{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:TKN2ZHXV32GSDXGAAOMNF3RCHX","short_pith_number":"pith:TKN2ZHXV","canonical_record":{"source":{"id":"2507.07853","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-07-10T15:33:28Z","cross_cats_sorted":["cs.AI","stat.ML"],"title_canon_sha256":"d7ef58a417be7966cee66fd59ef22c2f5effafb33ec197dd7e0735a7339e1aeb","abstract_canon_sha256":"4a28a56a48c72767ccf5a7347dcebe830380ec8d30753dd671e78145c63d4351"},"schema_version":"1.0"},"canonical_sha256":"9a9bac9ef5de8d21dcc00398d2ee223dc4f27c059cc94066741e4093e9cf6352","source":{"kind":"arxiv","id":"2507.07853","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.07853","created_at":"2026-07-05T11:35:06Z"},{"alias_kind":"arxiv_version","alias_value":"2507.07853v1","created_at":"2026-07-05T11:35:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.07853","created_at":"2026-07-05T11:35:06Z"},{"alias_kind":"pith_short_12","alias_value":"TKN2ZHXV32GS","created_at":"2026-07-05T11:35:06Z"},{"alias_kind":"pith_short_16","alias_value":"TKN2ZHXV32GSDXGA","created_at":"2026-07-05T11:35:06Z"},{"alias_kind":"pith_short_8","alias_value":"TKN2ZHXV","created_at":"2026-07-05T11:35:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:TKN2ZHXV32GSDXGAAOMNF3RCHX","target":"record","payload":{"canonical_record":{"source":{"id":"2507.07853","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-07-10T15:33:28Z","cross_cats_sorted":["cs.AI","stat.ML"],"title_canon_sha256":"d7ef58a417be7966cee66fd59ef22c2f5effafb33ec197dd7e0735a7339e1aeb","abstract_canon_sha256":"4a28a56a48c72767ccf5a7347dcebe830380ec8d30753dd671e78145c63d4351"},"schema_version":"1.0"},"canonical_sha256":"9a9bac9ef5de8d21dcc00398d2ee223dc4f27c059cc94066741e4093e9cf6352","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:35:06.226942Z","signature_b64":"GsF6C7YI/0Uk9UKQNScKPA1GlLuM++2YzJNzTYOM24eIzv/Ws7HxdDDD8prFoA3zwP+bLk0L4jeF5Nm7z1cDDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9a9bac9ef5de8d21dcc00398d2ee223dc4f27c059cc94066741e4093e9cf6352","last_reissued_at":"2026-07-05T11:35:06.226614Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:35:06.226614Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2507.07853","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":"2026-07-05T11:35:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"emTBe//HCMLfkNyfV0BK4k+MNbUYruJBQ9CUgakAaDWtN8rgJWuCCAXDZ2u141TCdpq5yXXQNYwodNPsgPosCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T10:37:11.066544Z"},"content_sha256":"274736188c55564dc6b91038791511cfd6662bbe63559adc11f7cc121df8c919","schema_version":"1.0","event_id":"sha256:274736188c55564dc6b91038791511cfd6662bbe63559adc11f7cc121df8c919"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:TKN2ZHXV32GSDXGAAOMNF3RCHX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimization Guarantees for Square-Root Natural-Gradient Variational Inference","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI","stat.ML"],"primary_cat":"cs.LG","authors_text":"Aurelien Lucchi, Mohammad Emtiyaz Khan, Navish Kumar, Thomas M\\\"ollenhoff","submitted_at":"2025-07-10T15:33:28Z","abstract_excerpt":"Variational inference with natural-gradient descent often shows fast convergence in practice, but its theoretical convergence guarantees have been challenging to establish. This is true even for the simplest cases that involve concave log-likelihoods and use a Gaussian approximation. We show that the challenge can be circumvented for such cases using a square-root parameterization for the Gaussian covariance. This approach establishes novel convergence guarantees for natural-gradient variational-Gaussian inference and its continuous-time gradient flow. Our experiments demonstrate the effective"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.07853","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/2507.07853/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":"2026-07-05T11:35:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s2pED8teoK68BhcGuKYMf+p9s6xtxVVu9hARm081xx/8HC5bd3hThfY3M5W1pFxErgrzjlX/upuJuEB9vlDFDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T10:37:11.071388Z"},"content_sha256":"1537bf9a0dbcbf9a480db3d366dc45efddb152d5de481ff0124744fb998386a0","schema_version":"1.0","event_id":"sha256:1537bf9a0dbcbf9a480db3d366dc45efddb152d5de481ff0124744fb998386a0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TKN2ZHXV32GSDXGAAOMNF3RCHX/bundle.json","state_url":"https://pith.science/pith/TKN2ZHXV32GSDXGAAOMNF3RCHX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TKN2ZHXV32GSDXGAAOMNF3RCHX/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":"2026-08-07T10:37:11Z","links":{"resolver":"https://pith.science/pith/TKN2ZHXV32GSDXGAAOMNF3RCHX","bundle":"https://pith.science/pith/TKN2ZHXV32GSDXGAAOMNF3RCHX/bundle.json","state":"https://pith.science/pith/TKN2ZHXV32GSDXGAAOMNF3RCHX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TKN2ZHXV32GSDXGAAOMNF3RCHX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:TKN2ZHXV32GSDXGAAOMNF3RCHX","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":"4a28a56a48c72767ccf5a7347dcebe830380ec8d30753dd671e78145c63d4351","cross_cats_sorted":["cs.AI","stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-07-10T15:33:28Z","title_canon_sha256":"d7ef58a417be7966cee66fd59ef22c2f5effafb33ec197dd7e0735a7339e1aeb"},"schema_version":"1.0","source":{"id":"2507.07853","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.07853","created_at":"2026-07-05T11:35:06Z"},{"alias_kind":"arxiv_version","alias_value":"2507.07853v1","created_at":"2026-07-05T11:35:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.07853","created_at":"2026-07-05T11:35:06Z"},{"alias_kind":"pith_short_12","alias_value":"TKN2ZHXV32GS","created_at":"2026-07-05T11:35:06Z"},{"alias_kind":"pith_short_16","alias_value":"TKN2ZHXV32GSDXGA","created_at":"2026-07-05T11:35:06Z"},{"alias_kind":"pith_short_8","alias_value":"TKN2ZHXV","created_at":"2026-07-05T11:35:06Z"}],"graph_snapshots":[{"event_id":"sha256:1537bf9a0dbcbf9a480db3d366dc45efddb152d5de481ff0124744fb998386a0","target":"graph","created_at":"2026-07-05T11:35:06Z","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/2507.07853/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Variational inference with natural-gradient descent often shows fast convergence in practice, but its theoretical convergence guarantees have been challenging to establish. This is true even for the simplest cases that involve concave log-likelihoods and use a Gaussian approximation. We show that the challenge can be circumvented for such cases using a square-root parameterization for the Gaussian covariance. This approach establishes novel convergence guarantees for natural-gradient variational-Gaussian inference and its continuous-time gradient flow. Our experiments demonstrate the effective","authors_text":"Aurelien Lucchi, Mohammad Emtiyaz Khan, Navish Kumar, Thomas M\\\"ollenhoff","cross_cats":["cs.AI","stat.ML"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-07-10T15:33:28Z","title":"Optimization Guarantees for Square-Root Natural-Gradient Variational Inference"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.07853","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":"sha256:274736188c55564dc6b91038791511cfd6662bbe63559adc11f7cc121df8c919","target":"record","created_at":"2026-07-05T11:35:06Z","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":"4a28a56a48c72767ccf5a7347dcebe830380ec8d30753dd671e78145c63d4351","cross_cats_sorted":["cs.AI","stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-07-10T15:33:28Z","title_canon_sha256":"d7ef58a417be7966cee66fd59ef22c2f5effafb33ec197dd7e0735a7339e1aeb"},"schema_version":"1.0","source":{"id":"2507.07853","kind":"arxiv","version":1}},"canonical_sha256":"9a9bac9ef5de8d21dcc00398d2ee223dc4f27c059cc94066741e4093e9cf6352","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9a9bac9ef5de8d21dcc00398d2ee223dc4f27c059cc94066741e4093e9cf6352","first_computed_at":"2026-07-05T11:35:06.226614Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:35:06.226614Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GsF6C7YI/0Uk9UKQNScKPA1GlLuM++2YzJNzTYOM24eIzv/Ws7HxdDDD8prFoA3zwP+bLk0L4jeF5Nm7z1cDDw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:35:06.226942Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.07853","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:274736188c55564dc6b91038791511cfd6662bbe63559adc11f7cc121df8c919","sha256:1537bf9a0dbcbf9a480db3d366dc45efddb152d5de481ff0124744fb998386a0"],"state_sha256":"fbadfa4d68699db6b57a96023883a36b1d9d3bb453643938ea3689a62c9c641c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Sgc+AcP6ZbHZ27TjE4FI8KpjEOifDOMQlT1IAcAG02w9Br7HBodNnOuH9Ri0zeP06t1FxZL/VJgyL1bH7CkMCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T10:37:11.086762Z","bundle_sha256":"a2499974ef3839136ce06ae1d50a268407cafe319d723ff9ac4dd27ed5149363"}}