7Pd9zwfVqXBl/JfvZj/0825gCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0f5cdd961fb3e5b75959dc7e8ee099f3bcf36ab6d69c0b2ccd50740c4002df64","last_reissued_at":"2026-07-05T11:19:03.304854Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:19:03.304854Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Optimal Spectral Transitions in High-Dimensional Multi-Index Models","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.dis-nn"],"primary_cat":"cs.LG","authors_text":"Bruno Loureiro, Florent Krzakala, Leonardo Defilippis, Pierre Mergny, Yatin Dandi","submitted_at":"2025-02-04T18:15:51Z","abstract_excerpt":"We consider the problem of how many samples from a Gaussian multi-index model are required to weakly reconstruct the relevant index subspace. Despite its increasing popularity as a testbed for investigating the computational complexity of neural networks, results beyond the single-index setting remain elusive. In this work, we introduce spectral algorithms based on the linearization of a message passing scheme tailored to this problem. Our main contribution is to show that the proposed methods achieve the optimal reconstruction threshold. Leveraging a high-dimensional characterization of the a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.02545","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.02545/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":"2502.02545","created_at":"2026-07-05T11:19:03.304918+00:00"},{"alias_kind":"arxiv_version","alias_value":"2502.02545v2","created_at":"2026-07-05T11:19:03.304918+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.02545","created_at":"2026-07-05T11:19:03.304918+00:00"},{"alias_kind":"pith_short_12","alias_value":"B5ON3FQ7WPS3","created_at":"2026-07-05T11:19:03.304918+00:00"},{"alias_kind":"pith_short_16","alias_value":"B5ON3FQ7WPS3OWKZ","created_at":"2026-07-05T11:19:03.304918+00:00"},{"alias_kind":"pith_short_8","alias_value":"B5ON3FQ7","created_at":"2026-07-05T11:19:03.304918+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2608.01654","citing_title":"Approximate Message Passing with Random Initialization for Phase Retrieval","ref_index":39,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/B5ON3FQ7WPS3OWKZ3R7I5YEZ6O","json":"https://pith.science/pith/B5ON3FQ7WPS3OWKZ3R7I5YEZ6O.json","graph_json":"https://pith.science/api/pith-number/B5ON3FQ7WPS3OWKZ3R7I5YEZ6O/graph.json","events_json":"https://pith.science/api/pith-number/B5ON3FQ7WPS3OWKZ3R7I5YEZ6O/events.json","paper":"https://pith.science/paper/B5ON3FQ7"},"agent_actions":{"view_html":"https://pith.science/pith/B5ON3FQ7WPS3OWKZ3R7I5YEZ6O","download_json":"https://pith.science/pith/B5ON3FQ7WPS3OWKZ3R7I5YEZ6O.json","view_paper":"https://pith.science/paper/B5ON3FQ7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2502.02545&json=true","fetch_graph":"https://pith.science/api/pith-number/B5ON3FQ7WPS3OWKZ3R7I5YEZ6O/graph.json","fetch_events":"https://pith.science/api/pith-number/B5ON3FQ7WPS3OWKZ3R7I5YEZ6O/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/B5ON3FQ7WPS3OWKZ3R7I5YEZ6O/action/timestamp_anchor","attest_storage":"https://pith.science/pith/B5ON3FQ7WPS3OWKZ3R7I5YEZ6O/action/storage_attestation","attest_author":"https://pith.science/pith/B5ON3FQ7WPS3OWKZ3R7I5YEZ6O/action/author_attestation","sign_citation":"https://pith.science/pith/B5ON3FQ7WPS3OWKZ3R7I5YEZ6O/action/citation_signature","submit_replication":"https://pith.science/pith/B5ON3FQ7WPS3OWKZ3R7I5YEZ6O/action/replication_record"}},"created_at":"2026-07-05T11:19:03.304918+00:00","updated_at":"2026-07-05T11:19:03.304918+00:00"}