{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:RIVHURFMCK3NXFYDRLXVNZBEKT","short_pith_number":"pith:RIVHURFM","canonical_record":{"source":{"id":"2605.12876","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-05-13T01:44:31Z","cross_cats_sorted":[],"title_canon_sha256":"069b08904844747f7c099c7513b19d1577d7dcb1e047a95182c64180e360d5a9","abstract_canon_sha256":"42a7e94add9dd79146598653c2462e5a6f2e250ada794afda1afee7286258a27"},"schema_version":"1.0"},"canonical_sha256":"8a2a7a44ac12b6db97038aef56e42454ed21a423ea5219052c9c2ba2e877eb80","source":{"kind":"arxiv","id":"2605.12876","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.12876","created_at":"2026-05-18T03:09:11Z"},{"alias_kind":"arxiv_version","alias_value":"2605.12876v1","created_at":"2026-05-18T03:09:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.12876","created_at":"2026-05-18T03:09:11Z"},{"alias_kind":"pith_short_12","alias_value":"RIVHURFMCK3N","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"RIVHURFMCK3NXFYD","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"RIVHURFM","created_at":"2026-05-18T12:33:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:RIVHURFMCK3NXFYDRLXVNZBEKT","target":"record","payload":{"canonical_record":{"source":{"id":"2605.12876","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-05-13T01:44:31Z","cross_cats_sorted":[],"title_canon_sha256":"069b08904844747f7c099c7513b19d1577d7dcb1e047a95182c64180e360d5a9","abstract_canon_sha256":"42a7e94add9dd79146598653c2462e5a6f2e250ada794afda1afee7286258a27"},"schema_version":"1.0"},"canonical_sha256":"8a2a7a44ac12b6db97038aef56e42454ed21a423ea5219052c9c2ba2e877eb80","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:09:11.204418Z","signature_b64":"SsvB51zXjEIGncsEzW0lW2nq2du/4ExpfLpgcUQAPxCM8RKk2/Gaf6l7JBEK/mVWXWquPhAHvI5MOKzK5W7PAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8a2a7a44ac12b6db97038aef56e42454ed21a423ea5219052c9c2ba2e877eb80","last_reissued_at":"2026-05-18T03:09:11.203825Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:09:11.203825Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.12876","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:09:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6oWRP356SMMrWBx2f67dzfxa7RI5MqtHN0sZcrGLFtt7ExIC04GTc1Vqjlws1qJZ2MuAJhWJr4xB26f7H1F5CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T03:34:07.833560Z"},"content_sha256":"4ebba3304134185b3a305ed0cf8b0c19974caaa0833845e067f3a31bb0a76a70","schema_version":"1.0","event_id":"sha256:4ebba3304134185b3a305ed0cf8b0c19974caaa0833845e067f3a31bb0a76a70"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:RIVHURFMCK3NXFYDRLXVNZBEKT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Certified Robustness under Heterogeneous Perturbations via Hybrid Randomized Smoothing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Hybrid randomized smoothing yields a closed-form one-dimensional certificate that generalizes both Gaussian and discrete smoothing for joint discrete-continuous inputs.","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Blaise Delattre, Hengyu Wu, Paul Caillon, Wei Yang Bryan Lim, Yang Cao","submitted_at":"2026-05-13T01:44:31Z","abstract_excerpt":"Randomized smoothing provides strong, model-agnostic robustness certificates, but existing guarantees are limited to single modalities, treating continuous and discrete inputs in isolation. This limitation becomes critical in multimodal models, where decisions depend on cross-modal semantics and adversaries can jointly perturb heterogeneous inputs, rendering unimodal certificates insufficient. We introduce a unified randomized smoothing framework for mixed discrete--continuous inputs based on an analytically tractable Neyman--Pearson formulation of the joint worst-case problem. By analyzing th"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"our approach yields a closed-form, one-dimensional certificate that strictly generalizes both Gaussian (image-only) and discrete (text-only) randomized smoothing","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The joint likelihood ordering induced by factorized discrete and continuous noise permits an analytically tractable Neyman-Pearson formulation of the worst-case problem.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A hybrid randomized smoothing method yields a closed-form certificate for joint discrete-continuous perturbations that generalizes prior Gaussian and discrete smoothing approaches.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Hybrid randomized smoothing yields a closed-form one-dimensional certificate that generalizes both Gaussian and discrete smoothing for joint discrete-continuous inputs.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"088c8bbfae37d832f33018c35686e1e70681cb98aff6a45f16c0e5d230f6f090"},"source":{"id":"2605.12876","kind":"arxiv","version":1},"verdict":{"id":"88a2435d-c52f-43e5-bd14-adfb509870d7","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T20:19:40.652530Z","strongest_claim":"our approach yields a closed-form, one-dimensional certificate that strictly generalizes both Gaussian (image-only) and discrete (text-only) randomized smoothing","one_line_summary":"A hybrid randomized smoothing method yields a closed-form certificate for joint discrete-continuous perturbations that generalizes prior Gaussian and discrete smoothing approaches.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The joint likelihood ordering induced by factorized discrete and continuous noise permits an analytically tractable Neyman-Pearson formulation of the worst-case problem.","pith_extraction_headline":"Hybrid randomized smoothing yields a closed-form one-dimensional certificate that generalizes both Gaussian and discrete smoothing for joint discrete-continuous inputs."},"references":{"count":22,"sample":[{"doi":"","year":2023,"title":"A., Jagielski, M., Gao, I., Awadalla, A., Koh, P","work_id":"490b95c3-2f53-4701-a7a7-c9ad219de0e6","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2024,"title":"A Survey on Multimodal Large Language Models for Autonomous Driving","work_id":"184f4f4a-d36f-4593-94cb-4b6420fa77b0","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Defeating Prompt Injections by Design","work_id":"86405b86-1c51-4042-9b04-aff0b6541411","ref_index":4,"cited_arxiv_id":"2503.18813","is_internal_anchor":true},{"doi":"","year":null,"title":"Ad- versarial attacks to multi-modal models.arXiv preprint arXiv:2409.06793,","work_id":"25ac5b53-65c4-42b2-8069-27b5dfd6311e","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Llavaguard: An open vlm- based framework for safeguarding vision datasets and mod- els","work_id":"6428946a-91bd-4dbe-b263-a8f502ab8aa0","ref_index":6,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":22,"snapshot_sha256":"c2284d38c6b069473c5988ad3246014f7007ae9a218f7fa3fb1d43bdbce5dbf5","internal_anchors":5},"formal_canon":{"evidence_count":2,"snapshot_sha256":"d7be81a3f67da361da43c82a6500f303f6b52a7a5355a318c0f2d7bf34bc667e"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":"88a2435d-c52f-43e5-bd14-adfb509870d7"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:09:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8vWcbzK4QEJQBRlJab23tFeFA+/qlYXoHWxyVrtTVRmQdqhAawxD2G6deLOgrTRJVxIW7SjPNaUdKSfGErNqDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T03:34:07.834686Z"},"content_sha256":"210c702eb4be8a6efd159f9def981900a038da1e422aff103e5141e3e55faad2","schema_version":"1.0","event_id":"sha256:210c702eb4be8a6efd159f9def981900a038da1e422aff103e5141e3e55faad2"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:RIVHURFMCK3NXFYDRLXVNZBEKT","target":"integrity","payload":{"note":"DOI in the printed bibliography is fragmented by whitespace or line breaks. A longer candidate (10.48550/arXiv.2307.15043.12) was visible in the surrounding text but could not be confirmed against doi.org as printed.","snippet":"doi: 10.48550/arXiv.2307. 15043. 12 Certified Robustness under Heterogeneous Perturbations A. Appendix A.1. Choice of Thresholdτ Randomized smoothing certifies robustness by bounding the smoothed classifier’s output under worst-case perturb","arxiv_id":"2605.12876","detector":"doi_compliance","evidence":{"ref_index":20,"verdict_class":"incontrovertible","resolved_title":null,"printed_excerpt":"doi: 10.48550/arXiv.2307. 15043. 12 Certified Robustness under Heterogeneous Perturbations A. Appendix A.1. Choice of Thresholdτ Randomized smoothing certifies robustness by bounding the smoothed classifier’s output under worst-case perturb","reconstructed_doi":"10.48550/arXiv.2307.15043.12"},"severity":"advisory","ref_index":20,"audited_at":"2026-05-19T06:59:55.994099Z","event_type":"pith.integrity.v1","detected_doi":"10.48550/arXiv.2307.15043.12","detector_url":"https://pith.science/pith-integrity-protocol#doi_compliance","external_url":null,"finding_type":"recoverable_identifier","evidence_hash":"0e7f8b4f9126a875107a3048d659ca5222657b0b73543e4ea4823b8400899bbe","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null,"integrity_event_id":248,"payload_sha256":"7dbd41f831760b0eb98e257b65ca75f4b8d112f4763b9fe2abfbb773fb88bc42","signature_b64":"UBbGAooaCZDvsxb03y/WGQiLiF1aaUkRNICTQ9VRk/5tbcyzhXH3JYLhuEsFveUWxc9FLVF73oO4xBnuZfb5CA==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-19T07:01:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HhxGXvx4uyyOn7Trpu1y3I9E8/s8d71zNbMT9cogtfx5m11nu9XigV9+ed1xnNVznTLeywYy0Ren+Bk3epyDCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T03:34:07.836698Z"},"content_sha256":"ffa010cda324f0598cf8a1136e2811b35bf5f9fa40b96f4d0bc4b60d8ac3bbe9","schema_version":"1.0","event_id":"sha256:ffa010cda324f0598cf8a1136e2811b35bf5f9fa40b96f4d0bc4b60d8ac3bbe9"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:RIVHURFMCK3NXFYDRLXVNZBEKT","target":"integrity","payload":{"note":"DOI in the printed bibliography is fragmented by whitespace or line breaks. A longer candidate (10.1162/colia) was visible in the surrounding text but could not be confirmed against doi.org as printed.","snippet":"doi: 10.1162/coli a 00476. Zhan, Q., Fang, R., Panchal, H. S., and Kang, D. Adaptive attacks break defenses against indirect prompt injection attacks on llm agents. InFindings of the Association for Computational Linguistics: NAACL,","arxiv_id":"2605.12876","detector":"doi_compliance","evidence":{"ref_index":18,"verdict_class":"incontrovertible","resolved_title":null,"printed_excerpt":"doi: 10.1162/coli a 00476. Zhan, Q., Fang, R., Panchal, H. S., and Kang, D. Adaptive attacks break defenses against indirect prompt injection attacks on llm agents. InFindings of the Association for Computational Linguistics: NAACL,","reconstructed_doi":"10.1162/colia"},"severity":"advisory","ref_index":18,"audited_at":"2026-05-19T06:59:55.994099Z","event_type":"pith.integrity.v1","detected_doi":"10.1162/colia","detector_url":"https://pith.science/pith-integrity-protocol#doi_compliance","external_url":null,"finding_type":"recoverable_identifier","evidence_hash":"a9e07f3f28e883bd066542d6200984e7667e4448a9256f86320efa2fc721b35a","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null,"integrity_event_id":247,"payload_sha256":"89340f414f1ad962e12f077642abb661a9f86203aeeadddae58b159fda0391f6","signature_b64":"mSE2t9BdbcPJkfmB9AphRRSmZ4B2cU2fx34/BtmyGwG8pRgXdPxs2o8M8Ng8NYCcqXxEreEVfIMEQdBEZFbkAA==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-19T07:01:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4NCSyRen7QdzLGds1i9zarXdlbAe7Mi8zF1bVNRk3TnvJnwTIDtYChyYn62YuaRJd60GSSLGYEaWdhZdJ2QkDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T03:34:07.837302Z"},"content_sha256":"0109e2998b3b0af8a8e4bb01ee886ecc157d3669d8a77ebe2478d998050f2a55","schema_version":"1.0","event_id":"sha256:0109e2998b3b0af8a8e4bb01ee886ecc157d3669d8a77ebe2478d998050f2a55"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:RIVHURFMCK3NXFYDRLXVNZBEKT","target":"integrity","payload":{"note":"DOI in the printed bibliography is fragmented by whitespace or line breaks. A longer candidate (10.48550/arXiv.2406.05113.10) was visible in the surrounding text but could not be confirmed against doi.org as printed.","snippet":"doi: 10.48550/arXiv. 2406.05113. 10 Certified Robustness under Heterogeneous Perturbations Huang, Z., Chu, W., Li, L., Xu, C., and Li, B. Commit: Cer- tifying robustness of multi-sensor fusion systems against semantic attacks. InProceedings","arxiv_id":"2605.12876","detector":"doi_compliance","evidence":{"ref_index":7,"verdict_class":"incontrovertible","resolved_title":null,"printed_excerpt":"doi: 10.48550/arXiv. 2406.05113. 10 Certified Robustness under Heterogeneous Perturbations Huang, Z., Chu, W., Li, L., Xu, C., and Li, B. Commit: Cer- tifying robustness of multi-sensor fusion systems against semantic attacks. InProceedings","reconstructed_doi":"10.48550/arXiv.2406.05113.10"},"severity":"advisory","ref_index":7,"audited_at":"2026-05-19T06:59:55.994099Z","event_type":"pith.integrity.v1","detected_doi":"10.48550/arXiv.2406.05113.10","detector_url":"https://pith.science/pith-integrity-protocol#doi_compliance","external_url":null,"finding_type":"recoverable_identifier","evidence_hash":"b9acc4eb62e60302dc737038a4db19923ec11fc4988e71622207cdc81356dcb6","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null,"integrity_event_id":246,"payload_sha256":"74ca52ea1b749c46020b03818e54931b12e4d45c1388c06d5d5a61f15503ecc0","signature_b64":"EzTpb6IGy/4FHop5JyP+dbOzMvTinpak9S8p3qX7ywtMA+RQeyayyFBt+HbE0v4YlaBxp8pcL9hBe4SH1LkoAg==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-19T07:01:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9vKQTpDMMEYvIJI77jH40LnWQ8MnTJ2GbRvjXRiwGx+qQBxd1tK/K0uM4NiPyWGo31BiCNHYUBmTDm2RuGVrCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T03:34:07.837940Z"},"content_sha256":"59d3c97c4ae91db219bdaf64457bd00e85981fdfe5466b9c9ffaa8b61831e61e","schema_version":"1.0","event_id":"sha256:59d3c97c4ae91db219bdaf64457bd00e85981fdfe5466b9c9ffaa8b61831e61e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RIVHURFMCK3NXFYDRLXVNZBEKT/bundle.json","state_url":"https://pith.science/pith/RIVHURFMCK3NXFYDRLXVNZBEKT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RIVHURFMCK3NXFYDRLXVNZBEKT/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-23T03:34:07Z","links":{"resolver":"https://pith.science/pith/RIVHURFMCK3NXFYDRLXVNZBEKT","bundle":"https://pith.science/pith/RIVHURFMCK3NXFYDRLXVNZBEKT/bundle.json","state":"https://pith.science/pith/RIVHURFMCK3NXFYDRLXVNZBEKT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RIVHURFMCK3NXFYDRLXVNZBEKT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:RIVHURFMCK3NXFYDRLXVNZBEKT","merge_version":"pith-open-graph-merge-v1","event_count":5,"valid_event_count":5,"invalid_event_count":0,"equivocation_count":1,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"42a7e94add9dd79146598653c2462e5a6f2e250ada794afda1afee7286258a27","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-05-13T01:44:31Z","title_canon_sha256":"069b08904844747f7c099c7513b19d1577d7dcb1e047a95182c64180e360d5a9"},"schema_version":"1.0","source":{"id":"2605.12876","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.12876","created_at":"2026-05-18T03:09:11Z"},{"alias_kind":"arxiv_version","alias_value":"2605.12876v1","created_at":"2026-05-18T03:09:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.12876","created_at":"2026-05-18T03:09:11Z"},{"alias_kind":"pith_short_12","alias_value":"RIVHURFMCK3N","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"RIVHURFMCK3NXFYD","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"RIVHURFM","created_at":"2026-05-18T12:33:37Z"}],"graph_snapshots":[{"event_id":"sha256:210c702eb4be8a6efd159f9def981900a038da1e422aff103e5141e3e55faad2","target":"graph","created_at":"2026-05-18T03:09:11Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"our approach yields a closed-form, one-dimensional certificate that strictly generalizes both Gaussian (image-only) and discrete (text-only) randomized smoothing"},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The joint likelihood ordering induced by factorized discrete and continuous noise permits an analytically tractable Neyman-Pearson formulation of the worst-case problem."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"A hybrid randomized smoothing method yields a closed-form certificate for joint discrete-continuous perturbations that generalizes prior Gaussian and discrete smoothing approaches."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Hybrid randomized smoothing yields a closed-form one-dimensional certificate that generalizes both Gaussian and discrete smoothing for joint discrete-continuous inputs."}],"snapshot_sha256":"088c8bbfae37d832f33018c35686e1e70681cb98aff6a45f16c0e5d230f6f090"},"formal_canon":{"evidence_count":2,"snapshot_sha256":"d7be81a3f67da361da43c82a6500f303f6b52a7a5355a318c0f2d7bf34bc667e"},"paper":{"abstract_excerpt":"Randomized smoothing provides strong, model-agnostic robustness certificates, but existing guarantees are limited to single modalities, treating continuous and discrete inputs in isolation. This limitation becomes critical in multimodal models, where decisions depend on cross-modal semantics and adversaries can jointly perturb heterogeneous inputs, rendering unimodal certificates insufficient. We introduce a unified randomized smoothing framework for mixed discrete--continuous inputs based on an analytically tractable Neyman--Pearson formulation of the joint worst-case problem. By analyzing th","authors_text":"Blaise Delattre, Hengyu Wu, Paul Caillon, Wei Yang Bryan Lim, Yang Cao","cross_cats":[],"headline":"Hybrid randomized smoothing yields a closed-form one-dimensional certificate that generalizes both Gaussian and discrete smoothing for joint discrete-continuous inputs.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-05-13T01:44:31Z","title":"Certified Robustness under Heterogeneous Perturbations via Hybrid Randomized Smoothing"},"references":{"count":22,"internal_anchors":5,"resolved_work":22,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":1,"title":"A., Jagielski, M., Gao, I., Awadalla, A., Koh, P","work_id":"490b95c3-2f53-4701-a7a7-c9ad219de0e6","year":2023},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":3,"title":"A Survey on Multimodal Large Language Models for Autonomous Driving","work_id":"184f4f4a-d36f-4593-94cb-4b6420fa77b0","year":2024},{"cited_arxiv_id":"2503.18813","doi":"","is_internal_anchor":true,"ref_index":4,"title":"Defeating Prompt Injections by Design","work_id":"86405b86-1c51-4042-9b04-aff0b6541411","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"title":"Ad- versarial attacks to multi-modal models.arXiv preprint arXiv:2409.06793,","work_id":"25ac5b53-65c4-42b2-8069-27b5dfd6311e","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":6,"title":"Llavaguard: An open vlm- based framework for safeguarding vision datasets and mod- els","work_id":"6428946a-91bd-4dbe-b263-a8f502ab8aa0","year":null}],"snapshot_sha256":"c2284d38c6b069473c5988ad3246014f7007ae9a218f7fa3fb1d43bdbce5dbf5"},"source":{"id":"2605.12876","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-14T20:19:40.652530Z","id":"88a2435d-c52f-43e5-bd14-adfb509870d7","model_set":{"reader":"grok-4.3"},"one_line_summary":"A hybrid randomized smoothing method yields a closed-form certificate for joint discrete-continuous perturbations that generalizes prior Gaussian and discrete smoothing approaches.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Hybrid randomized smoothing yields a closed-form one-dimensional certificate that generalizes both Gaussian and discrete smoothing for joint discrete-continuous inputs.","strongest_claim":"our approach yields a closed-form, one-dimensional certificate that strictly generalizes both Gaussian (image-only) and discrete (text-only) randomized smoothing","weakest_assumption":"The joint likelihood ordering induced by factorized discrete and continuous noise permits an analytically tractable Neyman-Pearson formulation of the worst-case problem."}},"verdict_id":"88a2435d-c52f-43e5-bd14-adfb509870d7"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:4ebba3304134185b3a305ed0cf8b0c19974caaa0833845e067f3a31bb0a76a70","target":"record","created_at":"2026-05-18T03:09:11Z","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":"42a7e94add9dd79146598653c2462e5a6f2e250ada794afda1afee7286258a27","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-05-13T01:44:31Z","title_canon_sha256":"069b08904844747f7c099c7513b19d1577d7dcb1e047a95182c64180e360d5a9"},"schema_version":"1.0","source":{"id":"2605.12876","kind":"arxiv","version":1}},"canonical_sha256":"8a2a7a44ac12b6db97038aef56e42454ed21a423ea5219052c9c2ba2e877eb80","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8a2a7a44ac12b6db97038aef56e42454ed21a423ea5219052c9c2ba2e877eb80","first_computed_at":"2026-05-18T03:09:11.203825Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:09:11.203825Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SsvB51zXjEIGncsEzW0lW2nq2du/4ExpfLpgcUQAPxCM8RKk2/Gaf6l7JBEK/mVWXWquPhAHvI5MOKzK5W7PAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:09:11.204418Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.12876","source_kind":"arxiv","source_version":1}}},"equivocations":[{"signer_id":"pith.science","event_type":"integrity_finding","target":"integrity","event_ids":["sha256:0109e2998b3b0af8a8e4bb01ee886ecc157d3669d8a77ebe2478d998050f2a55","sha256:59d3c97c4ae91db219bdaf64457bd00e85981fdfe5466b9c9ffaa8b61831e61e","sha256:ffa010cda324f0598cf8a1136e2811b35bf5f9fa40b96f4d0bc4b60d8ac3bbe9"]}],"invalid_events":[],"applied_event_ids":["sha256:4ebba3304134185b3a305ed0cf8b0c19974caaa0833845e067f3a31bb0a76a70","sha256:210c702eb4be8a6efd159f9def981900a038da1e422aff103e5141e3e55faad2"],"state_sha256":"7f76738b1eb0e73bdba5c408c6476dbbd0d756a6fb58ee9b4b941acb9c419f79"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0NozFrhLavZ+CGJEWgdFWrmPKxWiOVRmQFqmcGfElGCJtSg9ZUb7KDV7OQYRXzgDretVxrG23YbCmGmsPaU+Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T03:34:07.843661Z","bundle_sha256":"844f2e41d3679869be6a90c5d55e68c6097e60315d9e7df456f816c2775d8c55"}}