{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:4WMUM7V2LJMVKINSGMGVHSFM7L","short_pith_number":"pith:4WMUM7V2","schema_version":"1.0","canonical_sha256":"e599467eba5a595521b2330d53c8acfae227dd209504cb230bd6b6dcf57b8691","source":{"kind":"arxiv","id":"1708.03950","version":1},"attestation_state":"computed","paper":{"title":"State Evolution for Approximate Message Passing with Non-Separable Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Andrea Montanari, Phan-Minh Nguyen, Raphael Berthier","submitted_at":"2017-08-13T18:38:10Z","abstract_excerpt":"Given a high-dimensional data matrix ${\\boldsymbol A}\\in{\\mathbb R}^{m\\times n}$, Approximate Message Passing (AMP) algorithms construct sequences of vectors ${\\boldsymbol u}^t\\in{\\mathbb R}^n$, ${\\boldsymbol v}^t\\in{\\mathbb R}^m$, indexed by $t\\in\\{0,1,2\\dots\\}$ by iteratively applying ${\\boldsymbol A}$ or ${\\boldsymbol A}^{{\\sf T}}$, and suitable non-linear functions, which depend on the specific application. Special instances of this approach have been developed --among other applications-- for compressed sensing reconstruction, robust regression, Bayesian estimation, low-rank matrix recove"},"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":"1708.03950","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-08-13T18:38:10Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"11c5fe25a0bbb0c0f329a4823ddd326d22e949cf193931af502e00ca0a815625","abstract_canon_sha256":"a227eb2d4301ce9f76f7b36ae8ec5bb43e60e4182a85de39cb1a26bb4700a7c3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:07.443083Z","signature_b64":"Te/VBwFnkAtLqFNKCQ65fFpR0eL0Tru1XSkuj9yfaSSx7DyJwnlACdGAUqNzHlUY/eNa6BmZtT+mu2WD5VkFCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e599467eba5a595521b2330d53c8acfae227dd209504cb230bd6b6dcf57b8691","last_reissued_at":"2026-05-18T00:38:07.442674Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:07.442674Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"State Evolution for Approximate Message Passing with Non-Separable Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Andrea Montanari, Phan-Minh Nguyen, Raphael Berthier","submitted_at":"2017-08-13T18:38:10Z","abstract_excerpt":"Given a high-dimensional data matrix ${\\boldsymbol A}\\in{\\mathbb R}^{m\\times n}$, Approximate Message Passing (AMP) algorithms construct sequences of vectors ${\\boldsymbol u}^t\\in{\\mathbb R}^n$, ${\\boldsymbol v}^t\\in{\\mathbb R}^m$, indexed by $t\\in\\{0,1,2\\dots\\}$ by iteratively applying ${\\boldsymbol A}$ or ${\\boldsymbol A}^{{\\sf T}}$, and suitable non-linear functions, which depend on the specific application. Special instances of this approach have been developed --among other applications-- for compressed sensing reconstruction, robust regression, Bayesian estimation, low-rank matrix recove"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.03950","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":""},"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":"1708.03950","created_at":"2026-05-18T00:38:07.442732+00:00"},{"alias_kind":"arxiv_version","alias_value":"1708.03950v1","created_at":"2026-05-18T00:38:07.442732+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.03950","created_at":"2026-05-18T00:38:07.442732+00:00"},{"alias_kind":"pith_short_12","alias_value":"4WMUM7V2LJMV","created_at":"2026-05-18T12:31:00.734936+00:00"},{"alias_kind":"pith_short_16","alias_value":"4WMUM7V2LJMVKINS","created_at":"2026-05-18T12:31:00.734936+00:00"},{"alias_kind":"pith_short_8","alias_value":"4WMUM7V2","created_at":"2026-05-18T12:31:00.734936+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1907.07502","citing_title":"Algorithmic Analysis and Statistical Estimation of SLOPE via Approximate Message Passing","ref_index":8,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4WMUM7V2LJMVKINSGMGVHSFM7L","json":"https://pith.science/pith/4WMUM7V2LJMVKINSGMGVHSFM7L.json","graph_json":"https://pith.science/api/pith-number/4WMUM7V2LJMVKINSGMGVHSFM7L/graph.json","events_json":"https://pith.science/api/pith-number/4WMUM7V2LJMVKINSGMGVHSFM7L/events.json","paper":"https://pith.science/paper/4WMUM7V2"},"agent_actions":{"view_html":"https://pith.science/pith/4WMUM7V2LJMVKINSGMGVHSFM7L","download_json":"https://pith.science/pith/4WMUM7V2LJMVKINSGMGVHSFM7L.json","view_paper":"https://pith.science/paper/4WMUM7V2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1708.03950&json=true","fetch_graph":"https://pith.science/api/pith-number/4WMUM7V2LJMVKINSGMGVHSFM7L/graph.json","fetch_events":"https://pith.science/api/pith-number/4WMUM7V2LJMVKINSGMGVHSFM7L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4WMUM7V2LJMVKINSGMGVHSFM7L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4WMUM7V2LJMVKINSGMGVHSFM7L/action/storage_attestation","attest_author":"https://pith.science/pith/4WMUM7V2LJMVKINSGMGVHSFM7L/action/author_attestation","sign_citation":"https://pith.science/pith/4WMUM7V2LJMVKINSGMGVHSFM7L/action/citation_signature","submit_replication":"https://pith.science/pith/4WMUM7V2LJMVKINSGMGVHSFM7L/action/replication_record"}},"created_at":"2026-05-18T00:38:07.442732+00:00","updated_at":"2026-05-18T00:38:07.442732+00:00"}