{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:KGOPUXT3I7MOZ5C2RFAYYHGYUE","short_pith_number":"pith:KGOPUXT3","canonical_record":{"source":{"id":"2502.08730","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-02-12T19:04:26Z","cross_cats_sorted":["stat.ME","stat.ML"],"title_canon_sha256":"67f98c8670d77fac93d4367bbae72016659b5bc7e7e5c112b5b1a5fd7e8ec465","abstract_canon_sha256":"7a34d7283cff5a08e2a4fb3c919ff2c23f06ad735790447d0fc113924fef3858"},"schema_version":"1.0"},"canonical_sha256":"519cfa5e7b47d8ecf45a89418c1cd8a139dfa35d03136760f3b4154a05b95974","source":{"kind":"arxiv","id":"2502.08730","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.08730","created_at":"2026-07-05T11:27:24Z"},{"alias_kind":"arxiv_version","alias_value":"2502.08730v2","created_at":"2026-07-05T11:27:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.08730","created_at":"2026-07-05T11:27:24Z"},{"alias_kind":"pith_short_12","alias_value":"KGOPUXT3I7MO","created_at":"2026-07-05T11:27:24Z"},{"alias_kind":"pith_short_16","alias_value":"KGOPUXT3I7MOZ5C2","created_at":"2026-07-05T11:27:24Z"},{"alias_kind":"pith_short_8","alias_value":"KGOPUXT3","created_at":"2026-07-05T11:27:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:KGOPUXT3I7MOZ5C2RFAYYHGYUE","target":"record","payload":{"canonical_record":{"source":{"id":"2502.08730","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-02-12T19:04:26Z","cross_cats_sorted":["stat.ME","stat.ML"],"title_canon_sha256":"67f98c8670d77fac93d4367bbae72016659b5bc7e7e5c112b5b1a5fd7e8ec465","abstract_canon_sha256":"7a34d7283cff5a08e2a4fb3c919ff2c23f06ad735790447d0fc113924fef3858"},"schema_version":"1.0"},"canonical_sha256":"519cfa5e7b47d8ecf45a89418c1cd8a139dfa35d03136760f3b4154a05b95974","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:27:24.076793Z","signature_b64":"spkk6NVmCWwmzYMHveuiMhNZnpYhv72Jxfv+jhooTuekvRhb4PQCzxA6/N3h7Mwgrz7AkgVDra6OeOpIppAvBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"519cfa5e7b47d8ecf45a89418c1cd8a139dfa35d03136760f3b4154a05b95974","last_reissued_at":"2026-07-05T11:27:24.076289Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:27:24.076289Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2502.08730","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":"2026-07-05T11:27:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"td7BVSfztFV87JnTfQMO9PhgVmJm1m70+90ui5+iEanzdYsWPf+c1VLOHadAHtaKEON2V8egzZ9Mty2kuJuwCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T17:39:25.944587Z"},"content_sha256":"8de2438c9b3524d2fb77428c79cb0fb01555ff7cb679056ae54ec18b06de4371","schema_version":"1.0","event_id":"sha256:8de2438c9b3524d2fb77428c79cb0fb01555ff7cb679056ae54ec18b06de4371"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:KGOPUXT3I7MOZ5C2RFAYYHGYUE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"New Bounds for Sparse Variational Gaussian Processes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.ME","stat.ML"],"primary_cat":"cs.LG","authors_text":"Michalis K. Titsias","submitted_at":"2025-02-12T19:04:26Z","abstract_excerpt":"Sparse variational Gaussian processes (GPs) construct tractable posterior approximations to GP models. At the core of these methods is the assumption that the true posterior distribution over training function values ${\\bf f}$ and inducing variables ${\\bf u}$ is approximated by a variational distribution that incorporates the conditional GP prior $p({\\bf f} | {\\bf u})$ in its factorization. While this assumption is considered as fundamental, we show that for model training we can relax it through the use of a more general variational distribution $q({\\bf f} | {\\bf u})$ that depends on $N$ extr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.08730","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/2502.08730/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":"2026-07-05T11:27:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1WwirM/O4XcGG1a8nn9K4kgHYkxJS3iXq+4FeCjh7tSaBOUfQB/WgxK6z2yESb8jgJkhzpAKrIMIMoolV/BOBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T17:39:25.945079Z"},"content_sha256":"cf8284da86919cd3db4849267b6cfd7aa329cb68d9cec950ffa7566ca96e3366","schema_version":"1.0","event_id":"sha256:cf8284da86919cd3db4849267b6cfd7aa329cb68d9cec950ffa7566ca96e3366"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KGOPUXT3I7MOZ5C2RFAYYHGYUE/bundle.json","state_url":"https://pith.science/pith/KGOPUXT3I7MOZ5C2RFAYYHGYUE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KGOPUXT3I7MOZ5C2RFAYYHGYUE/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":"2026-08-09T17:39:25Z","links":{"resolver":"https://pith.science/pith/KGOPUXT3I7MOZ5C2RFAYYHGYUE","bundle":"https://pith.science/pith/KGOPUXT3I7MOZ5C2RFAYYHGYUE/bundle.json","state":"https://pith.science/pith/KGOPUXT3I7MOZ5C2RFAYYHGYUE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KGOPUXT3I7MOZ5C2RFAYYHGYUE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:KGOPUXT3I7MOZ5C2RFAYYHGYUE","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":"7a34d7283cff5a08e2a4fb3c919ff2c23f06ad735790447d0fc113924fef3858","cross_cats_sorted":["stat.ME","stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-02-12T19:04:26Z","title_canon_sha256":"67f98c8670d77fac93d4367bbae72016659b5bc7e7e5c112b5b1a5fd7e8ec465"},"schema_version":"1.0","source":{"id":"2502.08730","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.08730","created_at":"2026-07-05T11:27:24Z"},{"alias_kind":"arxiv_version","alias_value":"2502.08730v2","created_at":"2026-07-05T11:27:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.08730","created_at":"2026-07-05T11:27:24Z"},{"alias_kind":"pith_short_12","alias_value":"KGOPUXT3I7MO","created_at":"2026-07-05T11:27:24Z"},{"alias_kind":"pith_short_16","alias_value":"KGOPUXT3I7MOZ5C2","created_at":"2026-07-05T11:27:24Z"},{"alias_kind":"pith_short_8","alias_value":"KGOPUXT3","created_at":"2026-07-05T11:27:24Z"}],"graph_snapshots":[{"event_id":"sha256:cf8284da86919cd3db4849267b6cfd7aa329cb68d9cec950ffa7566ca96e3366","target":"graph","created_at":"2026-07-05T11:27:24Z","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/2502.08730/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Sparse variational Gaussian processes (GPs) construct tractable posterior approximations to GP models. At the core of these methods is the assumption that the true posterior distribution over training function values ${\\bf f}$ and inducing variables ${\\bf u}$ is approximated by a variational distribution that incorporates the conditional GP prior $p({\\bf f} | {\\bf u})$ in its factorization. While this assumption is considered as fundamental, we show that for model training we can relax it through the use of a more general variational distribution $q({\\bf f} | {\\bf u})$ that depends on $N$ extr","authors_text":"Michalis K. Titsias","cross_cats":["stat.ME","stat.ML"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-02-12T19:04:26Z","title":"New Bounds for Sparse Variational Gaussian Processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.08730","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":"sha256:8de2438c9b3524d2fb77428c79cb0fb01555ff7cb679056ae54ec18b06de4371","target":"record","created_at":"2026-07-05T11:27:24Z","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":"7a34d7283cff5a08e2a4fb3c919ff2c23f06ad735790447d0fc113924fef3858","cross_cats_sorted":["stat.ME","stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-02-12T19:04:26Z","title_canon_sha256":"67f98c8670d77fac93d4367bbae72016659b5bc7e7e5c112b5b1a5fd7e8ec465"},"schema_version":"1.0","source":{"id":"2502.08730","kind":"arxiv","version":2}},"canonical_sha256":"519cfa5e7b47d8ecf45a89418c1cd8a139dfa35d03136760f3b4154a05b95974","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"519cfa5e7b47d8ecf45a89418c1cd8a139dfa35d03136760f3b4154a05b95974","first_computed_at":"2026-07-05T11:27:24.076289Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:27:24.076289Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"spkk6NVmCWwmzYMHveuiMhNZnpYhv72Jxfv+jhooTuekvRhb4PQCzxA6/N3h7Mwgrz7AkgVDra6OeOpIppAvBw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:27:24.076793Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.08730","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8de2438c9b3524d2fb77428c79cb0fb01555ff7cb679056ae54ec18b06de4371","sha256:cf8284da86919cd3db4849267b6cfd7aa329cb68d9cec950ffa7566ca96e3366"],"state_sha256":"f17c3534d13ab7ed496c8ec044a7ccf75816828a2b120f94f28371f915966443"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zZuQz2PCp0FXG4XAsDRsX5QKVn017ZXIzUga8yvoqGvTy9s5fRyBg1FKRU1kwF16lbI2jy596DtPUI7UFzdZCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T17:39:25.948364Z","bundle_sha256":"ab879c6ff6ea7b5c83782e9adf0564a5ccc126e71c85997789e8125f166092df"}}