{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:6T7YJ5NSNHWJ2NA6HIJMQ2XYUT","short_pith_number":"pith:6T7YJ5NS","schema_version":"1.0","canonical_sha256":"f4ff84f5b269ec9d341e3a12c86af8a4dcb9f22a789ffc98e3dba9330e4e3355","source":{"kind":"arxiv","id":"2306.02666","version":2},"attestation_state":"computed","paper":{"title":"Does a sparse ReLU network training problem always admit an optimum?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.FA","math.OC"],"primary_cat":"cs.NE","authors_text":"Elisa Riccietti (OCKHAM), OCKHAM), Quoc-Tung Le (LIP, R\\'emi Gribonval (OCKHAM)","submitted_at":"2023-06-05T08:01:50Z","abstract_excerpt":"Given a training set, a loss function, and a neural network architecture, it is often taken for granted that optimal network parameters exist, and a common practice is to apply available optimization algorithms to search for them. In this work, we show that the existence of an optimal solution is not always guaranteed, especially in the context of {\\em sparse} ReLU neural networks. In particular, we first show that optimization problems involving deep networks with certain sparsity patterns do not always have optimal parameters, and that optimization algorithms may then  diverge. Via a new top"},"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":"2306.02666","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NE","submitted_at":"2023-06-05T08:01:50Z","cross_cats_sorted":["math.AG","math.FA","math.OC"],"title_canon_sha256":"84e71db97069b31f406d8a595c94678342a2601b3ee50ed04e565a93d4a3325e","abstract_canon_sha256":"20e234da8b09f5246f462e0a18cc20832e799cb62be44c02ff41a316884a145f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:20:08.756826Z","signature_b64":"FXYRj1aBIyhHbc00L13ZVaPlvO2TcxUNiT1Yjr3kV7H/QHL3nM10eRNsB4QxgM63wHLPtom1F9eG8TAUazGjBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f4ff84f5b269ec9d341e3a12c86af8a4dcb9f22a789ffc98e3dba9330e4e3355","last_reissued_at":"2026-07-05T07:20:08.756389Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:20:08.756389Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Does a sparse ReLU network training problem always admit an optimum?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.FA","math.OC"],"primary_cat":"cs.NE","authors_text":"Elisa Riccietti (OCKHAM), OCKHAM), Quoc-Tung Le (LIP, R\\'emi Gribonval (OCKHAM)","submitted_at":"2023-06-05T08:01:50Z","abstract_excerpt":"Given a training set, a loss function, and a neural network architecture, it is often taken for granted that optimal network parameters exist, and a common practice is to apply available optimization algorithms to search for them. In this work, we show that the existence of an optimal solution is not always guaranteed, especially in the context of {\\em sparse} ReLU neural networks. In particular, we first show that optimization problems involving deep networks with certain sparsity patterns do not always have optimal parameters, and that optimization algorithms may then  diverge. Via a new top"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.02666","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/2306.02666/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":"2306.02666","created_at":"2026-07-05T07:20:08.756450+00:00"},{"alias_kind":"arxiv_version","alias_value":"2306.02666v2","created_at":"2026-07-05T07:20:08.756450+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2306.02666","created_at":"2026-07-05T07:20:08.756450+00:00"},{"alias_kind":"pith_short_12","alias_value":"6T7YJ5NSNHWJ","created_at":"2026-07-05T07:20:08.756450+00:00"},{"alias_kind":"pith_short_16","alias_value":"6T7YJ5NSNHWJ2NA6","created_at":"2026-07-05T07:20:08.756450+00:00"},{"alias_kind":"pith_short_8","alias_value":"6T7YJ5NS","created_at":"2026-07-05T07:20:08.756450+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2501.15646","citing_title":"Mathematical analysis of the gradients in deep learning","ref_index":35,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6T7YJ5NSNHWJ2NA6HIJMQ2XYUT","json":"https://pith.science/pith/6T7YJ5NSNHWJ2NA6HIJMQ2XYUT.json","graph_json":"https://pith.science/api/pith-number/6T7YJ5NSNHWJ2NA6HIJMQ2XYUT/graph.json","events_json":"https://pith.science/api/pith-number/6T7YJ5NSNHWJ2NA6HIJMQ2XYUT/events.json","paper":"https://pith.science/paper/6T7YJ5NS"},"agent_actions":{"view_html":"https://pith.science/pith/6T7YJ5NSNHWJ2NA6HIJMQ2XYUT","download_json":"https://pith.science/pith/6T7YJ5NSNHWJ2NA6HIJMQ2XYUT.json","view_paper":"https://pith.science/paper/6T7YJ5NS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2306.02666&json=true","fetch_graph":"https://pith.science/api/pith-number/6T7YJ5NSNHWJ2NA6HIJMQ2XYUT/graph.json","fetch_events":"https://pith.science/api/pith-number/6T7YJ5NSNHWJ2NA6HIJMQ2XYUT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6T7YJ5NSNHWJ2NA6HIJMQ2XYUT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6T7YJ5NSNHWJ2NA6HIJMQ2XYUT/action/storage_attestation","attest_author":"https://pith.science/pith/6T7YJ5NSNHWJ2NA6HIJMQ2XYUT/action/author_attestation","sign_citation":"https://pith.science/pith/6T7YJ5NSNHWJ2NA6HIJMQ2XYUT/action/citation_signature","submit_replication":"https://pith.science/pith/6T7YJ5NSNHWJ2NA6HIJMQ2XYUT/action/replication_record"}},"created_at":"2026-07-05T07:20:08.756450+00:00","updated_at":"2026-07-05T07:20:08.756450+00:00"}