{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:4OSZJVJIDMT7553TPMVDTB257S","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":"536fa2ca7ae43289a011cf9fc6eec4d0f4006c0837178e2fd6737d41d043bc76","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2022-09-18T03:39:18Z","title_canon_sha256":"922644c66879b39576f2cf03e94336544ea7582a9e8265ab56fb2822e99a91f8"},"schema_version":"1.0","source":{"id":"2209.08461","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.08461","created_at":"2026-07-05T04:58:41Z"},{"alias_kind":"arxiv_version","alias_value":"2209.08461v1","created_at":"2026-07-05T04:58:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.08461","created_at":"2026-07-05T04:58:41Z"},{"alias_kind":"pith_short_12","alias_value":"4OSZJVJIDMT7","created_at":"2026-07-05T04:58:41Z"},{"alias_kind":"pith_short_16","alias_value":"4OSZJVJIDMT7553T","created_at":"2026-07-05T04:58:41Z"},{"alias_kind":"pith_short_8","alias_value":"4OSZJVJI","created_at":"2026-07-05T04:58:41Z"}],"graph_snapshots":[{"event_id":"sha256:70e0ad7f348d3e0591277270e83be6a36a07adb21bcca45160b2c6fd84f35716","target":"graph","created_at":"2026-07-05T04:58:41Z","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/2209.08461/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The random Fourier features (RFFs) method is a powerful and popular technique in kernel approximation for scalability of kernel methods. The theoretical foundation of RFFs is based on the Bochner theorem that relates symmetric, positive definite (PD) functions to probability measures. This condition naturally excludes asymmetric functions with a wide range applications in practice, e.g., directed graphs, conditional probability, and asymmetric kernels. Nevertheless, understanding asymmetric functions (kernels) and its scalability via RFFs is unclear both theoretically and empirically. In this ","authors_text":"Fanghui Liu, Fan He, Mingzhen He, Xiaolin Huang","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2022-09-18T03:39:18Z","title":"Random Fourier Features for Asymmetric Kernels"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.08461","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":"sha256:8c5c6f5e9fba95b2ba9f788b79d05bcb54ea9abb67a0f35a7ae97f67ff922808","target":"record","created_at":"2026-07-05T04:58:41Z","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":"536fa2ca7ae43289a011cf9fc6eec4d0f4006c0837178e2fd6737d41d043bc76","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2022-09-18T03:39:18Z","title_canon_sha256":"922644c66879b39576f2cf03e94336544ea7582a9e8265ab56fb2822e99a91f8"},"schema_version":"1.0","source":{"id":"2209.08461","kind":"arxiv","version":1}},"canonical_sha256":"e3a594d5281b27fef7737b2a39875dfcb9ba7c9c359c2c0170beeb897ee34e66","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e3a594d5281b27fef7737b2a39875dfcb9ba7c9c359c2c0170beeb897ee34e66","first_computed_at":"2026-07-05T04:58:41.677025Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:58:41.677025Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kVHk/L2XLiz0NB8hwXxrIfIR5Uh/EJhsl2UoZmK/fTWfUnXgRFH2HyH7F8sYxHtQdAqY9cExyAtOaKOWWf/qDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T04:58:41.677510Z","signed_message":"canonical_sha256_bytes"},"source_id":"2209.08461","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8c5c6f5e9fba95b2ba9f788b79d05bcb54ea9abb67a0f35a7ae97f67ff922808","sha256:70e0ad7f348d3e0591277270e83be6a36a07adb21bcca45160b2c6fd84f35716"],"state_sha256":"577b8c66b3e420b1a5e79f277f8ea970c041d368281eb5dc028ffb42e2d67fba"}