{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:5JFRMUCUN3HMBMD44TQJ6OY4II","short_pith_number":"pith:5JFRMUCU","canonical_record":{"source":{"id":"2206.04569","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2022-06-09T15:35:22Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"5e6538990a62697f69b7ae73af0e55c3ab719005a5d1b1209b363be33e1b562c","abstract_canon_sha256":"d5007697f16639efbbe53c566558423303c1d41fcbc2d9eb4b2ad8e6fe04ae14"},"schema_version":"1.0"},"canonical_sha256":"ea4b1650546ecec0b07ce4e09f3b1c4238904dd583ea35aa8af1ea1a29a6e8fe","source":{"kind":"arxiv","id":"2206.04569","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2206.04569","created_at":"2026-07-05T04:30:35Z"},{"alias_kind":"arxiv_version","alias_value":"2206.04569v1","created_at":"2026-07-05T04:30:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2206.04569","created_at":"2026-07-05T04:30:35Z"},{"alias_kind":"pith_short_12","alias_value":"5JFRMUCUN3HM","created_at":"2026-07-05T04:30:35Z"},{"alias_kind":"pith_short_16","alias_value":"5JFRMUCUN3HMBMD4","created_at":"2026-07-05T04:30:35Z"},{"alias_kind":"pith_short_8","alias_value":"5JFRMUCU","created_at":"2026-07-05T04:30:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:5JFRMUCUN3HMBMD44TQJ6OY4II","target":"record","payload":{"canonical_record":{"source":{"id":"2206.04569","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2022-06-09T15:35:22Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"5e6538990a62697f69b7ae73af0e55c3ab719005a5d1b1209b363be33e1b562c","abstract_canon_sha256":"d5007697f16639efbbe53c566558423303c1d41fcbc2d9eb4b2ad8e6fe04ae14"},"schema_version":"1.0"},"canonical_sha256":"ea4b1650546ecec0b07ce4e09f3b1c4238904dd583ea35aa8af1ea1a29a6e8fe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:30:35.028893Z","signature_b64":"YHkNW7wIXsr1X+r6LSV+K7rYkQb+VPmNzFzozzRtQIH5AwObWrml8NogPRzScZkMH/3zp1cA/+ZDZm3DrrRGBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ea4b1650546ecec0b07ce4e09f3b1c4238904dd583ea35aa8af1ea1a29a6e8fe","last_reissued_at":"2026-07-05T04:30:35.028506Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:30:35.028506Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2206.04569","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:30:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ny4gJY1rCPo3eQirSicLFYXyrjvwnwRaRWIWmXMNBlMDlo7vVAeCJ1YJOV3fv+0QUbNOjRbcW1hNBnC3sFSkDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-11T13:02:46.343913Z"},"content_sha256":"3c539b57f5fe8b131e51263aa7c181dff5b0c64afb2ab21b50495792e350a237","schema_version":"1.0","event_id":"sha256:3c539b57f5fe8b131e51263aa7c181dff5b0c64afb2ab21b50495792e350a237"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:5JFRMUCUN3HMBMD44TQJ6OY4II","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Benefits of Overparameterized Convolutional Residual Networks: Function Approximation under Smoothness Constraint","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Hao Liu, Minshuo Chen, Siawpeng Er, Tong Zhang, Tuo Zhao, Wenjing Liao","submitted_at":"2022-06-09T15:35:22Z","abstract_excerpt":"Overparameterized neural networks enjoy great representation power on complex data, and more importantly yield sufficiently smooth output, which is crucial to their generalization and robustness. Most existing function approximation theories suggest that with sufficiently many parameters, neural networks can well approximate certain classes of functions in terms of the function value. The neural network themselves, however, can be highly nonsmooth. To bridge this gap, we take convolutional residual networks (ConvResNets) as an example, and prove that large ConvResNets can not only approximate "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.04569","kind":"arxiv","version":1},"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/2206.04569/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":"2026-07-05T04:30:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"okSnPKGQEWhQmAJ1uWD2mrSUoRwHHj7gEaSNu29lrTx2eZ9M7HAv09t34AQosToR+DfiypPOS5+XTB41ztxBCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-11T13:02:46.344287Z"},"content_sha256":"917f12f4800c0495f92b28242981540d14da0828ed15256838692d8cf3d53a39","schema_version":"1.0","event_id":"sha256:917f12f4800c0495f92b28242981540d14da0828ed15256838692d8cf3d53a39"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5JFRMUCUN3HMBMD44TQJ6OY4II/bundle.json","state_url":"https://pith.science/pith/5JFRMUCUN3HMBMD44TQJ6OY4II/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5JFRMUCUN3HMBMD44TQJ6OY4II/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":"2026-07-11T13:02:46Z","links":{"resolver":"https://pith.science/pith/5JFRMUCUN3HMBMD44TQJ6OY4II","bundle":"https://pith.science/pith/5JFRMUCUN3HMBMD44TQJ6OY4II/bundle.json","state":"https://pith.science/pith/5JFRMUCUN3HMBMD44TQJ6OY4II/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5JFRMUCUN3HMBMD44TQJ6OY4II/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:5JFRMUCUN3HMBMD44TQJ6OY4II","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":"d5007697f16639efbbe53c566558423303c1d41fcbc2d9eb4b2ad8e6fe04ae14","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2022-06-09T15:35:22Z","title_canon_sha256":"5e6538990a62697f69b7ae73af0e55c3ab719005a5d1b1209b363be33e1b562c"},"schema_version":"1.0","source":{"id":"2206.04569","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2206.04569","created_at":"2026-07-05T04:30:35Z"},{"alias_kind":"arxiv_version","alias_value":"2206.04569v1","created_at":"2026-07-05T04:30:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2206.04569","created_at":"2026-07-05T04:30:35Z"},{"alias_kind":"pith_short_12","alias_value":"5JFRMUCUN3HM","created_at":"2026-07-05T04:30:35Z"},{"alias_kind":"pith_short_16","alias_value":"5JFRMUCUN3HMBMD4","created_at":"2026-07-05T04:30:35Z"},{"alias_kind":"pith_short_8","alias_value":"5JFRMUCU","created_at":"2026-07-05T04:30:35Z"}],"graph_snapshots":[{"event_id":"sha256:917f12f4800c0495f92b28242981540d14da0828ed15256838692d8cf3d53a39","target":"graph","created_at":"2026-07-05T04:30:35Z","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/2206.04569/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Overparameterized neural networks enjoy great representation power on complex data, and more importantly yield sufficiently smooth output, which is crucial to their generalization and robustness. Most existing function approximation theories suggest that with sufficiently many parameters, neural networks can well approximate certain classes of functions in terms of the function value. The neural network themselves, however, can be highly nonsmooth. To bridge this gap, we take convolutional residual networks (ConvResNets) as an example, and prove that large ConvResNets can not only approximate ","authors_text":"Hao Liu, Minshuo Chen, Siawpeng Er, Tong Zhang, Tuo Zhao, Wenjing Liao","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2022-06-09T15:35:22Z","title":"Benefits of Overparameterized Convolutional Residual Networks: Function Approximation under Smoothness Constraint"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.04569","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":"sha256:3c539b57f5fe8b131e51263aa7c181dff5b0c64afb2ab21b50495792e350a237","target":"record","created_at":"2026-07-05T04:30:35Z","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":"d5007697f16639efbbe53c566558423303c1d41fcbc2d9eb4b2ad8e6fe04ae14","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2022-06-09T15:35:22Z","title_canon_sha256":"5e6538990a62697f69b7ae73af0e55c3ab719005a5d1b1209b363be33e1b562c"},"schema_version":"1.0","source":{"id":"2206.04569","kind":"arxiv","version":1}},"canonical_sha256":"ea4b1650546ecec0b07ce4e09f3b1c4238904dd583ea35aa8af1ea1a29a6e8fe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ea4b1650546ecec0b07ce4e09f3b1c4238904dd583ea35aa8af1ea1a29a6e8fe","first_computed_at":"2026-07-05T04:30:35.028506Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:30:35.028506Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YHkNW7wIXsr1X+r6LSV+K7rYkQb+VPmNzFzozzRtQIH5AwObWrml8NogPRzScZkMH/3zp1cA/+ZDZm3DrrRGBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T04:30:35.028893Z","signed_message":"canonical_sha256_bytes"},"source_id":"2206.04569","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3c539b57f5fe8b131e51263aa7c181dff5b0c64afb2ab21b50495792e350a237","sha256:917f12f4800c0495f92b28242981540d14da0828ed15256838692d8cf3d53a39"],"state_sha256":"6c96988ee9eb344fd186e3bf0035cec65dd6e4d427932bb3837e6cc1fa14d827"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HZonTrNAJZ5Uf+LO2FZDuMMqHOR/3Pt0LIEgP6yJaaoZKTqi6RyVSuUwYXH1MIGm/Z8HFRLeCG1irKngg4X3Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-11T13:02:46.346393Z","bundle_sha256":"45afa133309abefa4363e327ba46c79db6df3c6502604136db6ce0f138259502"}}