{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:72PII6TO2UD55MDP6QINHC6T4F","short_pith_number":"pith:72PII6TO","canonical_record":{"source":{"id":"1905.06076","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2019-05-15T10:34:17Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"1be5e2391fd1ce1bf788ae73f8a1428e54cddde675f5ce7e899b57cc32393bab","abstract_canon_sha256":"1740065844c34c944cfc3ecb182ae6b175b984a22b318eec47ee22d12f20c770"},"schema_version":"1.0"},"canonical_sha256":"fe9e847a6ed507deb06ff410d38bd3e147f2187d2677a6be654f3410cdc6acd8","source":{"kind":"arxiv","id":"1905.06076","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.06076","created_at":"2026-05-17T23:42:02Z"},{"alias_kind":"arxiv_version","alias_value":"1905.06076v2","created_at":"2026-05-17T23:42:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.06076","created_at":"2026-05-17T23:42:02Z"},{"alias_kind":"pith_short_12","alias_value":"72PII6TO2UD5","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"72PII6TO2UD55MDP","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"72PII6TO","created_at":"2026-05-18T12:33:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:72PII6TO2UD55MDP6QINHC6T4F","target":"record","payload":{"canonical_record":{"source":{"id":"1905.06076","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2019-05-15T10:34:17Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"1be5e2391fd1ce1bf788ae73f8a1428e54cddde675f5ce7e899b57cc32393bab","abstract_canon_sha256":"1740065844c34c944cfc3ecb182ae6b175b984a22b318eec47ee22d12f20c770"},"schema_version":"1.0"},"canonical_sha256":"fe9e847a6ed507deb06ff410d38bd3e147f2187d2677a6be654f3410cdc6acd8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:02.185623Z","signature_b64":"qCibZ6ulLXb4n7yr5HioH8pbh9f8M4Ogtm8qvZ3ansSCnOa4LEbxBKYf5AdsO5oyVv6L5bnoTpbnJ14MiF6rBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fe9e847a6ed507deb06ff410d38bd3e147f2187d2677a6be654f3410cdc6acd8","last_reissued_at":"2026-05-17T23:42:02.185110Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:02.185110Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1905.06076","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":"2026-05-17T23:42:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E/9OLE3AC/r8qUfEGauqZOdcXbXVTVaRB4FMKmF1VBFsyeCLwg/EZvyoLreVczMbCODZApe2YT7/1yPzScucAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T19:48:17.167863Z"},"content_sha256":"4765658c7bbce89f5791752a102a5e68ea3e3ff68b6f5f5b2d3e1eec192aaaca","schema_version":"1.0","event_id":"sha256:4765658c7bbce89f5791752a102a5e68ea3e3ff68b6f5f5b2d3e1eec192aaaca"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:72PII6TO2UD55MDP6QINHC6T4F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Expressive Priors in Bayesian Neural Networks: Kernel Combinations and Periodic Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Alexandra Brintrup, Andy Neely, Mohamed Zaki, Russell Tsuchida, Tim Pearce","submitted_at":"2019-05-15T10:34:17Z","abstract_excerpt":"A simple, flexible approach to creating expressive priors in Gaussian process (GP) models makes new kernels from a combination of basic kernels, e.g. summing a periodic and linear kernel can capture seasonal variation with a long term trend. Despite a well-studied link between GPs and Bayesian neural networks (BNNs), the BNN analogue of this has not yet been explored. This paper derives BNN architectures mirroring such kernel combinations. Furthermore, it shows how BNNs can produce periodic kernels, which are often useful in this context. These ideas provide a principled approach to designing "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.06076","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":""},"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":"2026-05-17T23:42:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"blFKUedtWcneswcR4CeOc7a9fJ6QKSZlJeMf5m1Y57F95g6L8koZAWQuBmJChlk8tYOO+UAaSCQaU+i6pwH6Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T19:48:17.168202Z"},"content_sha256":"cfd22b5779fdc355bd3cac7e2745f0918ea921b558517c1897b80e2423864093","schema_version":"1.0","event_id":"sha256:cfd22b5779fdc355bd3cac7e2745f0918ea921b558517c1897b80e2423864093"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/72PII6TO2UD55MDP6QINHC6T4F/bundle.json","state_url":"https://pith.science/pith/72PII6TO2UD55MDP6QINHC6T4F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/72PII6TO2UD55MDP6QINHC6T4F/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":"2026-06-01T19:48:17Z","links":{"resolver":"https://pith.science/pith/72PII6TO2UD55MDP6QINHC6T4F","bundle":"https://pith.science/pith/72PII6TO2UD55MDP6QINHC6T4F/bundle.json","state":"https://pith.science/pith/72PII6TO2UD55MDP6QINHC6T4F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/72PII6TO2UD55MDP6QINHC6T4F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:72PII6TO2UD55MDP6QINHC6T4F","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":"1740065844c34c944cfc3ecb182ae6b175b984a22b318eec47ee22d12f20c770","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2019-05-15T10:34:17Z","title_canon_sha256":"1be5e2391fd1ce1bf788ae73f8a1428e54cddde675f5ce7e899b57cc32393bab"},"schema_version":"1.0","source":{"id":"1905.06076","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.06076","created_at":"2026-05-17T23:42:02Z"},{"alias_kind":"arxiv_version","alias_value":"1905.06076v2","created_at":"2026-05-17T23:42:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.06076","created_at":"2026-05-17T23:42:02Z"},{"alias_kind":"pith_short_12","alias_value":"72PII6TO2UD5","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"72PII6TO2UD55MDP","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"72PII6TO","created_at":"2026-05-18T12:33:10Z"}],"graph_snapshots":[{"event_id":"sha256:cfd22b5779fdc355bd3cac7e2745f0918ea921b558517c1897b80e2423864093","target":"graph","created_at":"2026-05-17T23:42:02Z","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"},"paper":{"abstract_excerpt":"A simple, flexible approach to creating expressive priors in Gaussian process (GP) models makes new kernels from a combination of basic kernels, e.g. summing a periodic and linear kernel can capture seasonal variation with a long term trend. Despite a well-studied link between GPs and Bayesian neural networks (BNNs), the BNN analogue of this has not yet been explored. This paper derives BNN architectures mirroring such kernel combinations. Furthermore, it shows how BNNs can produce periodic kernels, which are often useful in this context. These ideas provide a principled approach to designing ","authors_text":"Alexandra Brintrup, Andy Neely, Mohamed Zaki, Russell Tsuchida, Tim Pearce","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2019-05-15T10:34:17Z","title":"Expressive Priors in Bayesian Neural Networks: Kernel Combinations and Periodic Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.06076","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":"sha256:4765658c7bbce89f5791752a102a5e68ea3e3ff68b6f5f5b2d3e1eec192aaaca","target":"record","created_at":"2026-05-17T23:42:02Z","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":"1740065844c34c944cfc3ecb182ae6b175b984a22b318eec47ee22d12f20c770","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2019-05-15T10:34:17Z","title_canon_sha256":"1be5e2391fd1ce1bf788ae73f8a1428e54cddde675f5ce7e899b57cc32393bab"},"schema_version":"1.0","source":{"id":"1905.06076","kind":"arxiv","version":2}},"canonical_sha256":"fe9e847a6ed507deb06ff410d38bd3e147f2187d2677a6be654f3410cdc6acd8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fe9e847a6ed507deb06ff410d38bd3e147f2187d2677a6be654f3410cdc6acd8","first_computed_at":"2026-05-17T23:42:02.185110Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:02.185110Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qCibZ6ulLXb4n7yr5HioH8pbh9f8M4Ogtm8qvZ3ansSCnOa4LEbxBKYf5AdsO5oyVv6L5bnoTpbnJ14MiF6rBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:02.185623Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.06076","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4765658c7bbce89f5791752a102a5e68ea3e3ff68b6f5f5b2d3e1eec192aaaca","sha256:cfd22b5779fdc355bd3cac7e2745f0918ea921b558517c1897b80e2423864093"],"state_sha256":"3e727b92c195934ca9a492183c6b92f524e01a7c0f2cfd1133e34dcfcc3e2857"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wCy2v56vqd/7f/tb1rYi7GhtZ2hCdp0q1hbRMhFKa+uv4mT9MeJXERnpVBim71GprS142qhUSfbktSBp9cyfBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T19:48:17.170116Z","bundle_sha256":"2bd837a172e7d6e0ad98f2c11378bd420df050cf2b9a86a738b0f57ec8922f5f"}}