{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:F6N5UNGWMZCGIHVUCQAQMPZOVY","short_pith_number":"pith:F6N5UNGW","canonical_record":{"source":{"id":"2406.03334","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-06-05T14:49:15Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"11b0d4ad9d14e3c0cbd8c9c3adc2c9d4b2001aace244d9fac469d20ebf5b69f8","abstract_canon_sha256":"ee0858fd8fb235b4ae5798f112341f5f6aab88c54413c0f330de7ae21da07bac"},"schema_version":"1.0"},"canonical_sha256":"2f9bda34d66644641eb41401063f2eae04a384eced88996975a70d3bbb661e96","source":{"kind":"arxiv","id":"2406.03334","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.03334","created_at":"2026-07-05T10:12:16Z"},{"alias_kind":"arxiv_version","alias_value":"2406.03334v2","created_at":"2026-07-05T10:12:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.03334","created_at":"2026-07-05T10:12:16Z"},{"alias_kind":"pith_short_12","alias_value":"F6N5UNGWMZCG","created_at":"2026-07-05T10:12:16Z"},{"alias_kind":"pith_short_16","alias_value":"F6N5UNGWMZCGIHVU","created_at":"2026-07-05T10:12:16Z"},{"alias_kind":"pith_short_8","alias_value":"F6N5UNGW","created_at":"2026-07-05T10:12:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:F6N5UNGWMZCGIHVUCQAQMPZOVY","target":"record","payload":{"canonical_record":{"source":{"id":"2406.03334","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-06-05T14:49:15Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"11b0d4ad9d14e3c0cbd8c9c3adc2c9d4b2001aace244d9fac469d20ebf5b69f8","abstract_canon_sha256":"ee0858fd8fb235b4ae5798f112341f5f6aab88c54413c0f330de7ae21da07bac"},"schema_version":"1.0"},"canonical_sha256":"2f9bda34d66644641eb41401063f2eae04a384eced88996975a70d3bbb661e96","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:12:16.849213Z","signature_b64":"JgwcPN9C9i4JE0Ygnj68xPB8/9VmcD6Q+BCI1sEX1xNVRT80L1eNq64loG1W+7Oj3ORD40iBeCaU72KVYTK8Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2f9bda34d66644641eb41401063f2eae04a384eced88996975a70d3bbb661e96","last_reissued_at":"2026-07-05T10:12:16.848732Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:12:16.848732Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2406.03334","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":"2026-07-05T10:12:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SoJ9yRHOZaEQHCN144MZeHnObDvmIJpabtE878e0/qMYGWg+LzUhu5jq1YSR4BmCC8j+taj0OeJier9id8rPDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T19:07:20.226937Z"},"content_sha256":"fa021bbe768c460e6b53b4139d812eab9733a50c417140a2d1f31ef2d693dca1","schema_version":"1.0","event_id":"sha256:fa021bbe768c460e6b53b4139d812eab9733a50c417140a2d1f31ef2d693dca1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:F6N5UNGWMZCGIHVUCQAQMPZOVY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Reparameterization invariance in approximate Bayesian inference","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Carl Henrik Ek, Hrittik Roy, Lukas Tatzel, Marco Miani, Marvin Pf\\\"ortner, Philipp Hennig, S{\\o}ren Hauberg","submitted_at":"2024-06-05T14:49:15Z","abstract_excerpt":"Current approximate posteriors in Bayesian neural networks (BNNs) exhibit a crucial limitation: they fail to maintain invariance under reparameterization, i.e. BNNs assign different posterior densities to different parametrizations of identical functions. This creates a fundamental flaw in the application of Bayesian principles as it breaks the correspondence between uncertainty over the parameters with uncertainty over the parametrized function. In this paper, we investigate this issue in the context of the increasingly popular linearized Laplace approximation. Specifically, it has been obser"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.03334","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/2406.03334/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":"2026-07-05T10:12:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b5BqQFnR5OpJ1dqCJ+i7wBkRdcrAa6OsI4s0QpKJH/XOvEyctJNIxm08+SxJSiILxVR/jtZdfRBGqRWX+wIFBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T19:07:20.227443Z"},"content_sha256":"73d1ec2ca0840b22a1f9d94f66cc8f9edef567b28ff60b9b9390296f151a369c","schema_version":"1.0","event_id":"sha256:73d1ec2ca0840b22a1f9d94f66cc8f9edef567b28ff60b9b9390296f151a369c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F6N5UNGWMZCGIHVUCQAQMPZOVY/bundle.json","state_url":"https://pith.science/pith/F6N5UNGWMZCGIHVUCQAQMPZOVY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F6N5UNGWMZCGIHVUCQAQMPZOVY/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":"2026-08-04T19:07:20Z","links":{"resolver":"https://pith.science/pith/F6N5UNGWMZCGIHVUCQAQMPZOVY","bundle":"https://pith.science/pith/F6N5UNGWMZCGIHVUCQAQMPZOVY/bundle.json","state":"https://pith.science/pith/F6N5UNGWMZCGIHVUCQAQMPZOVY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F6N5UNGWMZCGIHVUCQAQMPZOVY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:F6N5UNGWMZCGIHVUCQAQMPZOVY","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":"ee0858fd8fb235b4ae5798f112341f5f6aab88c54413c0f330de7ae21da07bac","cross_cats_sorted":["stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-06-05T14:49:15Z","title_canon_sha256":"11b0d4ad9d14e3c0cbd8c9c3adc2c9d4b2001aace244d9fac469d20ebf5b69f8"},"schema_version":"1.0","source":{"id":"2406.03334","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.03334","created_at":"2026-07-05T10:12:16Z"},{"alias_kind":"arxiv_version","alias_value":"2406.03334v2","created_at":"2026-07-05T10:12:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.03334","created_at":"2026-07-05T10:12:16Z"},{"alias_kind":"pith_short_12","alias_value":"F6N5UNGWMZCG","created_at":"2026-07-05T10:12:16Z"},{"alias_kind":"pith_short_16","alias_value":"F6N5UNGWMZCGIHVU","created_at":"2026-07-05T10:12:16Z"},{"alias_kind":"pith_short_8","alias_value":"F6N5UNGW","created_at":"2026-07-05T10:12:16Z"}],"graph_snapshots":[{"event_id":"sha256:73d1ec2ca0840b22a1f9d94f66cc8f9edef567b28ff60b9b9390296f151a369c","target":"graph","created_at":"2026-07-05T10:12:16Z","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/2406.03334/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Current approximate posteriors in Bayesian neural networks (BNNs) exhibit a crucial limitation: they fail to maintain invariance under reparameterization, i.e. BNNs assign different posterior densities to different parametrizations of identical functions. This creates a fundamental flaw in the application of Bayesian principles as it breaks the correspondence between uncertainty over the parameters with uncertainty over the parametrized function. In this paper, we investigate this issue in the context of the increasingly popular linearized Laplace approximation. Specifically, it has been obser","authors_text":"Carl Henrik Ek, Hrittik Roy, Lukas Tatzel, Marco Miani, Marvin Pf\\\"ortner, Philipp Hennig, S{\\o}ren Hauberg","cross_cats":["stat.ML"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-06-05T14:49:15Z","title":"Reparameterization invariance in approximate Bayesian inference"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.03334","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:fa021bbe768c460e6b53b4139d812eab9733a50c417140a2d1f31ef2d693dca1","target":"record","created_at":"2026-07-05T10:12:16Z","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":"ee0858fd8fb235b4ae5798f112341f5f6aab88c54413c0f330de7ae21da07bac","cross_cats_sorted":["stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-06-05T14:49:15Z","title_canon_sha256":"11b0d4ad9d14e3c0cbd8c9c3adc2c9d4b2001aace244d9fac469d20ebf5b69f8"},"schema_version":"1.0","source":{"id":"2406.03334","kind":"arxiv","version":2}},"canonical_sha256":"2f9bda34d66644641eb41401063f2eae04a384eced88996975a70d3bbb661e96","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2f9bda34d66644641eb41401063f2eae04a384eced88996975a70d3bbb661e96","first_computed_at":"2026-07-05T10:12:16.848732Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:12:16.848732Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JgwcPN9C9i4JE0Ygnj68xPB8/9VmcD6Q+BCI1sEX1xNVRT80L1eNq64loG1W+7Oj3ORD40iBeCaU72KVYTK8Dg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:12:16.849213Z","signed_message":"canonical_sha256_bytes"},"source_id":"2406.03334","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fa021bbe768c460e6b53b4139d812eab9733a50c417140a2d1f31ef2d693dca1","sha256:73d1ec2ca0840b22a1f9d94f66cc8f9edef567b28ff60b9b9390296f151a369c"],"state_sha256":"9f09e6406ecb448ed89b3a7eb202fb1fcbae731d1d0f2e42d96c05f197009d59"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f3GAvbPtByVQ5+9mTZdKfqmoPuwLgkED4c5Ux+u/6Kg0kZ3EciNf9sGiGy2Ov1uFWiuE1R8eOS4j89xj7MWoDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T19:07:20.238220Z","bundle_sha256":"66f7e209a8449923448d29a0bfe7a317078f469ccd9b7dd3b44e739f826b22f3"}}