{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:7VKDWXPLCDOM4U7R5BBI2PSN43","short_pith_number":"pith:7VKDWXPL","canonical_record":{"source":{"id":"2401.02890","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2024-01-05T16:43:39Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"a5a8b3d778c23d4b90648f3e87740807727825a2cbcb08d215eecb72a54321c4","abstract_canon_sha256":"62bd686e835d84a33aa3c8b12816e8774233a41db3d84fa9d4a60694430169a6"},"schema_version":"1.0"},"canonical_sha256":"fd543b5deb10dcce53f1e8428d3e4de6c768bc1ac0a5c0cb0e73c6a54fdccefc","source":{"kind":"arxiv","id":"2401.02890","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2401.02890","created_at":"2026-07-05T11:01:22Z"},{"alias_kind":"arxiv_version","alias_value":"2401.02890v2","created_at":"2026-07-05T11:01:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.02890","created_at":"2026-07-05T11:01:22Z"},{"alias_kind":"pith_short_12","alias_value":"7VKDWXPLCDOM","created_at":"2026-07-05T11:01:22Z"},{"alias_kind":"pith_short_16","alias_value":"7VKDWXPLCDOM4U7R","created_at":"2026-07-05T11:01:22Z"},{"alias_kind":"pith_short_8","alias_value":"7VKDWXPL","created_at":"2026-07-05T11:01:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:7VKDWXPLCDOM4U7R5BBI2PSN43","target":"record","payload":{"canonical_record":{"source":{"id":"2401.02890","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2024-01-05T16:43:39Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"a5a8b3d778c23d4b90648f3e87740807727825a2cbcb08d215eecb72a54321c4","abstract_canon_sha256":"62bd686e835d84a33aa3c8b12816e8774233a41db3d84fa9d4a60694430169a6"},"schema_version":"1.0"},"canonical_sha256":"fd543b5deb10dcce53f1e8428d3e4de6c768bc1ac0a5c0cb0e73c6a54fdccefc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:01:22.898289Z","signature_b64":"4ONm2x1BB9zc6+rVTxcXsEHf+R9XsBZ2Xc38ju8NyIFcHSHUPMAGPUdca6Ln+nhilFHAKYYiYt/9G5JrjbNnCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fd543b5deb10dcce53f1e8428d3e4de6c768bc1ac0a5c0cb0e73c6a54fdccefc","last_reissued_at":"2026-07-05T11:01:22.897780Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:01:22.897780Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2401.02890","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":"2026-07-05T11:01:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j671d9M7L5rubNVnzooiEgXhQDVhKJf1N1uNYAMFm++8z96K/c4adydc1LD7tN3N1voc81rK7+L2ysF550XKAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T04:48:58.310178Z"},"content_sha256":"39df61180c2c770952dd2dd3d9bf7d58a2596b2916c5159d0c18c97e8c04c72f","schema_version":"1.0","event_id":"sha256:39df61180c2c770952dd2dd3d9bf7d58a2596b2916c5159d0c18c97e8c04c72f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:7VKDWXPLCDOM4U7R5BBI2PSN43","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nonlinear functional regression by functional deep neural network with kernel embedding","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Ding-Xuan Zhou, Johan A.K. Suykens, Jun Fan, Linhao Song, Zhongjie Shi","submitted_at":"2024-01-05T16:43:39Z","abstract_excerpt":"Recently, deep learning has been widely applied in functional data analysis (FDA) with notable empirical success. However, the infinite dimensionality of functional data necessitates an effective dimension reduction approach for functional learning tasks, particularly in nonlinear functional regression. In this paper, we introduce a functional deep neural network with an adaptive and discretization-invariant dimension reduction method. Our functional network architecture consists of three parts: first, a kernel embedding step that features an integral transformation with an adaptive smooth ker"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.02890","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/2401.02890/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":"2026-07-05T11:01:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qqzg1gmcTTdk5PEO/XY2N0F7OHYpcRl0G/jwDEaD/EuPT0wKO92+/Gjl120JpDAFKzywLA38jnOvVrrFdwnNBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T04:48:58.310696Z"},"content_sha256":"9129ef28368c4fed78bccf11f5e0c7da14e897ff211eef149770b4da8a8f3383","schema_version":"1.0","event_id":"sha256:9129ef28368c4fed78bccf11f5e0c7da14e897ff211eef149770b4da8a8f3383"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7VKDWXPLCDOM4U7R5BBI2PSN43/bundle.json","state_url":"https://pith.science/pith/7VKDWXPLCDOM4U7R5BBI2PSN43/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7VKDWXPLCDOM4U7R5BBI2PSN43/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":"2026-08-12T04:48:58Z","links":{"resolver":"https://pith.science/pith/7VKDWXPLCDOM4U7R5BBI2PSN43","bundle":"https://pith.science/pith/7VKDWXPLCDOM4U7R5BBI2PSN43/bundle.json","state":"https://pith.science/pith/7VKDWXPLCDOM4U7R5BBI2PSN43/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7VKDWXPLCDOM4U7R5BBI2PSN43/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:7VKDWXPLCDOM4U7R5BBI2PSN43","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":"62bd686e835d84a33aa3c8b12816e8774233a41db3d84fa9d4a60694430169a6","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2024-01-05T16:43:39Z","title_canon_sha256":"a5a8b3d778c23d4b90648f3e87740807727825a2cbcb08d215eecb72a54321c4"},"schema_version":"1.0","source":{"id":"2401.02890","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2401.02890","created_at":"2026-07-05T11:01:22Z"},{"alias_kind":"arxiv_version","alias_value":"2401.02890v2","created_at":"2026-07-05T11:01:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.02890","created_at":"2026-07-05T11:01:22Z"},{"alias_kind":"pith_short_12","alias_value":"7VKDWXPLCDOM","created_at":"2026-07-05T11:01:22Z"},{"alias_kind":"pith_short_16","alias_value":"7VKDWXPLCDOM4U7R","created_at":"2026-07-05T11:01:22Z"},{"alias_kind":"pith_short_8","alias_value":"7VKDWXPL","created_at":"2026-07-05T11:01:22Z"}],"graph_snapshots":[{"event_id":"sha256:9129ef28368c4fed78bccf11f5e0c7da14e897ff211eef149770b4da8a8f3383","target":"graph","created_at":"2026-07-05T11:01:22Z","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/2401.02890/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Recently, deep learning has been widely applied in functional data analysis (FDA) with notable empirical success. However, the infinite dimensionality of functional data necessitates an effective dimension reduction approach for functional learning tasks, particularly in nonlinear functional regression. In this paper, we introduce a functional deep neural network with an adaptive and discretization-invariant dimension reduction method. Our functional network architecture consists of three parts: first, a kernel embedding step that features an integral transformation with an adaptive smooth ker","authors_text":"Ding-Xuan Zhou, Johan A.K. Suykens, Jun Fan, Linhao Song, Zhongjie Shi","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2024-01-05T16:43:39Z","title":"Nonlinear functional regression by functional deep neural network with kernel embedding"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.02890","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":"sha256:39df61180c2c770952dd2dd3d9bf7d58a2596b2916c5159d0c18c97e8c04c72f","target":"record","created_at":"2026-07-05T11:01:22Z","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":"62bd686e835d84a33aa3c8b12816e8774233a41db3d84fa9d4a60694430169a6","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2024-01-05T16:43:39Z","title_canon_sha256":"a5a8b3d778c23d4b90648f3e87740807727825a2cbcb08d215eecb72a54321c4"},"schema_version":"1.0","source":{"id":"2401.02890","kind":"arxiv","version":2}},"canonical_sha256":"fd543b5deb10dcce53f1e8428d3e4de6c768bc1ac0a5c0cb0e73c6a54fdccefc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fd543b5deb10dcce53f1e8428d3e4de6c768bc1ac0a5c0cb0e73c6a54fdccefc","first_computed_at":"2026-07-05T11:01:22.897780Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:01:22.897780Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4ONm2x1BB9zc6+rVTxcXsEHf+R9XsBZ2Xc38ju8NyIFcHSHUPMAGPUdca6Ln+nhilFHAKYYiYt/9G5JrjbNnCA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:01:22.898289Z","signed_message":"canonical_sha256_bytes"},"source_id":"2401.02890","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:39df61180c2c770952dd2dd3d9bf7d58a2596b2916c5159d0c18c97e8c04c72f","sha256:9129ef28368c4fed78bccf11f5e0c7da14e897ff211eef149770b4da8a8f3383"],"state_sha256":"9232447800b54e2ec5f31bbb157f9d2557b5dcca2c7578f50f09169830b36b93"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x19cMdUwZiB8miyS5n7qrEAiOMQETZJM6agMXhzYEA3ifuXlb6C7VC3hhllJYVB5VG/Qy/SkwN+ctzZrwq0SBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T04:48:58.314414Z","bundle_sha256":"8638675a6edf111aff21c37e498faef5be0e7dc2acfa4d12a282858c66d263bd"}}