{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:D6567CEBSYXIPM7E7XUEMVQWSC","short_pith_number":"pith:D6567CEB","canonical_record":{"source":{"id":"1904.02311","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-04-04T02:18:08Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"2490c4c1492b19f69d5f382afd0e5b522bfcf4b6addd9fa7b264e1fceab04400","abstract_canon_sha256":"39870f4f7756edf9ddc30538750e4dbd02bafc57b2c1c4478247f8f877dca2f5"},"schema_version":"1.0"},"canonical_sha256":"1fbbef8881962e87b3e4fde846561690bdeaa04fa5944abf7cd572edd73cdc12","source":{"kind":"arxiv","id":"1904.02311","version":7},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.02311","created_at":"2026-07-05T02:04:03Z"},{"alias_kind":"arxiv_version","alias_value":"1904.02311v7","created_at":"2026-07-05T02:04:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.02311","created_at":"2026-07-05T02:04:03Z"},{"alias_kind":"pith_short_12","alias_value":"D6567CEBSYXI","created_at":"2026-07-05T02:04:03Z"},{"alias_kind":"pith_short_16","alias_value":"D6567CEBSYXIPM7E","created_at":"2026-07-05T02:04:03Z"},{"alias_kind":"pith_short_8","alias_value":"D6567CEB","created_at":"2026-07-05T02:04:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:D6567CEBSYXIPM7E7XUEMVQWSC","target":"record","payload":{"canonical_record":{"source":{"id":"1904.02311","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-04-04T02:18:08Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"2490c4c1492b19f69d5f382afd0e5b522bfcf4b6addd9fa7b264e1fceab04400","abstract_canon_sha256":"39870f4f7756edf9ddc30538750e4dbd02bafc57b2c1c4478247f8f877dca2f5"},"schema_version":"1.0"},"canonical_sha256":"1fbbef8881962e87b3e4fde846561690bdeaa04fa5944abf7cd572edd73cdc12","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:04:03.085147Z","signature_b64":"XB5Mrz3vdZgOVmcOM4uoFcAeLsM9QnkU1Y6qrL0oMxPlkJrPnAHhJ3tNuMDUFZZ7IvVRP2nsfKem8DkXFi8WDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1fbbef8881962e87b3e4fde846561690bdeaa04fa5944abf7cd572edd73cdc12","last_reissued_at":"2026-07-05T02:04:03.084745Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:04:03.084745Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.02311","source_version":7,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T02:04:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cctpzixQqA7rj3NNd2vq87Dmygql0C+GjQGODAurrxmvaqofE8Ym0I0isTf7eQ7ChLT91qzsiuWN7VzrJOpWCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T07:19:02.072537Z"},"content_sha256":"d98d46fd6eb9aa951cf5a0f7dd04aca21697d2cc50ba118fa38771f2f0610c83","schema_version":"1.0","event_id":"sha256:d98d46fd6eb9aa951cf5a0f7dd04aca21697d2cc50ba118fa38771f2f0610c83"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:D6567CEBSYXIPM7E7XUEMVQWSC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Approximation Rates for Neural Networks with General Activation Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"math.CA","authors_text":"Jinchao Xu, Jonathan W. Siegel","submitted_at":"2019-04-04T02:18:08Z","abstract_excerpt":"We prove some new results concerning the approximation rate of neural networks with general activation functions. Our first result concerns the rate of approximation of a two layer neural network with a polynomially-decaying non-sigmoidal activation function. We extend the dimension independent approximation rates previously obtained to this new class of activation functions. Our second result gives a weaker, but still dimension independent, approximation rate for a larger class of activation functions, removing the polynomial decay assumption. This result applies to any bounded, integrable ac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.02311","kind":"arxiv","version":7},"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/1904.02311/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":"2026-07-05T02:04:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1We4cPAeZbLyd4Uudn5pambu3MZJvzhgTk1B2mKFNZ6nLGWwkdaqAcFdtp0kMD/ZHFundYnqsDxXpaLlh4DsCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T07:19:02.073107Z"},"content_sha256":"8e6833fda6eab05e25d7c5dcb45fa8f5bdd717e6a6e62d40125d5e02db0ca310","schema_version":"1.0","event_id":"sha256:8e6833fda6eab05e25d7c5dcb45fa8f5bdd717e6a6e62d40125d5e02db0ca310"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D6567CEBSYXIPM7E7XUEMVQWSC/bundle.json","state_url":"https://pith.science/pith/D6567CEBSYXIPM7E7XUEMVQWSC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D6567CEBSYXIPM7E7XUEMVQWSC/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":"2026-08-09T07:19:02Z","links":{"resolver":"https://pith.science/pith/D6567CEBSYXIPM7E7XUEMVQWSC","bundle":"https://pith.science/pith/D6567CEBSYXIPM7E7XUEMVQWSC/bundle.json","state":"https://pith.science/pith/D6567CEBSYXIPM7E7XUEMVQWSC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D6567CEBSYXIPM7E7XUEMVQWSC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:D6567CEBSYXIPM7E7XUEMVQWSC","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":"39870f4f7756edf9ddc30538750e4dbd02bafc57b2c1c4478247f8f877dca2f5","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-04-04T02:18:08Z","title_canon_sha256":"2490c4c1492b19f69d5f382afd0e5b522bfcf4b6addd9fa7b264e1fceab04400"},"schema_version":"1.0","source":{"id":"1904.02311","kind":"arxiv","version":7}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.02311","created_at":"2026-07-05T02:04:03Z"},{"alias_kind":"arxiv_version","alias_value":"1904.02311v7","created_at":"2026-07-05T02:04:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.02311","created_at":"2026-07-05T02:04:03Z"},{"alias_kind":"pith_short_12","alias_value":"D6567CEBSYXI","created_at":"2026-07-05T02:04:03Z"},{"alias_kind":"pith_short_16","alias_value":"D6567CEBSYXIPM7E","created_at":"2026-07-05T02:04:03Z"},{"alias_kind":"pith_short_8","alias_value":"D6567CEB","created_at":"2026-07-05T02:04:03Z"}],"graph_snapshots":[{"event_id":"sha256:8e6833fda6eab05e25d7c5dcb45fa8f5bdd717e6a6e62d40125d5e02db0ca310","target":"graph","created_at":"2026-07-05T02:04:03Z","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/1904.02311/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove some new results concerning the approximation rate of neural networks with general activation functions. Our first result concerns the rate of approximation of a two layer neural network with a polynomially-decaying non-sigmoidal activation function. We extend the dimension independent approximation rates previously obtained to this new class of activation functions. Our second result gives a weaker, but still dimension independent, approximation rate for a larger class of activation functions, removing the polynomial decay assumption. This result applies to any bounded, integrable ac","authors_text":"Jinchao Xu, Jonathan W. Siegel","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-04-04T02:18:08Z","title":"Approximation Rates for Neural Networks with General Activation Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.02311","kind":"arxiv","version":7},"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:d98d46fd6eb9aa951cf5a0f7dd04aca21697d2cc50ba118fa38771f2f0610c83","target":"record","created_at":"2026-07-05T02:04:03Z","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":"39870f4f7756edf9ddc30538750e4dbd02bafc57b2c1c4478247f8f877dca2f5","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-04-04T02:18:08Z","title_canon_sha256":"2490c4c1492b19f69d5f382afd0e5b522bfcf4b6addd9fa7b264e1fceab04400"},"schema_version":"1.0","source":{"id":"1904.02311","kind":"arxiv","version":7}},"canonical_sha256":"1fbbef8881962e87b3e4fde846561690bdeaa04fa5944abf7cd572edd73cdc12","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1fbbef8881962e87b3e4fde846561690bdeaa04fa5944abf7cd572edd73cdc12","first_computed_at":"2026-07-05T02:04:03.084745Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:04:03.084745Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XB5Mrz3vdZgOVmcOM4uoFcAeLsM9QnkU1Y6qrL0oMxPlkJrPnAHhJ3tNuMDUFZZ7IvVRP2nsfKem8DkXFi8WDw==","signature_status":"signed_v1","signed_at":"2026-07-05T02:04:03.085147Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.02311","source_kind":"arxiv","source_version":7}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d98d46fd6eb9aa951cf5a0f7dd04aca21697d2cc50ba118fa38771f2f0610c83","sha256:8e6833fda6eab05e25d7c5dcb45fa8f5bdd717e6a6e62d40125d5e02db0ca310"],"state_sha256":"572fa7202c5476a3438779821797039ef1e439eba686d92edde290e8f533ea88"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vwD0mw7erGRGX7597PcpoF+a0kierLxLJpM13RN5q5aMEUCILwQukrf9Y6Oc5mVmTVaYgZVcSqLgGGnQv21GDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T07:19:02.077919Z","bundle_sha256":"b57cfaf91ad3f59e20201522fdf3b4a7fc4ea02860998e1c0014642e8c3b0069"}}