{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:MWIJ3CHPWERZOIDKEET45ZSXHL","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":"d95b45e31e71a6802c0a246af267e805a004b0380d0b9b6d92b76b49c33347d1","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-03-14T08:45:13Z","title_canon_sha256":"c4393441621119b2cab3bf89c222dd17c941be92f6b83b792a0a95e11e371f73"},"schema_version":"1.0","source":{"id":"1903.05858","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.05858","created_at":"2026-07-05T00:44:06Z"},{"alias_kind":"arxiv_version","alias_value":"1903.05858v4","created_at":"2026-07-05T00:44:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.05858","created_at":"2026-07-05T00:44:06Z"},{"alias_kind":"pith_short_12","alias_value":"MWIJ3CHPWERZ","created_at":"2026-07-05T00:44:06Z"},{"alias_kind":"pith_short_16","alias_value":"MWIJ3CHPWERZOIDK","created_at":"2026-07-05T00:44:06Z"},{"alias_kind":"pith_short_8","alias_value":"MWIJ3CHP","created_at":"2026-07-05T00:44:06Z"}],"graph_snapshots":[{"event_id":"sha256:d21444adc082d97d865023926a5034f310f38274ab435fa7b9308e596a20de25","target":"graph","created_at":"2026-07-05T00:44:06Z","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/1903.05858/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Deep neural networks with rectified linear units (ReLU) are getting more and more popular due to their universal representation power and successful applications. Some theoretical progress regarding the approximation power of deep ReLU network for functions in Sobolev space and Korobov space have recently been made by [D. Yarotsky, Neural Network, 94:103-114, 2017] and [H. Montanelli and Q. Du, SIAM J Math. Data Sci., 1:78-92, 2019], etc. In this paper, we show that deep networks with rectified power units (RePU) can give better approximations for smooth functions than deep ReLU networks. Our ","authors_text":"Bo Li, Haijun Yu, Shanshan Tang","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-03-14T08:45:13Z","title":"Better Approximations of High Dimensional Smooth Functions by Deep Neural Networks with Rectified Power Units"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.05858","kind":"arxiv","version":4},"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":"sha256:1a1150ff1c44258894ba1c05651694930425b106c3eb2a5d3ad253f26861ba6f","target":"record","created_at":"2026-07-05T00:44:06Z","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":"d95b45e31e71a6802c0a246af267e805a004b0380d0b9b6d92b76b49c33347d1","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-03-14T08:45:13Z","title_canon_sha256":"c4393441621119b2cab3bf89c222dd17c941be92f6b83b792a0a95e11e371f73"},"schema_version":"1.0","source":{"id":"1903.05858","kind":"arxiv","version":4}},"canonical_sha256":"65909d88efb12397206a2127cee6573acbbb10f829d4609d389cf8e960fcfe79","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"65909d88efb12397206a2127cee6573acbbb10f829d4609d389cf8e960fcfe79","first_computed_at":"2026-07-05T00:44:06.259139Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:44:06.259139Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yLRW6sOfha9yEb7lHEE9pgahEf6LCVMsQuv6sJoEzU0wBWZfc0UU+nrtAAdIP+Zcbbg7QGf7TFmVSnxY55fADA==","signature_status":"signed_v1","signed_at":"2026-07-05T00:44:06.259587Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.05858","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1a1150ff1c44258894ba1c05651694930425b106c3eb2a5d3ad253f26861ba6f","sha256:d21444adc082d97d865023926a5034f310f38274ab435fa7b9308e596a20de25"],"state_sha256":"d0d67a1b5ef91351dc8e68fbe9f572bce39e497d2f18450e043a69cb5f974fa0"}