{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:BCNBR4AXARQ5YZPWIKPDURGBN7","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":"3052b0ceff259d7c871a0d7cb7c57b3524f293c4b71234940457efa3a64549db","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2016-05-09T11:36:40Z","title_canon_sha256":"2af829604204b584830721851750a45975ff728f91d9f17f9f018b013eabbdc6"},"schema_version":"1.0","source":{"id":"1605.02536","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.02536","created_at":"2026-05-18T00:15:05Z"},{"alias_kind":"arxiv_version","alias_value":"1605.02536v3","created_at":"2026-05-18T00:15:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.02536","created_at":"2026-05-18T00:15:05Z"},{"alias_kind":"pith_short_12","alias_value":"BCNBR4AXARQ5","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"BCNBR4AXARQ5YZPW","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"BCNBR4AX","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:4f5266fc922199e9f0d25c52a6f8334e60cf7e97c76376936dea71e2c7f64e91","target":"graph","created_at":"2026-05-18T00:15:05Z","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":"Devoted to multi-task learning and structured output learning, operator-valued kernels provide a flexible tool to build vector-valued functions in the context of Reproducing Kernel Hilbert Spaces. To scale up these methods, we extend the celebrated Random Fourier Feature methodology to get an approximation of operator-valued kernels. We propose a general principle for Operator-valued Random Fourier Feature construction relying on a generalization of Bochner's theorem for translation-invariant operator-valued Mercer kernels. We prove the uniform convergence of the kernel approximation for bound","authors_text":"Florence d'Alch\\'e-Buc, Markus Heinonen, Romain Brault","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2016-05-09T11:36:40Z","title":"Random Fourier Features for Operator-Valued Kernels"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.02536","kind":"arxiv","version":3},"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:fbf34faf8bd232e8f2ed883cbcf2f0cc671783fabe512363582f6b2944c026ef","target":"record","created_at":"2026-05-18T00:15:05Z","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":"3052b0ceff259d7c871a0d7cb7c57b3524f293c4b71234940457efa3a64549db","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2016-05-09T11:36:40Z","title_canon_sha256":"2af829604204b584830721851750a45975ff728f91d9f17f9f018b013eabbdc6"},"schema_version":"1.0","source":{"id":"1605.02536","kind":"arxiv","version":3}},"canonical_sha256":"089a18f0170461dc65f6429e3a44c16fe8b4776c18cf3c42522a64dde99deac7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"089a18f0170461dc65f6429e3a44c16fe8b4776c18cf3c42522a64dde99deac7","first_computed_at":"2026-05-18T00:15:05.775147Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:05.775147Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eaR3qzJt8fBEtZjW5XAJrxOBhWCu6uJaJh9jh2x902cOdEjkNpKROHHiySXPnLZ9QLYU4i9BsChJm6nfLDpODw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:05.775650Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.02536","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fbf34faf8bd232e8f2ed883cbcf2f0cc671783fabe512363582f6b2944c026ef","sha256:4f5266fc922199e9f0d25c52a6f8334e60cf7e97c76376936dea71e2c7f64e91"],"state_sha256":"5a0e0081dc78f64487dab331e39917642327959afd5da396e48bc03265fb669c"}