{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:A5Z6F5OAYVUTB4NYNT7AX3XT2D","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":"e298a200b6644fc1321fabd7666c1e73b2c0e4ce8cb8a24f10ba72e2311c9501","cross_cats_sorted":["math.AG","math.CO","math.MG","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-03-28T17:41:17Z","title_canon_sha256":"d2e9a52a95b78b79136790bbdf8502e5ee7118285dd72e432036bb5b90176517"},"schema_version":"1.0","source":{"id":"2503.22653","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.22653","created_at":"2026-07-05T10:41:08Z"},{"alias_kind":"arxiv_version","alias_value":"2503.22653v1","created_at":"2026-07-05T10:41:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.22653","created_at":"2026-07-05T10:41:08Z"},{"alias_kind":"pith_short_12","alias_value":"A5Z6F5OAYVUT","created_at":"2026-07-05T10:41:08Z"},{"alias_kind":"pith_short_16","alias_value":"A5Z6F5OAYVUTB4NY","created_at":"2026-07-05T10:41:08Z"},{"alias_kind":"pith_short_8","alias_value":"A5Z6F5OA","created_at":"2026-07-05T10:41:08Z"}],"graph_snapshots":[{"event_id":"sha256:83ddcd89f91b4949b2a1b4d35f45e3f82f214dc628d07abcb3c952e307e8675c","target":"graph","created_at":"2026-07-05T10:41:08Z","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/2503.22653/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Pasque et al. showed that using a tropical symmetric metric as an activation function in the last layer can improve the robustness of convolutional neural networks (CNNs) against state-of-the-art attacks, including the Carlini-Wagner attack. This improvement occurs when the attacks are not specifically adapted to the non-differentiability of the tropical layer. Moreover, they showed that the decision boundary of a tropical CNN is defined by tropical bisectors. In this paper, we explore the combinatorics of tropical bisectors and analyze how the tropical embedding layer enhances robustness agai","authors_text":"Daniela Schkoda, Gillian Grindstaff, Julia Lindberg, Miruna-Stefana Sorea, Ruriko Yoshida","cross_cats":["math.AG","math.CO","math.MG","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-03-28T17:41:17Z","title":"Tropical Bisectors and Carlini-Wagner Attacks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.22653","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":"sha256:36d41b292ac33f696ba1488ede7a0a227db83b5030a8ac455ccd0f5fbf105b9c","target":"record","created_at":"2026-07-05T10:41:08Z","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":"e298a200b6644fc1321fabd7666c1e73b2c0e4ce8cb8a24f10ba72e2311c9501","cross_cats_sorted":["math.AG","math.CO","math.MG","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-03-28T17:41:17Z","title_canon_sha256":"d2e9a52a95b78b79136790bbdf8502e5ee7118285dd72e432036bb5b90176517"},"schema_version":"1.0","source":{"id":"2503.22653","kind":"arxiv","version":1}},"canonical_sha256":"0773e2f5c0c56930f1b86cfe0beef3d0f409ee280ee95f751280892a60e32b3c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0773e2f5c0c56930f1b86cfe0beef3d0f409ee280ee95f751280892a60e32b3c","first_computed_at":"2026-07-05T10:41:08.399374Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:41:08.399374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hTRrrjmrx0CAcID7cg4ZebpHfoRsvCK4piy68eSIY6e/IQfgfmAiyw+PjLgtiNLPdCez/7UTldvLVMSk7XqSCg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:41:08.399827Z","signed_message":"canonical_sha256_bytes"},"source_id":"2503.22653","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:36d41b292ac33f696ba1488ede7a0a227db83b5030a8ac455ccd0f5fbf105b9c","sha256:83ddcd89f91b4949b2a1b4d35f45e3f82f214dc628d07abcb3c952e307e8675c"],"state_sha256":"a0bb254b4c650b5639ca4991fdea8e9466617ff33bbb3618a0451b4efa3430a7"}