{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:34KCBVFEVZIJMVDFTF5VFASKEK","short_pith_number":"pith:34KCBVFE","canonical_record":{"source":{"id":"2412.11057","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-12-15T05:22:38Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"ac0de721274e8d7e1c67340a2d63357abf9e590d780fb3fd878de7777e5496c5","abstract_canon_sha256":"c377aef76ab099c8e4ef3377f759db0eba1437cd897e2af679baf6af0225378e"},"schema_version":"1.0"},"canonical_sha256":"df1420d4a4ae50965465997b52824a22b1da540a9abad0e172e80601e6d88d67","source":{"kind":"arxiv","id":"2412.11057","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.11057","created_at":"2026-07-05T09:49:47Z"},{"alias_kind":"arxiv_version","alias_value":"2412.11057v1","created_at":"2026-07-05T09:49:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.11057","created_at":"2026-07-05T09:49:47Z"},{"alias_kind":"pith_short_12","alias_value":"34KCBVFEVZIJ","created_at":"2026-07-05T09:49:47Z"},{"alias_kind":"pith_short_16","alias_value":"34KCBVFEVZIJMVDF","created_at":"2026-07-05T09:49:47Z"},{"alias_kind":"pith_short_8","alias_value":"34KCBVFE","created_at":"2026-07-05T09:49:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:34KCBVFEVZIJMVDFTF5VFASKEK","target":"record","payload":{"canonical_record":{"source":{"id":"2412.11057","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-12-15T05:22:38Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"ac0de721274e8d7e1c67340a2d63357abf9e590d780fb3fd878de7777e5496c5","abstract_canon_sha256":"c377aef76ab099c8e4ef3377f759db0eba1437cd897e2af679baf6af0225378e"},"schema_version":"1.0"},"canonical_sha256":"df1420d4a4ae50965465997b52824a22b1da540a9abad0e172e80601e6d88d67","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:49:47.772880Z","signature_b64":"IAl8aaPMGp4dpGo0fLG1ucd310D02ZuMtQbA4epCwlF9wxJDw0mabKEtExtRQztZ+tN7EbZPL9EEPOWGCmfZDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"df1420d4a4ae50965465997b52824a22b1da540a9abad0e172e80601e6d88d67","last_reissued_at":"2026-07-05T09:49:47.772187Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:49:47.772187Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2412.11057","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":"2026-07-05T09:49:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MnYaOejrbnmZJK2RWp0qrFvEqowGs+7sOHBT3MYHR7gnNIo39rqWEhnxZ/frvlHMKFoInbV5vX33JG1lZpn4Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-12T08:41:20.163074Z"},"content_sha256":"df38958a2937a70287de1dfc3fdd630b2a261b71cfc4edbcc2e35f8faf67ea6a","schema_version":"1.0","event_id":"sha256:df38958a2937a70287de1dfc3fdd630b2a261b71cfc4edbcc2e35f8faf67ea6a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:34KCBVFEVZIJMVDFTF5VFASKEK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Set-Valued Sensitivity Analysis of Deep Neural Networks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Feilong Wang, Xin Wang, Xuegang Ban","submitted_at":"2024-12-15T05:22:38Z","abstract_excerpt":"This paper proposes a sensitivity analysis framework based on set valued mapping for deep neural networks (DNN) to understand and compute how the solutions (model weights) of DNN respond to perturbations in the training data. As a DNN may not exhibit a unique solution (minima) and the algorithm of solving a DNN may lead to different solutions with minor perturbations to input data, we focus on the sensitivity of the solution set of DNN, instead of studying a single solution. In particular, we are interested in the expansion and contraction of the set in response to data perturbations. If the c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.11057","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.11057/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:49:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n+WLfjH+0kNAHMGSYucZun5PkeowtukL8tHq+yrIAsEQKmd3ZjHJqVvJbvSKXE4Mt9NpL/PlXSm6zXyYQjtwCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-12T08:41:20.163492Z"},"content_sha256":"ff9b5ff5d1a9aeb8811d5004e5fe86e6055c20eb4df497bbfc14bc0747f91c80","schema_version":"1.0","event_id":"sha256:ff9b5ff5d1a9aeb8811d5004e5fe86e6055c20eb4df497bbfc14bc0747f91c80"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/34KCBVFEVZIJMVDFTF5VFASKEK/bundle.json","state_url":"https://pith.science/pith/34KCBVFEVZIJMVDFTF5VFASKEK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/34KCBVFEVZIJMVDFTF5VFASKEK/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":"2026-07-12T08:41:20Z","links":{"resolver":"https://pith.science/pith/34KCBVFEVZIJMVDFTF5VFASKEK","bundle":"https://pith.science/pith/34KCBVFEVZIJMVDFTF5VFASKEK/bundle.json","state":"https://pith.science/pith/34KCBVFEVZIJMVDFTF5VFASKEK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/34KCBVFEVZIJMVDFTF5VFASKEK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:34KCBVFEVZIJMVDFTF5VFASKEK","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":"c377aef76ab099c8e4ef3377f759db0eba1437cd897e2af679baf6af0225378e","cross_cats_sorted":["cs.AI"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-12-15T05:22:38Z","title_canon_sha256":"ac0de721274e8d7e1c67340a2d63357abf9e590d780fb3fd878de7777e5496c5"},"schema_version":"1.0","source":{"id":"2412.11057","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.11057","created_at":"2026-07-05T09:49:47Z"},{"alias_kind":"arxiv_version","alias_value":"2412.11057v1","created_at":"2026-07-05T09:49:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.11057","created_at":"2026-07-05T09:49:47Z"},{"alias_kind":"pith_short_12","alias_value":"34KCBVFEVZIJ","created_at":"2026-07-05T09:49:47Z"},{"alias_kind":"pith_short_16","alias_value":"34KCBVFEVZIJMVDF","created_at":"2026-07-05T09:49:47Z"},{"alias_kind":"pith_short_8","alias_value":"34KCBVFE","created_at":"2026-07-05T09:49:47Z"}],"graph_snapshots":[{"event_id":"sha256:ff9b5ff5d1a9aeb8811d5004e5fe86e6055c20eb4df497bbfc14bc0747f91c80","target":"graph","created_at":"2026-07-05T09:49:47Z","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/2412.11057/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper proposes a sensitivity analysis framework based on set valued mapping for deep neural networks (DNN) to understand and compute how the solutions (model weights) of DNN respond to perturbations in the training data. As a DNN may not exhibit a unique solution (minima) and the algorithm of solving a DNN may lead to different solutions with minor perturbations to input data, we focus on the sensitivity of the solution set of DNN, instead of studying a single solution. In particular, we are interested in the expansion and contraction of the set in response to data perturbations. If the c","authors_text":"Feilong Wang, Xin Wang, Xuegang Ban","cross_cats":["cs.AI"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-12-15T05:22:38Z","title":"Set-Valued Sensitivity Analysis of Deep Neural Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.11057","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:df38958a2937a70287de1dfc3fdd630b2a261b71cfc4edbcc2e35f8faf67ea6a","target":"record","created_at":"2026-07-05T09:49:47Z","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":"c377aef76ab099c8e4ef3377f759db0eba1437cd897e2af679baf6af0225378e","cross_cats_sorted":["cs.AI"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-12-15T05:22:38Z","title_canon_sha256":"ac0de721274e8d7e1c67340a2d63357abf9e590d780fb3fd878de7777e5496c5"},"schema_version":"1.0","source":{"id":"2412.11057","kind":"arxiv","version":1}},"canonical_sha256":"df1420d4a4ae50965465997b52824a22b1da540a9abad0e172e80601e6d88d67","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"df1420d4a4ae50965465997b52824a22b1da540a9abad0e172e80601e6d88d67","first_computed_at":"2026-07-05T09:49:47.772187Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:49:47.772187Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IAl8aaPMGp4dpGo0fLG1ucd310D02ZuMtQbA4epCwlF9wxJDw0mabKEtExtRQztZ+tN7EbZPL9EEPOWGCmfZDw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:49:47.772880Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.11057","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:df38958a2937a70287de1dfc3fdd630b2a261b71cfc4edbcc2e35f8faf67ea6a","sha256:ff9b5ff5d1a9aeb8811d5004e5fe86e6055c20eb4df497bbfc14bc0747f91c80"],"state_sha256":"58f972443c50b698b4be0dfd579525d5e3749ad3d94d11272694b1d494a84971"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CMYYMRUF76XqgkZ/yYImRh+GcoYtcArCBtu/ICeTyoIlgIhqgTLxpZkVh0mJ2XHj/8lXmCvD+vZxVT3rCcabAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-12T08:41:20.165993Z","bundle_sha256":"173e67e72ae9836399adf859c1a8ca9d99502789d86b0ece33392d199ea5ec18"}}