{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:LKIM7VBLDZMYNMBI6AKVFSNRYX","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":"318ac29ca3e54ce4b36a6f2fee8cc4982460f3889b4c54be0d7edf38dbed8a85","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-11-13T16:15:22Z","title_canon_sha256":"ccb762e3d91c7dd4f4a8489783e3924629a8ea63d479814c6b9ff4e266d38977"},"schema_version":"1.0","source":{"id":"1811.05381","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.05381","created_at":"2026-05-17T23:43:37Z"},{"alias_kind":"arxiv_version","alias_value":"1811.05381v2","created_at":"2026-05-17T23:43:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.05381","created_at":"2026-05-17T23:43:37Z"},{"alias_kind":"pith_short_12","alias_value":"LKIM7VBLDZMY","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"LKIM7VBLDZMYNMBI","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"LKIM7VBL","created_at":"2026-05-18T12:32:37Z"}],"graph_snapshots":[{"event_id":"sha256:d778fb12d58242d112a2a4e2c2386386ab5ca47e37f54627a1e9d9edf368db78","target":"graph","created_at":"2026-05-17T23:43:37Z","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"},"paper":{"abstract_excerpt":"Training neural networks under a strict Lipschitz constraint is useful for provable adversarial robustness, generalization bounds, interpretable gradients, and Wasserstein distance estimation. By the composition property of Lipschitz functions, it suffices to ensure that each individual affine transformation or nonlinear activation is 1-Lipschitz. The challenge is to do this while maintaining the expressive power. We identify a necessary property for such an architecture: each of the layers must preserve the gradient norm during backpropagation. Based on this, we propose to combine a gradient ","authors_text":"Cem Anil, James Lucas, Roger Grosse","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-11-13T16:15:22Z","title":"Sorting out Lipschitz function approximation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.05381","kind":"arxiv","version":2},"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:ae8f90e1b1c1d01e56a6be37fbb2f849c53e30639a56bdd7e0a5bff3b0bb0538","target":"record","created_at":"2026-05-17T23:43:37Z","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":"318ac29ca3e54ce4b36a6f2fee8cc4982460f3889b4c54be0d7edf38dbed8a85","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-11-13T16:15:22Z","title_canon_sha256":"ccb762e3d91c7dd4f4a8489783e3924629a8ea63d479814c6b9ff4e266d38977"},"schema_version":"1.0","source":{"id":"1811.05381","kind":"arxiv","version":2}},"canonical_sha256":"5a90cfd42b1e5986b028f01552c9b1c5c73d83fb84b3c92849df472dec8948a5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5a90cfd42b1e5986b028f01552c9b1c5c73d83fb84b3c92849df472dec8948a5","first_computed_at":"2026-05-17T23:43:37.779496Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:37.779496Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pBjZ3AYr0T1jMrpzgMGebwWZN0UmhNXKGDQpwqemglO1OePcqIl8wDQbtiOYYUN3u4pX533xoPOzSnL8HlzyBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:37.780265Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.05381","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ae8f90e1b1c1d01e56a6be37fbb2f849c53e30639a56bdd7e0a5bff3b0bb0538","sha256:d778fb12d58242d112a2a4e2c2386386ab5ca47e37f54627a1e9d9edf368db78"],"state_sha256":"660331d5f098b4c242ac1888e71d305d1058c40e17fba1f792bad5337626c5c5"}