{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:BM6LKQT5XOUYJ4KFAXQUF7SW4Q","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":"65c5f2cf1e5809c6c9ee33cd089302186c1f867881ec11e27ab77ae2785550a6","cross_cats_sorted":["cs.CR","cs.CV","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-04-16T17:24:51Z","title_canon_sha256":"5fdfdca08fd3b03e0350487652ad02ad4f0c59051c7c0e38f8f49cc4726a88e4"},"schema_version":"1.0","source":{"id":"1804.05805","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.05805","created_at":"2026-05-18T00:00:21Z"},{"alias_kind":"arxiv_version","alias_value":"1804.05805v2","created_at":"2026-05-18T00:00:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.05805","created_at":"2026-05-18T00:00:21Z"},{"alias_kind":"pith_short_12","alias_value":"BM6LKQT5XOUY","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"BM6LKQT5XOUYJ4KF","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"BM6LKQT5","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:357ae86a3aaa8aaca756e4c9c1fde81365b20948c37e06dd4ac532987de88fec","target":"graph","created_at":"2026-05-18T00:00:21Z","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":"Deployment of deep neural networks (DNNs) in safety- or security-critical systems requires provable guarantees on their correct behaviour. A common requirement is robustness to adversarial perturbations in a neighbourhood around an input. In this paper we focus on the $L_0$ norm and aim to compute, for a trained DNN and an input, the maximal radius of a safe norm ball around the input within which there are no adversarial examples. Then we define global robustness as an expectation of the maximal safe radius over a test data set. We first show that the problem is NP-hard, and then propose an a","authors_text":"Daniel Kroening, Marta Kwiatkowska, Min Wu, Wenjie Ruan, Xiaowei Huang, Youcheng Sun","cross_cats":["cs.CR","cs.CV","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-04-16T17:24:51Z","title":"Global Robustness Evaluation of Deep Neural Networks with Provable Guarantees for the $L_0$ Norm"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.05805","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:b89da7e9f7413e082e1e6c0e9a359f648c17cfc6169d3e2842b593666e160b37","target":"record","created_at":"2026-05-18T00:00:21Z","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":"65c5f2cf1e5809c6c9ee33cd089302186c1f867881ec11e27ab77ae2785550a6","cross_cats_sorted":["cs.CR","cs.CV","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-04-16T17:24:51Z","title_canon_sha256":"5fdfdca08fd3b03e0350487652ad02ad4f0c59051c7c0e38f8f49cc4726a88e4"},"schema_version":"1.0","source":{"id":"1804.05805","kind":"arxiv","version":2}},"canonical_sha256":"0b3cb5427dbba984f14505e142fe56e40e77839674ad0ee959d2f673d8b4eda3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0b3cb5427dbba984f14505e142fe56e40e77839674ad0ee959d2f673d8b4eda3","first_computed_at":"2026-05-18T00:00:21.535555Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:21.535555Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YL7+jWjdmkafOfj099Gonphc0Rz1zW9njr5sGl6pVCLmdjzO0gPZSQfWROGVmLIEzBY0BGNBvR9Vl1bNPfN8Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:21.536195Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.05805","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b89da7e9f7413e082e1e6c0e9a359f648c17cfc6169d3e2842b593666e160b37","sha256:357ae86a3aaa8aaca756e4c9c1fde81365b20948c37e06dd4ac532987de88fec"],"state_sha256":"6050944a11fa264ed05c38b7546bd33761cbb49184bf730399dcd555b619bdc7"}