{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:YP7GXASA7R2WZA4Y6QEDHJR3UV","short_pith_number":"pith:YP7GXASA","schema_version":"1.0","canonical_sha256":"c3fe6b8240fc756c8398f40833a63ba55c02004bed352f3b22160aa8b0f7858e","source":{"kind":"arxiv","id":"2106.06097","version":4},"attestation_state":"computed","paper":{"title":"Neural Optimization Kernel: Towards Robust Deep Learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Ivor Tsang, Yueming Lyu","submitted_at":"2021-06-11T00:34:55Z","abstract_excerpt":"Deep neural networks (NN) have achieved great success in many applications. However, why do deep neural networks obtain good generalization at an over-parameterization regime is still unclear. To better understand deep NN, we establish the connection between deep NN and a novel kernel family, i.e., Neural Optimization Kernel (NOK). The architecture of structured approximation of NOK performs monotonic descent updates of implicit regularization problems. We can implicitly choose the regularization problems by employing different activation functions, e.g., ReLU, max pooling, and soft-thresholdi"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2106.06097","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2021-06-11T00:34:55Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"af6af73e731075e7dabf115ea768f32f1a0a61baf0b772a2a2ba0d959a52facb","abstract_canon_sha256":"f9fc1250850cba408a07156693dac5912e1a5fcb28c23adae32270678f790a54"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:36:38.217959Z","signature_b64":"xa5uvsAsWgdWx1rD+BrqBxEQwSsa2IosvTofgI/NIZGYExk+GlaiSHG10CcExNysm4Qx9P83YYW5C8jbTh0dDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c3fe6b8240fc756c8398f40833a63ba55c02004bed352f3b22160aa8b0f7858e","last_reissued_at":"2026-07-05T03:36:38.217499Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:36:38.217499Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Neural Optimization Kernel: Towards Robust Deep Learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Ivor Tsang, Yueming Lyu","submitted_at":"2021-06-11T00:34:55Z","abstract_excerpt":"Deep neural networks (NN) have achieved great success in many applications. However, why do deep neural networks obtain good generalization at an over-parameterization regime is still unclear. To better understand deep NN, we establish the connection between deep NN and a novel kernel family, i.e., Neural Optimization Kernel (NOK). The architecture of structured approximation of NOK performs monotonic descent updates of implicit regularization problems. We can implicitly choose the regularization problems by employing different activation functions, e.g., ReLU, max pooling, and soft-thresholdi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.06097","kind":"arxiv","version":4},"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/2106.06097/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2106.06097","created_at":"2026-07-05T03:36:38.217558+00:00"},{"alias_kind":"arxiv_version","alias_value":"2106.06097v4","created_at":"2026-07-05T03:36:38.217558+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.06097","created_at":"2026-07-05T03:36:38.217558+00:00"},{"alias_kind":"pith_short_12","alias_value":"YP7GXASA7R2W","created_at":"2026-07-05T03:36:38.217558+00:00"},{"alias_kind":"pith_short_16","alias_value":"YP7GXASA7R2WZA4Y","created_at":"2026-07-05T03:36:38.217558+00:00"},{"alias_kind":"pith_short_8","alias_value":"YP7GXASA","created_at":"2026-07-05T03:36:38.217558+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YP7GXASA7R2WZA4Y6QEDHJR3UV","json":"https://pith.science/pith/YP7GXASA7R2WZA4Y6QEDHJR3UV.json","graph_json":"https://pith.science/api/pith-number/YP7GXASA7R2WZA4Y6QEDHJR3UV/graph.json","events_json":"https://pith.science/api/pith-number/YP7GXASA7R2WZA4Y6QEDHJR3UV/events.json","paper":"https://pith.science/paper/YP7GXASA"},"agent_actions":{"view_html":"https://pith.science/pith/YP7GXASA7R2WZA4Y6QEDHJR3UV","download_json":"https://pith.science/pith/YP7GXASA7R2WZA4Y6QEDHJR3UV.json","view_paper":"https://pith.science/paper/YP7GXASA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2106.06097&json=true","fetch_graph":"https://pith.science/api/pith-number/YP7GXASA7R2WZA4Y6QEDHJR3UV/graph.json","fetch_events":"https://pith.science/api/pith-number/YP7GXASA7R2WZA4Y6QEDHJR3UV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YP7GXASA7R2WZA4Y6QEDHJR3UV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YP7GXASA7R2WZA4Y6QEDHJR3UV/action/storage_attestation","attest_author":"https://pith.science/pith/YP7GXASA7R2WZA4Y6QEDHJR3UV/action/author_attestation","sign_citation":"https://pith.science/pith/YP7GXASA7R2WZA4Y6QEDHJR3UV/action/citation_signature","submit_replication":"https://pith.science/pith/YP7GXASA7R2WZA4Y6QEDHJR3UV/action/replication_record"}},"created_at":"2026-07-05T03:36:38.217558+00:00","updated_at":"2026-07-05T03:36:38.217558+00:00"}