{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:WHS4MPFNXK63F5ROUAFUX6P2XZ","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":"a893c9b01bdc7de6931406f4aeafefea2251e1e050a5c06fea726ba894dc0dd9","cross_cats_sorted":["cs.NA","math.NA","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-06-22T13:27:33Z","title_canon_sha256":"c4f1d0c1448452d84a7f3f74314792d96aa4b567afe3cbc8585f5f924e50c7bd"},"schema_version":"1.0","source":{"id":"2006.12231","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2006.12231","created_at":"2026-07-05T02:26:48Z"},{"alias_kind":"arxiv_version","alias_value":"2006.12231v6","created_at":"2026-07-05T02:26:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.12231","created_at":"2026-07-05T02:26:48Z"},{"alias_kind":"pith_short_12","alias_value":"WHS4MPFNXK63","created_at":"2026-07-05T02:26:48Z"},{"alias_kind":"pith_short_16","alias_value":"WHS4MPFNXK63F5RO","created_at":"2026-07-05T02:26:48Z"},{"alias_kind":"pith_short_8","alias_value":"WHS4MPFN","created_at":"2026-07-05T02:26:48Z"}],"graph_snapshots":[{"event_id":"sha256:dccc78d43651048bb0808dae7cfa7142df6a62fec76cbfc2a737613961c010e4","target":"graph","created_at":"2026-07-05T02:26:48Z","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/2006.12231/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A new network with super approximation power is introduced. This network is built with Floor ($\\lfloor x\\rfloor$) or ReLU ($\\max\\{0,x\\}$) activation function in each neuron and hence we call such networks Floor-ReLU networks. For any hyper-parameters $N\\in\\mathbb{N}^+$ and $L\\in\\mathbb{N}^+$, it is shown that Floor-ReLU networks with width $\\max\\{d,\\, 5N+13\\}$ and depth $64dL+3$ can uniformly approximate a H\\\"older function $f$ on $[0,1]^d$ with an approximation error $3\\lambda d^{\\alpha/2}N^{-\\alpha\\sqrt{L}}$, where $\\alpha \\in(0,1]$ and $\\lambda$ are the H\\\"older order and constant, respecti","authors_text":"Haizhao Yang, Shijun Zhang, Zuowei Shen","cross_cats":["cs.NA","math.NA","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-06-22T13:27:33Z","title":"Deep Network with Approximation Error Being Reciprocal of Width to Power of Square Root of Depth"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.12231","kind":"arxiv","version":6},"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":"sha256:6f779051d0b7046cc50ce5b0b0c90b1c7c85208baef289ee1c3f13c7a385a54d","target":"record","created_at":"2026-07-05T02:26:48Z","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":"a893c9b01bdc7de6931406f4aeafefea2251e1e050a5c06fea726ba894dc0dd9","cross_cats_sorted":["cs.NA","math.NA","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-06-22T13:27:33Z","title_canon_sha256":"c4f1d0c1448452d84a7f3f74314792d96aa4b567afe3cbc8585f5f924e50c7bd"},"schema_version":"1.0","source":{"id":"2006.12231","kind":"arxiv","version":6}},"canonical_sha256":"b1e5c63cadbabdb2f62ea00b4bf9fabe4f87d1aa2ab4c68abdc2955d99aa6f8b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b1e5c63cadbabdb2f62ea00b4bf9fabe4f87d1aa2ab4c68abdc2955d99aa6f8b","first_computed_at":"2026-07-05T02:26:48.623769Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:26:48.623769Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qsgAX0y823/xUtMFGRbY0agKLVxj+9vx7fOsucOUe0rHHiTFaeVWcjMRS65LXEXdCGEUFNOAvsvhxSvymrXiDg==","signature_status":"signed_v1","signed_at":"2026-07-05T02:26:48.624252Z","signed_message":"canonical_sha256_bytes"},"source_id":"2006.12231","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6f779051d0b7046cc50ce5b0b0c90b1c7c85208baef289ee1c3f13c7a385a54d","sha256:dccc78d43651048bb0808dae7cfa7142df6a62fec76cbfc2a737613961c010e4"],"state_sha256":"a66851dc0103fa7a8cdc7469a095fe424d7153a43823257808260639f98c7a40"}