{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:UVO6FTC2QLQVG5QJPUP2S7BKDM","short_pith_number":"pith:UVO6FTC2","schema_version":"1.0","canonical_sha256":"a55de2cc5a82e15376097d1fa97c2a1b134c36ee862e66b28ea2d958585812b5","source":{"kind":"arxiv","id":"2401.14961","version":4},"attestation_state":"computed","paper":{"title":"Set-Based Training for Neural Network Verification","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CR","cs.LO"],"primary_cat":"cs.LG","authors_text":"Lukas Koller, Matthias Althoff, Tobias Ladner","submitted_at":"2024-01-26T15:52:41Z","abstract_excerpt":"Neural networks are vulnerable to adversarial attacks, i.e., small input perturbations can significantly affect the outputs of a neural network. Therefore, to ensure safety of neural networks in safety-critical environments, the robustness of a neural network must be formally verified against input perturbations, e.g., from noisy sensors. To improve the robustness of neural networks and thus simplify the formal verification, we present a novel set-based training procedure in which we compute the set of possible outputs given the set of possible inputs and compute for the first time a gradient "},"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":"2401.14961","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-01-26T15:52:41Z","cross_cats_sorted":["cs.CR","cs.LO"],"title_canon_sha256":"d7fa318466c4b9ed371d2560d28f07bb6fa63e6c807a56db5cac40d41b38c05f","abstract_canon_sha256":"614bdcf83e92fb5a63355c9ee47a07d7e3d4ee30270be94229a9a28b7e978319"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:48:45.129283Z","signature_b64":"WGjp/lsMPutkQHuoO7ODaUTyfcUtbDrk/tkRGxEAca5V3MGemABRPfhhmvcEoXCKn7LXj1IO6ANyxXtZMctDDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a55de2cc5a82e15376097d1fa97c2a1b134c36ee862e66b28ea2d958585812b5","last_reissued_at":"2026-07-05T11:48:45.128867Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:48:45.128867Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Set-Based Training for Neural Network Verification","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CR","cs.LO"],"primary_cat":"cs.LG","authors_text":"Lukas Koller, Matthias Althoff, Tobias Ladner","submitted_at":"2024-01-26T15:52:41Z","abstract_excerpt":"Neural networks are vulnerable to adversarial attacks, i.e., small input perturbations can significantly affect the outputs of a neural network. Therefore, to ensure safety of neural networks in safety-critical environments, the robustness of a neural network must be formally verified against input perturbations, e.g., from noisy sensors. To improve the robustness of neural networks and thus simplify the formal verification, we present a novel set-based training procedure in which we compute the set of possible outputs given the set of possible inputs and compute for the first time a gradient "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.14961","kind":"arxiv","version":4},"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/2401.14961/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":"2401.14961","created_at":"2026-07-05T11:48:45.128924+00:00"},{"alias_kind":"arxiv_version","alias_value":"2401.14961v4","created_at":"2026-07-05T11:48:45.128924+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.14961","created_at":"2026-07-05T11:48:45.128924+00:00"},{"alias_kind":"pith_short_12","alias_value":"UVO6FTC2QLQV","created_at":"2026-07-05T11:48:45.128924+00:00"},{"alias_kind":"pith_short_16","alias_value":"UVO6FTC2QLQVG5QJ","created_at":"2026-07-05T11:48:45.128924+00:00"},{"alias_kind":"pith_short_8","alias_value":"UVO6FTC2","created_at":"2026-07-05T11:48:45.128924+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/UVO6FTC2QLQVG5QJPUP2S7BKDM","json":"https://pith.science/pith/UVO6FTC2QLQVG5QJPUP2S7BKDM.json","graph_json":"https://pith.science/api/pith-number/UVO6FTC2QLQVG5QJPUP2S7BKDM/graph.json","events_json":"https://pith.science/api/pith-number/UVO6FTC2QLQVG5QJPUP2S7BKDM/events.json","paper":"https://pith.science/paper/UVO6FTC2"},"agent_actions":{"view_html":"https://pith.science/pith/UVO6FTC2QLQVG5QJPUP2S7BKDM","download_json":"https://pith.science/pith/UVO6FTC2QLQVG5QJPUP2S7BKDM.json","view_paper":"https://pith.science/paper/UVO6FTC2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2401.14961&json=true","fetch_graph":"https://pith.science/api/pith-number/UVO6FTC2QLQVG5QJPUP2S7BKDM/graph.json","fetch_events":"https://pith.science/api/pith-number/UVO6FTC2QLQVG5QJPUP2S7BKDM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UVO6FTC2QLQVG5QJPUP2S7BKDM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UVO6FTC2QLQVG5QJPUP2S7BKDM/action/storage_attestation","attest_author":"https://pith.science/pith/UVO6FTC2QLQVG5QJPUP2S7BKDM/action/author_attestation","sign_citation":"https://pith.science/pith/UVO6FTC2QLQVG5QJPUP2S7BKDM/action/citation_signature","submit_replication":"https://pith.science/pith/UVO6FTC2QLQVG5QJPUP2S7BKDM/action/replication_record"}},"created_at":"2026-07-05T11:48:45.128924+00:00","updated_at":"2026-07-05T11:48:45.128924+00:00"}