{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:WFX3M73BH2XXC5U6FM33G52U5L","short_pith_number":"pith:WFX3M73B","schema_version":"1.0","canonical_sha256":"b16fb67f613eaf71769e2b37b37754eaf7bf93d9939721a57d3ae9aa9b1c5173","source":{"kind":"arxiv","id":"1912.02938","version":1},"attestation_state":"computed","paper":{"title":"Lower Bounds for Compressed Sensing with Generative Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","cs.LG","math.IT"],"primary_cat":"cs.DS","authors_text":"Akshay Kamath, Eric Price, Sushrut Karmalkar","submitted_at":"2019-12-06T00:51:51Z","abstract_excerpt":"The goal of compressed sensing is to learn a structured signal $x$ from a limited number of noisy linear measurements $y \\approx Ax$. In traditional compressed sensing, \"structure\" is represented by sparsity in some known basis. Inspired by the success of deep learning in modeling images, recent work starting with~\\cite{BJPD17} has instead considered structure to come from a generative model $G: \\mathbb{R}^k \\to \\mathbb{R}^n$. We present two results establishing the difficulty of this latter task, showing that existing bounds are tight. First, we provide a lower bound matching the~\\cite{BJPD17"},"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":"1912.02938","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-12-06T00:51:51Z","cross_cats_sorted":["cs.IT","cs.LG","math.IT"],"title_canon_sha256":"a205892509e3d892454fa926462771ef27c4717e787ba204af4a4963cac4daf5","abstract_canon_sha256":"395a7b5c1307e79f23f6f56ea20ddbd72d8f0e3207bc2f9054f6c2e4308a5219"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:24:19.731288Z","signature_b64":"dzzHiJFDjwy+QvnvLCrw54o18NAhjJXL1IkmV8pC2vmunE1VxtGG5ii3A3qr4gc1C14UCQAJgNHRKPXCxVp/Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b16fb67f613eaf71769e2b37b37754eaf7bf93d9939721a57d3ae9aa9b1c5173","last_reissued_at":"2026-07-05T00:24:19.730945Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:24:19.730945Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lower Bounds for Compressed Sensing with Generative Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","cs.LG","math.IT"],"primary_cat":"cs.DS","authors_text":"Akshay Kamath, Eric Price, Sushrut Karmalkar","submitted_at":"2019-12-06T00:51:51Z","abstract_excerpt":"The goal of compressed sensing is to learn a structured signal $x$ from a limited number of noisy linear measurements $y \\approx Ax$. In traditional compressed sensing, \"structure\" is represented by sparsity in some known basis. Inspired by the success of deep learning in modeling images, recent work starting with~\\cite{BJPD17} has instead considered structure to come from a generative model $G: \\mathbb{R}^k \\to \\mathbb{R}^n$. We present two results establishing the difficulty of this latter task, showing that existing bounds are tight. First, we provide a lower bound matching the~\\cite{BJPD17"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1912.02938","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/1912.02938/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":"1912.02938","created_at":"2026-07-05T00:24:19.731006+00:00"},{"alias_kind":"arxiv_version","alias_value":"1912.02938v1","created_at":"2026-07-05T00:24:19.731006+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1912.02938","created_at":"2026-07-05T00:24:19.731006+00:00"},{"alias_kind":"pith_short_12","alias_value":"WFX3M73BH2XX","created_at":"2026-07-05T00:24:19.731006+00:00"},{"alias_kind":"pith_short_16","alias_value":"WFX3M73BH2XXC5U6","created_at":"2026-07-05T00:24:19.731006+00:00"},{"alias_kind":"pith_short_8","alias_value":"WFX3M73B","created_at":"2026-07-05T00:24:19.731006+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1908.10744","citing_title":"Information-Theoretic Lower Bounds for Compressive Sensing with Generative Models","ref_index":23,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WFX3M73BH2XXC5U6FM33G52U5L","json":"https://pith.science/pith/WFX3M73BH2XXC5U6FM33G52U5L.json","graph_json":"https://pith.science/api/pith-number/WFX3M73BH2XXC5U6FM33G52U5L/graph.json","events_json":"https://pith.science/api/pith-number/WFX3M73BH2XXC5U6FM33G52U5L/events.json","paper":"https://pith.science/paper/WFX3M73B"},"agent_actions":{"view_html":"https://pith.science/pith/WFX3M73BH2XXC5U6FM33G52U5L","download_json":"https://pith.science/pith/WFX3M73BH2XXC5U6FM33G52U5L.json","view_paper":"https://pith.science/paper/WFX3M73B","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1912.02938&json=true","fetch_graph":"https://pith.science/api/pith-number/WFX3M73BH2XXC5U6FM33G52U5L/graph.json","fetch_events":"https://pith.science/api/pith-number/WFX3M73BH2XXC5U6FM33G52U5L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WFX3M73BH2XXC5U6FM33G52U5L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WFX3M73BH2XXC5U6FM33G52U5L/action/storage_attestation","attest_author":"https://pith.science/pith/WFX3M73BH2XXC5U6FM33G52U5L/action/author_attestation","sign_citation":"https://pith.science/pith/WFX3M73BH2XXC5U6FM33G52U5L/action/citation_signature","submit_replication":"https://pith.science/pith/WFX3M73BH2XXC5U6FM33G52U5L/action/replication_record"}},"created_at":"2026-07-05T00:24:19.731006+00:00","updated_at":"2026-07-05T00:24:19.731006+00:00"}