{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:6UBCZ4YPXIRP5AEP3XJGQ4AKAE","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"7618c2f5b5c45b7d47dd176c5afd2d69b8179ea089dca86793323544d50824ce","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-04-22T17:58:36Z","title_canon_sha256":"fb9dc3c86d7cd1b4f0797231a4d5e7187fcf19acc6858caa9c185a8359990d6b"},"schema_version":"1.0","source":{"id":"2404.14402","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.14402","created_at":"2026-07-05T10:07:41Z"},{"alias_kind":"arxiv_version","alias_value":"2404.14402v1","created_at":"2026-07-05T10:07:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.14402","created_at":"2026-07-05T10:07:41Z"},{"alias_kind":"pith_short_12","alias_value":"6UBCZ4YPXIRP","created_at":"2026-07-05T10:07:41Z"},{"alias_kind":"pith_short_16","alias_value":"6UBCZ4YPXIRP5AEP","created_at":"2026-07-05T10:07:41Z"},{"alias_kind":"pith_short_8","alias_value":"6UBCZ4YP","created_at":"2026-07-05T10:07:41Z"}],"graph_snapshots":[{"event_id":"sha256:d55cc0582df8d6d08a21fe23644f8a9bf68ee0a656db33c9e8aba22c8de8cd1e","target":"graph","created_at":"2026-07-05T10:07:41Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2404.14402/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We connect adversarial training for binary classification to a geometric evolution equation for the decision boundary. Relying on a perspective that recasts adversarial training as a regularization problem, we introduce a modified training scheme that constitutes a minimizing movements scheme for a nonlocal perimeter functional. We prove that the scheme is monotone and consistent as the adversarial budget vanishes and the perimeter localizes, and as a consequence we rigorously show that the scheme approximates a weighted mean curvature flow. This highlights that the efficacy of adversarial tra","authors_text":"Kerrek Stinson, Leon Bungert, Tim Laux","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-04-22T17:58:36Z","title":"A mean curvature flow arising in adversarial training"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.14402","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:547eb17b85eb9c8fc00b9bbead0bf011659b05f19a5405a10ff4cf82fe93c1b3","target":"record","created_at":"2026-07-05T10:07:41Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"7618c2f5b5c45b7d47dd176c5afd2d69b8179ea089dca86793323544d50824ce","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-04-22T17:58:36Z","title_canon_sha256":"fb9dc3c86d7cd1b4f0797231a4d5e7187fcf19acc6858caa9c185a8359990d6b"},"schema_version":"1.0","source":{"id":"2404.14402","kind":"arxiv","version":1}},"canonical_sha256":"f5022cf30fba22fe808fddd268700a010d311b639075efae2965237c6bc25a97","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f5022cf30fba22fe808fddd268700a010d311b639075efae2965237c6bc25a97","first_computed_at":"2026-07-05T10:07:41.072358Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:07:41.072358Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+Y6C9yUTBdcZwqelu5/M6SsbxrJunA87qjucp5te0EkHqTLP223hM67MJch+eaSrGFpuIpTF/u0qqV0vaIC0DA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:07:41.072810Z","signed_message":"canonical_sha256_bytes"},"source_id":"2404.14402","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:547eb17b85eb9c8fc00b9bbead0bf011659b05f19a5405a10ff4cf82fe93c1b3","sha256:d55cc0582df8d6d08a21fe23644f8a9bf68ee0a656db33c9e8aba22c8de8cd1e"],"state_sha256":"64af4a44ef84176986ea431f3bf1f1a921f7aeafdbdf85ccb5b7d7c0135be5f2"}