{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:WK6DXEFSI5QDELWKMIKZLFPUSX","short_pith_number":"pith:WK6DXEFS","canonical_record":{"source":{"id":"2410.06266","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2024-10-08T18:05:56Z","cross_cats_sorted":[],"title_canon_sha256":"26a3593558407a83f1d8ef20b85099ab75a08096ea2c879a3ef8e43b78b487ec","abstract_canon_sha256":"ec73cd823980c74ddaa79d10518b2a2e1c95b58d71e0bc5216ef847d1eb10c29"},"schema_version":"1.0"},"canonical_sha256":"b2bc3b90b24760322eca62159595f495e75a0f3f057b9ae268777e4f3f3c5a74","source":{"kind":"arxiv","id":"2410.06266","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.06266","created_at":"2026-07-05T10:36:29Z"},{"alias_kind":"arxiv_version","alias_value":"2410.06266v2","created_at":"2026-07-05T10:36:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.06266","created_at":"2026-07-05T10:36:29Z"},{"alias_kind":"pith_short_12","alias_value":"WK6DXEFSI5QD","created_at":"2026-07-05T10:36:29Z"},{"alias_kind":"pith_short_16","alias_value":"WK6DXEFSI5QDELWK","created_at":"2026-07-05T10:36:29Z"},{"alias_kind":"pith_short_8","alias_value":"WK6DXEFS","created_at":"2026-07-05T10:36:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:WK6DXEFSI5QDELWKMIKZLFPUSX","target":"record","payload":{"canonical_record":{"source":{"id":"2410.06266","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2024-10-08T18:05:56Z","cross_cats_sorted":[],"title_canon_sha256":"26a3593558407a83f1d8ef20b85099ab75a08096ea2c879a3ef8e43b78b487ec","abstract_canon_sha256":"ec73cd823980c74ddaa79d10518b2a2e1c95b58d71e0bc5216ef847d1eb10c29"},"schema_version":"1.0"},"canonical_sha256":"b2bc3b90b24760322eca62159595f495e75a0f3f057b9ae268777e4f3f3c5a74","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:36:29.634946Z","signature_b64":"B3R87eUrRVNH2r7IAW9HnBAy7Gt1UKFAsPqLxjKAjLdKA0x9oKS6SjYy3EeYhgw2qdVd5uR+374eX1M1GBfMAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b2bc3b90b24760322eca62159595f495e75a0f3f057b9ae268777e4f3f3c5a74","last_reissued_at":"2026-07-05T10:36:29.634393Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:36:29.634393Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2410.06266","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:36:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z639G0LpuHm8d5Nlxh/FmJyjsHVIu8oWM72FiL+KckO97XYMfaQBsWPxGlxXugmXIVQcOrqr2jKy4PCVi2QoCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T05:56:36.035042Z"},"content_sha256":"0e757d6e9652655817032afa30ab705fc9b133b6bc3ca98d46ce261ceff0a448","schema_version":"1.0","event_id":"sha256:0e757d6e9652655817032afa30ab705fc9b133b6bc3ca98d46ce261ceff0a448"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:WK6DXEFSI5QDELWKMIKZLFPUSX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Near Exact Privacy Amplification for Matrix Mechanisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CR","authors_text":"Abhradeep Thakurta, Arun Ganesh, Christopher A. Choquette-Choo, Saminul Haque, Thomas Steinke","submitted_at":"2024-10-08T18:05:56Z","abstract_excerpt":"We study the problem of computing the privacy parameters for DP machine learning when using privacy amplification via random batching and noise correlated across rounds via a correlation matrix $\\textbf{C}$ (i.e., the matrix mechanism). Past work on this problem either only applied to banded $\\textbf{C}$, or gave loose privacy parameters. In this work, we give a framework for computing near-exact privacy parameters for any lower-triangular, non-negative $\\textbf{C}$. Our framework allows us to optimize the correlation matrix $\\textbf{C}$ while accounting for amplification, whereas past work co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.06266","kind":"arxiv","version":2},"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/2410.06266/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":"2026-07-05T10:36:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AXZgs0NhPlqpMLsL1AydqRSsaZFIp4hjWsb8j4v2Eb8V9wYQfS3q5mWCL5KUKU+u9ikYuUMU2j0DK2dKyoMcBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T05:56:36.035567Z"},"content_sha256":"656e2a037cefd26e3add39230b731c3b1efed90b9fece6b46be7fa8121b9a196","schema_version":"1.0","event_id":"sha256:656e2a037cefd26e3add39230b731c3b1efed90b9fece6b46be7fa8121b9a196"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WK6DXEFSI5QDELWKMIKZLFPUSX/bundle.json","state_url":"https://pith.science/pith/WK6DXEFSI5QDELWKMIKZLFPUSX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WK6DXEFSI5QDELWKMIKZLFPUSX/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":"2026-08-10T05:56:36Z","links":{"resolver":"https://pith.science/pith/WK6DXEFSI5QDELWKMIKZLFPUSX","bundle":"https://pith.science/pith/WK6DXEFSI5QDELWKMIKZLFPUSX/bundle.json","state":"https://pith.science/pith/WK6DXEFSI5QDELWKMIKZLFPUSX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WK6DXEFSI5QDELWKMIKZLFPUSX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:WK6DXEFSI5QDELWKMIKZLFPUSX","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":"ec73cd823980c74ddaa79d10518b2a2e1c95b58d71e0bc5216ef847d1eb10c29","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2024-10-08T18:05:56Z","title_canon_sha256":"26a3593558407a83f1d8ef20b85099ab75a08096ea2c879a3ef8e43b78b487ec"},"schema_version":"1.0","source":{"id":"2410.06266","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.06266","created_at":"2026-07-05T10:36:29Z"},{"alias_kind":"arxiv_version","alias_value":"2410.06266v2","created_at":"2026-07-05T10:36:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.06266","created_at":"2026-07-05T10:36:29Z"},{"alias_kind":"pith_short_12","alias_value":"WK6DXEFSI5QD","created_at":"2026-07-05T10:36:29Z"},{"alias_kind":"pith_short_16","alias_value":"WK6DXEFSI5QDELWK","created_at":"2026-07-05T10:36:29Z"},{"alias_kind":"pith_short_8","alias_value":"WK6DXEFS","created_at":"2026-07-05T10:36:29Z"}],"graph_snapshots":[{"event_id":"sha256:656e2a037cefd26e3add39230b731c3b1efed90b9fece6b46be7fa8121b9a196","target":"graph","created_at":"2026-07-05T10:36:29Z","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/2410.06266/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the problem of computing the privacy parameters for DP machine learning when using privacy amplification via random batching and noise correlated across rounds via a correlation matrix $\\textbf{C}$ (i.e., the matrix mechanism). Past work on this problem either only applied to banded $\\textbf{C}$, or gave loose privacy parameters. In this work, we give a framework for computing near-exact privacy parameters for any lower-triangular, non-negative $\\textbf{C}$. Our framework allows us to optimize the correlation matrix $\\textbf{C}$ while accounting for amplification, whereas past work co","authors_text":"Abhradeep Thakurta, Arun Ganesh, Christopher A. Choquette-Choo, Saminul Haque, Thomas Steinke","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2024-10-08T18:05:56Z","title":"Near Exact Privacy Amplification for Matrix Mechanisms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.06266","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":"sha256:0e757d6e9652655817032afa30ab705fc9b133b6bc3ca98d46ce261ceff0a448","target":"record","created_at":"2026-07-05T10:36:29Z","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":"ec73cd823980c74ddaa79d10518b2a2e1c95b58d71e0bc5216ef847d1eb10c29","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2024-10-08T18:05:56Z","title_canon_sha256":"26a3593558407a83f1d8ef20b85099ab75a08096ea2c879a3ef8e43b78b487ec"},"schema_version":"1.0","source":{"id":"2410.06266","kind":"arxiv","version":2}},"canonical_sha256":"b2bc3b90b24760322eca62159595f495e75a0f3f057b9ae268777e4f3f3c5a74","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b2bc3b90b24760322eca62159595f495e75a0f3f057b9ae268777e4f3f3c5a74","first_computed_at":"2026-07-05T10:36:29.634393Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:36:29.634393Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B3R87eUrRVNH2r7IAW9HnBAy7Gt1UKFAsPqLxjKAjLdKA0x9oKS6SjYy3EeYhgw2qdVd5uR+374eX1M1GBfMAw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:36:29.634946Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.06266","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0e757d6e9652655817032afa30ab705fc9b133b6bc3ca98d46ce261ceff0a448","sha256:656e2a037cefd26e3add39230b731c3b1efed90b9fece6b46be7fa8121b9a196"],"state_sha256":"8cb9ecf8730aa4e36dced5cafd7a7794e3b5b870012a824e622b2d3daa855e17"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6MI9TvQTFUEP1oj+DS/CUdJvwreu5xde2XxUj2ASTzxxOAquop8AQ1abTfgfbmYiEMkfWYU75qr3+M+ylUCoBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T05:56:36.040034Z","bundle_sha256":"e5e9893d38b52524a669fcc4c8bc11d39d443637c1e7510b409b20894430b466"}}