{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:3EA4NGPRV55YNCIZMOWRVHZRBM","short_pith_number":"pith:3EA4NGPR","schema_version":"1.0","canonical_sha256":"d901c699f1af7b86891963ad1a9f310b007810cddf65f1362c48c6dde0cbc704","source":{"kind":"arxiv","id":"2501.03017","version":2},"attestation_state":"computed","paper":{"title":"Convexity in ReLU Neural Networks: beyond ICNNs?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Anne Gagneux, Emmanuel Soubies, Mathurin Massias, R\\'emi Gribonval","submitted_at":"2025-01-06T13:53:59Z","abstract_excerpt":"Convex functions and their gradients play a critical role in mathematical imaging, from proximal optimization to Optimal Transport. The successes of deep learning has led many to use learning-based methods, where fixed functions or operators are replaced by learned neural networks. Regardless of their empirical superiority, establishing rigorous guarantees for these methods often requires to impose structural constraints on neural architectures, in particular convexity. The most popular way to do so is to use so-called Input Convex Neural Networks (ICNNs). In order to explore the expressivity "},"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":"2501.03017","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-01-06T13:53:59Z","cross_cats_sorted":[],"title_canon_sha256":"661dbeca0274db55f67778cf4d40c620638710bc88eed707a3496512faf9494f","abstract_canon_sha256":"4a544282001a9f2b42024047d3bc40cb625c35318e18b1eb8abc3bb5d35f46ba"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:45:58.947119Z","signature_b64":"RRrfBMhYnxLGgB6U/B8rglTeR3SrHrP5wz9e1/HldcRrw7/U/pGAzUFc1curdCA8MNA1VhDfNsoN7OQ5q8vsDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d901c699f1af7b86891963ad1a9f310b007810cddf65f1362c48c6dde0cbc704","last_reissued_at":"2026-07-05T10:45:58.946690Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:45:58.946690Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Convexity in ReLU Neural Networks: beyond ICNNs?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Anne Gagneux, Emmanuel Soubies, Mathurin Massias, R\\'emi Gribonval","submitted_at":"2025-01-06T13:53:59Z","abstract_excerpt":"Convex functions and their gradients play a critical role in mathematical imaging, from proximal optimization to Optimal Transport. The successes of deep learning has led many to use learning-based methods, where fixed functions or operators are replaced by learned neural networks. Regardless of their empirical superiority, establishing rigorous guarantees for these methods often requires to impose structural constraints on neural architectures, in particular convexity. The most popular way to do so is to use so-called Input Convex Neural Networks (ICNNs). In order to explore the expressivity "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.03017","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/2501.03017/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":"2501.03017","created_at":"2026-07-05T10:45:58.946745+00:00"},{"alias_kind":"arxiv_version","alias_value":"2501.03017v2","created_at":"2026-07-05T10:45:58.946745+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.03017","created_at":"2026-07-05T10:45:58.946745+00:00"},{"alias_kind":"pith_short_12","alias_value":"3EA4NGPRV55Y","created_at":"2026-07-05T10:45:58.946745+00:00"},{"alias_kind":"pith_short_16","alias_value":"3EA4NGPRV55YNCIZ","created_at":"2026-07-05T10:45:58.946745+00:00"},{"alias_kind":"pith_short_8","alias_value":"3EA4NGPR","created_at":"2026-07-05T10:45:58.946745+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2505.06169","citing_title":"On the Depth of Monotone ReLU Neural Networks and ICNNs","ref_index":15,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3EA4NGPRV55YNCIZMOWRVHZRBM","json":"https://pith.science/pith/3EA4NGPRV55YNCIZMOWRVHZRBM.json","graph_json":"https://pith.science/api/pith-number/3EA4NGPRV55YNCIZMOWRVHZRBM/graph.json","events_json":"https://pith.science/api/pith-number/3EA4NGPRV55YNCIZMOWRVHZRBM/events.json","paper":"https://pith.science/paper/3EA4NGPR"},"agent_actions":{"view_html":"https://pith.science/pith/3EA4NGPRV55YNCIZMOWRVHZRBM","download_json":"https://pith.science/pith/3EA4NGPRV55YNCIZMOWRVHZRBM.json","view_paper":"https://pith.science/paper/3EA4NGPR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2501.03017&json=true","fetch_graph":"https://pith.science/api/pith-number/3EA4NGPRV55YNCIZMOWRVHZRBM/graph.json","fetch_events":"https://pith.science/api/pith-number/3EA4NGPRV55YNCIZMOWRVHZRBM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3EA4NGPRV55YNCIZMOWRVHZRBM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3EA4NGPRV55YNCIZMOWRVHZRBM/action/storage_attestation","attest_author":"https://pith.science/pith/3EA4NGPRV55YNCIZMOWRVHZRBM/action/author_attestation","sign_citation":"https://pith.science/pith/3EA4NGPRV55YNCIZMOWRVHZRBM/action/citation_signature","submit_replication":"https://pith.science/pith/3EA4NGPRV55YNCIZMOWRVHZRBM/action/replication_record"}},"created_at":"2026-07-05T10:45:58.946745+00:00","updated_at":"2026-07-05T10:45:58.946745+00:00"}