{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:LAUCTWO2PO27IKXODMJXD54S4L","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":"a15acf7bad1ca90b82af57df0dc6fab56eb7a432d0e70d4b48e9fe32d72b2979","cross_cats_sorted":["cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2018-11-13T11:48:43Z","title_canon_sha256":"c870bace8f2b3d72ffbca34bc63f3080ecbbcb3fa8087e52f8a274dc82f93f29"},"schema_version":"1.0","source":{"id":"1811.05232","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.05232","created_at":"2026-05-17T23:55:38Z"},{"alias_kind":"arxiv_version","alias_value":"1811.05232v2","created_at":"2026-05-17T23:55:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.05232","created_at":"2026-05-17T23:55:38Z"},{"alias_kind":"pith_short_12","alias_value":"LAUCTWO2PO27","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"LAUCTWO2PO27IKXO","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"LAUCTWO2","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:371862653ddaec6a4c7d8b701d80a4973d7da072863030aec5c9b3a3467848c4","target":"graph","created_at":"2026-05-17T23:55:38Z","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":"Here we propose a general theoretical method for analyzing the risk bound in the presence of adversaries. Specifically, we try to fit the adversarial learning problem into the minimax framework. We first show that the original adversarial learning problem can be reduced to a minimax statistical learning problem by introducing a transport map between distributions. Then, we prove a new risk bound for this minimax problem in terms of covering numbers under a weak version of Lipschitz condition. Our method can be applied to multi-class classification problems and commonly used loss functions such","authors_text":"Dacheng Tao, Jingwei Zhang, Zhuozhuo Tu","cross_cats":["cs.LG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2018-11-13T11:48:43Z","title":"Theoretical Analysis of Adversarial Learning: A Minimax Approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.05232","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:ae1ae2bcafa1b44f5c239024c350e79005b75f658d3a733c0da60f2704227211","target":"record","created_at":"2026-05-17T23:55:38Z","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":"a15acf7bad1ca90b82af57df0dc6fab56eb7a432d0e70d4b48e9fe32d72b2979","cross_cats_sorted":["cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2018-11-13T11:48:43Z","title_canon_sha256":"c870bace8f2b3d72ffbca34bc63f3080ecbbcb3fa8087e52f8a274dc82f93f29"},"schema_version":"1.0","source":{"id":"1811.05232","kind":"arxiv","version":2}},"canonical_sha256":"582829d9da7bb5f42aee1b1371f792e2ebee0caf18d64af9a9433c1240050d70","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"582829d9da7bb5f42aee1b1371f792e2ebee0caf18d64af9a9433c1240050d70","first_computed_at":"2026-05-17T23:55:38.251332Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:55:38.251332Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fCUcJ1X9Xr73JCmpWhlivImVfMVHehgdJNArupGm33Vwqakdc0XvKcxU4Yb2xkc1it6Ne6CvohPhaBVBK2UmBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:55:38.251788Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.05232","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ae1ae2bcafa1b44f5c239024c350e79005b75f658d3a733c0da60f2704227211","sha256:371862653ddaec6a4c7d8b701d80a4973d7da072863030aec5c9b3a3467848c4"],"state_sha256":"310772d16bf7494222018cbd4ab228dca6bde7a945bb7a5cc2baa6c1ca29cc2c"}