{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:H3MJA4RCE566ZZFGMM2F5UWT6G","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":"f1cd2f2a5f446cc8aa3c642ba3974446fe12a95c0a8380bb71fb17ba229aba26","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-01-04T10:01:17Z","title_canon_sha256":"2ac26ac9f933792ea6e69cfbda536b857e32e7c0b80b0a2ef8c47aea0ede5bcc"},"schema_version":"1.0","source":{"id":"1901.01036","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.01036","created_at":"2026-05-17T23:56:57Z"},{"alias_kind":"arxiv_version","alias_value":"1901.01036v1","created_at":"2026-05-17T23:56:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.01036","created_at":"2026-05-17T23:56:57Z"},{"alias_kind":"pith_short_12","alias_value":"H3MJA4RCE566","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"H3MJA4RCE566ZZFG","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"H3MJA4RC","created_at":"2026-05-18T12:33:18Z"}],"graph_snapshots":[{"event_id":"sha256:945c3ea6c7e78d53b664a2c58e3c29bab6504518c1d3822345c2ad43568148d9","target":"graph","created_at":"2026-05-17T23:56:57Z","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":"Targeting at sparse multi-task learning, we consider regularization models with an $\\ell^1$ penalty on the coefficients of kernel functions. In order to provide a kernel method for this model, we construct a class of vector-valued reproducing kernel Banach spaces with the $\\ell^1$ norm. The notion of multi-task admissible kernels is proposed so that the constructed spaces could have desirable properties including the crucial linear representer theorem. Such kernels are related to bounded Lebesgue constants of a kernel interpolation question. We study the Lebesgue constant of multi-task kernels","authors_text":"Guohui Song, Haizhang Zhang, Rongrong Lin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-01-04T10:01:17Z","title":"Multi-task Learning in Vector-valued Reproducing Kernel Banach Spaces with the $\\ell^1$ Norm"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.01036","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:f51c8e5f234770f345a56a525a005716d1c42a2e72f25595938e67dfba523c48","target":"record","created_at":"2026-05-17T23:56:57Z","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":"f1cd2f2a5f446cc8aa3c642ba3974446fe12a95c0a8380bb71fb17ba229aba26","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-01-04T10:01:17Z","title_canon_sha256":"2ac26ac9f933792ea6e69cfbda536b857e32e7c0b80b0a2ef8c47aea0ede5bcc"},"schema_version":"1.0","source":{"id":"1901.01036","kind":"arxiv","version":1}},"canonical_sha256":"3ed8907222277dece4a663345ed2d3f18e9ac99d65bb0568b6029e7237319048","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3ed8907222277dece4a663345ed2d3f18e9ac99d65bb0568b6029e7237319048","first_computed_at":"2026-05-17T23:56:57.311476Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:57.311476Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lqK5iB+qkR7zZFySBO70jVMi/nVm/jIm4d7CErVoJxEyp8F+nPAX/aB22upybLQyoMXEt6dFJzR5sqeFPq9KBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:57.312092Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.01036","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f51c8e5f234770f345a56a525a005716d1c42a2e72f25595938e67dfba523c48","sha256:945c3ea6c7e78d53b664a2c58e3c29bab6504518c1d3822345c2ad43568148d9"],"state_sha256":"3584eb374d5c572f5d38a9840d4439b32ea10b69e34ed0f16663fe33b003e2a2"}