{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:JESK775APIMZI6QRF7DQYT6K3P","short_pith_number":"pith:JESK775A","canonical_record":{"source":{"id":"2407.16735","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2024-07-23T16:23:38Z","cross_cats_sorted":["cs.AI","cs.LG","stat.ML"],"title_canon_sha256":"0c683a5721715ac1d868e37bf9f87246511309b7673aa319c3cb594e3bf90986","abstract_canon_sha256":"4ce1009f66db8ddd067d23d9ef929e50d7640a33159689dc1ee66bc5eaab382f"},"schema_version":"1.0"},"canonical_sha256":"4924afffa07a19947a112fc70c4fcadbea22e8f8f539e29bf8e61340b044096d","source":{"kind":"arxiv","id":"2407.16735","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.16735","created_at":"2026-07-05T08:47:37Z"},{"alias_kind":"arxiv_version","alias_value":"2407.16735v1","created_at":"2026-07-05T08:47:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.16735","created_at":"2026-07-05T08:47:37Z"},{"alias_kind":"pith_short_12","alias_value":"JESK775APIMZ","created_at":"2026-07-05T08:47:37Z"},{"alias_kind":"pith_short_16","alias_value":"JESK775APIMZI6QR","created_at":"2026-07-05T08:47:37Z"},{"alias_kind":"pith_short_8","alias_value":"JESK775A","created_at":"2026-07-05T08:47:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:JESK775APIMZI6QRF7DQYT6K3P","target":"record","payload":{"canonical_record":{"source":{"id":"2407.16735","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2024-07-23T16:23:38Z","cross_cats_sorted":["cs.AI","cs.LG","stat.ML"],"title_canon_sha256":"0c683a5721715ac1d868e37bf9f87246511309b7673aa319c3cb594e3bf90986","abstract_canon_sha256":"4ce1009f66db8ddd067d23d9ef929e50d7640a33159689dc1ee66bc5eaab382f"},"schema_version":"1.0"},"canonical_sha256":"4924afffa07a19947a112fc70c4fcadbea22e8f8f539e29bf8e61340b044096d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:47:37.789815Z","signature_b64":"byCAO6VzutNgaPJDyCW57fs72MpIWwD+ritdtsCK7U7GscD7VVHT1R8lzPR4bRHNilHtVMtxweqatM/izwVsCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4924afffa07a19947a112fc70c4fcadbea22e8f8f539e29bf8e61340b044096d","last_reissued_at":"2026-07-05T08:47:37.789389Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:47:37.789389Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2407.16735","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":"2026-07-05T08:47:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"386yKuNI+2raGk+WsxMI6sw2RqUWpvAV8t+mrNtJ5e4pF5EWn+HIIUt9sKfCN5BOQX+PvsCcsuMsUzrpfILcAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T00:14:33.509002Z"},"content_sha256":"2b51f7ced0d9247f0e576196de9c4a575b76c0870063141ceabd46d674abfbd5","schema_version":"1.0","event_id":"sha256:2b51f7ced0d9247f0e576196de9c4a575b76c0870063141ceabd46d674abfbd5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:JESK775APIMZI6QRF7DQYT6K3P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Theoretical Analysis of Privacy Leakage in Trustworthy Federated Learning: A Perspective from Linear Algebra and Optimization Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","cs.LG","stat.ML"],"primary_cat":"cs.CR","authors_text":"Wei Chen, Xiaojin Zhang","submitted_at":"2024-07-23T16:23:38Z","abstract_excerpt":"Federated learning has emerged as a promising paradigm for collaborative model training while preserving data privacy. However, recent studies have shown that it is vulnerable to various privacy attacks, such as data reconstruction attacks. In this paper, we provide a theoretical analysis of privacy leakage in federated learning from two perspectives: linear algebra and optimization theory. From the linear algebra perspective, we prove that when the Jacobian matrix of the batch data is not full rank, there exist different batches of data that produce the same model update, thereby ensuring a l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.16735","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/2407.16735/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":"2026-07-05T08:47:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gJSBwPMOn/lSiJntkxadM8E23UOP6xhWvPxOaR7mHggbvwuAlel15GJJqqUJSrA43+Yoset/DHJZrBKgDMXUBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T00:14:33.509550Z"},"content_sha256":"8440a13d1195760ac807995d29f540f2b672eec0256ffe443ba263d1ded698b4","schema_version":"1.0","event_id":"sha256:8440a13d1195760ac807995d29f540f2b672eec0256ffe443ba263d1ded698b4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JESK775APIMZI6QRF7DQYT6K3P/bundle.json","state_url":"https://pith.science/pith/JESK775APIMZI6QRF7DQYT6K3P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JESK775APIMZI6QRF7DQYT6K3P/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":"2026-08-15T00:14:33Z","links":{"resolver":"https://pith.science/pith/JESK775APIMZI6QRF7DQYT6K3P","bundle":"https://pith.science/pith/JESK775APIMZI6QRF7DQYT6K3P/bundle.json","state":"https://pith.science/pith/JESK775APIMZI6QRF7DQYT6K3P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JESK775APIMZI6QRF7DQYT6K3P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:JESK775APIMZI6QRF7DQYT6K3P","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":"4ce1009f66db8ddd067d23d9ef929e50d7640a33159689dc1ee66bc5eaab382f","cross_cats_sorted":["cs.AI","cs.LG","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2024-07-23T16:23:38Z","title_canon_sha256":"0c683a5721715ac1d868e37bf9f87246511309b7673aa319c3cb594e3bf90986"},"schema_version":"1.0","source":{"id":"2407.16735","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.16735","created_at":"2026-07-05T08:47:37Z"},{"alias_kind":"arxiv_version","alias_value":"2407.16735v1","created_at":"2026-07-05T08:47:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.16735","created_at":"2026-07-05T08:47:37Z"},{"alias_kind":"pith_short_12","alias_value":"JESK775APIMZ","created_at":"2026-07-05T08:47:37Z"},{"alias_kind":"pith_short_16","alias_value":"JESK775APIMZI6QR","created_at":"2026-07-05T08:47:37Z"},{"alias_kind":"pith_short_8","alias_value":"JESK775A","created_at":"2026-07-05T08:47:37Z"}],"graph_snapshots":[{"event_id":"sha256:8440a13d1195760ac807995d29f540f2b672eec0256ffe443ba263d1ded698b4","target":"graph","created_at":"2026-07-05T08:47:37Z","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/2407.16735/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Federated learning has emerged as a promising paradigm for collaborative model training while preserving data privacy. However, recent studies have shown that it is vulnerable to various privacy attacks, such as data reconstruction attacks. In this paper, we provide a theoretical analysis of privacy leakage in federated learning from two perspectives: linear algebra and optimization theory. From the linear algebra perspective, we prove that when the Jacobian matrix of the batch data is not full rank, there exist different batches of data that produce the same model update, thereby ensuring a l","authors_text":"Wei Chen, Xiaojin Zhang","cross_cats":["cs.AI","cs.LG","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2024-07-23T16:23:38Z","title":"Theoretical Analysis of Privacy Leakage in Trustworthy Federated Learning: A Perspective from Linear Algebra and Optimization Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.16735","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":"sha256:2b51f7ced0d9247f0e576196de9c4a575b76c0870063141ceabd46d674abfbd5","target":"record","created_at":"2026-07-05T08:47:37Z","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":"4ce1009f66db8ddd067d23d9ef929e50d7640a33159689dc1ee66bc5eaab382f","cross_cats_sorted":["cs.AI","cs.LG","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2024-07-23T16:23:38Z","title_canon_sha256":"0c683a5721715ac1d868e37bf9f87246511309b7673aa319c3cb594e3bf90986"},"schema_version":"1.0","source":{"id":"2407.16735","kind":"arxiv","version":1}},"canonical_sha256":"4924afffa07a19947a112fc70c4fcadbea22e8f8f539e29bf8e61340b044096d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4924afffa07a19947a112fc70c4fcadbea22e8f8f539e29bf8e61340b044096d","first_computed_at":"2026-07-05T08:47:37.789389Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:47:37.789389Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"byCAO6VzutNgaPJDyCW57fs72MpIWwD+ritdtsCK7U7GscD7VVHT1R8lzPR4bRHNilHtVMtxweqatM/izwVsCg==","signature_status":"signed_v1","signed_at":"2026-07-05T08:47:37.789815Z","signed_message":"canonical_sha256_bytes"},"source_id":"2407.16735","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2b51f7ced0d9247f0e576196de9c4a575b76c0870063141ceabd46d674abfbd5","sha256:8440a13d1195760ac807995d29f540f2b672eec0256ffe443ba263d1ded698b4"],"state_sha256":"8b6d0b8b6db42420c0bf1e04f8e38299a354a5305faa5ce9b07d5cebf55af473"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KKgm8jEKhnQx7RvZz+dIoinVO4TVaO8+qwu/5sjNePSc5TI6YqQ3e8XKlsmig5K/ydR4ramjIDBrujsXaNJ5AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T00:14:33.516594Z","bundle_sha256":"e896ea33341b7a54a57e6840124cfd0e64af4d05e2b148a5e240600ee739e440"}}