{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:RFIDBTZSBDWMFWTNQY4RO67WOS","short_pith_number":"pith:RFIDBTZS","canonical_record":{"source":{"id":"2008.02545","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2020-08-06T09:50:29Z","cross_cats_sorted":["cs.LG","math.ST","stat.TH"],"title_canon_sha256":"cb3f6cb1a5c8aa52d146b7b39795a1d6efa4a0f5fb59986d48192ebe16995d27","abstract_canon_sha256":"551a0d1b8f81ec9a2e09e73b1f35f34bef25e737e6cd8b3aa7ff140f1e30adf1"},"schema_version":"1.0"},"canonical_sha256":"895030cf3208ecc2da6d8639177bf6749157e52106b49443f658ffeeac572a5c","source":{"kind":"arxiv","id":"2008.02545","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2008.02545","created_at":"2026-07-05T02:34:41Z"},{"alias_kind":"arxiv_version","alias_value":"2008.02545v3","created_at":"2026-07-05T02:34:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2008.02545","created_at":"2026-07-05T02:34:41Z"},{"alias_kind":"pith_short_12","alias_value":"RFIDBTZSBDWM","created_at":"2026-07-05T02:34:41Z"},{"alias_kind":"pith_short_16","alias_value":"RFIDBTZSBDWMFWTN","created_at":"2026-07-05T02:34:41Z"},{"alias_kind":"pith_short_8","alias_value":"RFIDBTZS","created_at":"2026-07-05T02:34:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:RFIDBTZSBDWMFWTNQY4RO67WOS","target":"record","payload":{"canonical_record":{"source":{"id":"2008.02545","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2020-08-06T09:50:29Z","cross_cats_sorted":["cs.LG","math.ST","stat.TH"],"title_canon_sha256":"cb3f6cb1a5c8aa52d146b7b39795a1d6efa4a0f5fb59986d48192ebe16995d27","abstract_canon_sha256":"551a0d1b8f81ec9a2e09e73b1f35f34bef25e737e6cd8b3aa7ff140f1e30adf1"},"schema_version":"1.0"},"canonical_sha256":"895030cf3208ecc2da6d8639177bf6749157e52106b49443f658ffeeac572a5c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:34:41.637879Z","signature_b64":"/eqBX4bZ6hohC4QO9DhI2Jk1AI3YNl3ZLyUHRYfnY28VVep1HS0wm9LSCok3gIage23+Exl3b5UZjLlpED07Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"895030cf3208ecc2da6d8639177bf6749157e52106b49443f658ffeeac572a5c","last_reissued_at":"2026-07-05T02:34:41.637408Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:34:41.637408Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2008.02545","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T02:34:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m7O3LmW1DMe4Qb33kQekGV+InkFCCUOiknre1PmWotguufoEZj0KXfu9jyTYGlVj2E4WLlip/QpEEpp7KuJNCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T04:27:24.762172Z"},"content_sha256":"cf9f53ecea563dfd1392510e9958dea106d25f7407aff6ce3dc9b3ee711360d3","schema_version":"1.0","event_id":"sha256:cf9f53ecea563dfd1392510e9958dea106d25f7407aff6ce3dc9b3ee711360d3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:RFIDBTZSBDWMFWTNQY4RO67WOS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A deep network construction that adapts to intrinsic dimensionality beyond the domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.ST","stat.TH"],"primary_cat":"stat.ML","authors_text":"Alexander Cloninger, Timo Klock","submitted_at":"2020-08-06T09:50:29Z","abstract_excerpt":"We study the approximation of two-layer compositions $f(x) = g(\\phi(x))$ via deep networks with ReLU activation, where $\\phi$ is a geometrically intuitive, dimensionality reducing feature map. We focus on two intuitive and practically relevant choices for $\\phi$: the projection onto a low-dimensional embedded submanifold and a distance to a collection of low-dimensional sets. We achieve near optimal approximation rates, which depend only on the complexity of the dimensionality reducing map $\\phi$ rather than the ambient dimension. Since $\\phi$ encapsulates all nonlinear features that are mater"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.02545","kind":"arxiv","version":3},"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/2008.02545/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":"2026-07-05T02:34:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AsfiEjnLbWF4rJbkqF2nuVcwk8vKMISYVN3xG6FOrk7GON8CulRpdpcKQkM3vzyVEbNWNhSYiONakSSYx4ftBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T04:27:24.762677Z"},"content_sha256":"c0d216f92bc50f48734c3740243efab78f376c4ac4a9f90f365ac6bb4744efed","schema_version":"1.0","event_id":"sha256:c0d216f92bc50f48734c3740243efab78f376c4ac4a9f90f365ac6bb4744efed"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RFIDBTZSBDWMFWTNQY4RO67WOS/bundle.json","state_url":"https://pith.science/pith/RFIDBTZSBDWMFWTNQY4RO67WOS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RFIDBTZSBDWMFWTNQY4RO67WOS/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":"2026-08-08T04:27:24Z","links":{"resolver":"https://pith.science/pith/RFIDBTZSBDWMFWTNQY4RO67WOS","bundle":"https://pith.science/pith/RFIDBTZSBDWMFWTNQY4RO67WOS/bundle.json","state":"https://pith.science/pith/RFIDBTZSBDWMFWTNQY4RO67WOS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RFIDBTZSBDWMFWTNQY4RO67WOS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:RFIDBTZSBDWMFWTNQY4RO67WOS","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":"551a0d1b8f81ec9a2e09e73b1f35f34bef25e737e6cd8b3aa7ff140f1e30adf1","cross_cats_sorted":["cs.LG","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2020-08-06T09:50:29Z","title_canon_sha256":"cb3f6cb1a5c8aa52d146b7b39795a1d6efa4a0f5fb59986d48192ebe16995d27"},"schema_version":"1.0","source":{"id":"2008.02545","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2008.02545","created_at":"2026-07-05T02:34:41Z"},{"alias_kind":"arxiv_version","alias_value":"2008.02545v3","created_at":"2026-07-05T02:34:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2008.02545","created_at":"2026-07-05T02:34:41Z"},{"alias_kind":"pith_short_12","alias_value":"RFIDBTZSBDWM","created_at":"2026-07-05T02:34:41Z"},{"alias_kind":"pith_short_16","alias_value":"RFIDBTZSBDWMFWTN","created_at":"2026-07-05T02:34:41Z"},{"alias_kind":"pith_short_8","alias_value":"RFIDBTZS","created_at":"2026-07-05T02:34:41Z"}],"graph_snapshots":[{"event_id":"sha256:c0d216f92bc50f48734c3740243efab78f376c4ac4a9f90f365ac6bb4744efed","target":"graph","created_at":"2026-07-05T02:34:41Z","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/2008.02545/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the approximation of two-layer compositions $f(x) = g(\\phi(x))$ via deep networks with ReLU activation, where $\\phi$ is a geometrically intuitive, dimensionality reducing feature map. We focus on two intuitive and practically relevant choices for $\\phi$: the projection onto a low-dimensional embedded submanifold and a distance to a collection of low-dimensional sets. We achieve near optimal approximation rates, which depend only on the complexity of the dimensionality reducing map $\\phi$ rather than the ambient dimension. Since $\\phi$ encapsulates all nonlinear features that are mater","authors_text":"Alexander Cloninger, Timo Klock","cross_cats":["cs.LG","math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2020-08-06T09:50:29Z","title":"A deep network construction that adapts to intrinsic dimensionality beyond the domain"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.02545","kind":"arxiv","version":3},"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:cf9f53ecea563dfd1392510e9958dea106d25f7407aff6ce3dc9b3ee711360d3","target":"record","created_at":"2026-07-05T02:34:41Z","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":"551a0d1b8f81ec9a2e09e73b1f35f34bef25e737e6cd8b3aa7ff140f1e30adf1","cross_cats_sorted":["cs.LG","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2020-08-06T09:50:29Z","title_canon_sha256":"cb3f6cb1a5c8aa52d146b7b39795a1d6efa4a0f5fb59986d48192ebe16995d27"},"schema_version":"1.0","source":{"id":"2008.02545","kind":"arxiv","version":3}},"canonical_sha256":"895030cf3208ecc2da6d8639177bf6749157e52106b49443f658ffeeac572a5c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"895030cf3208ecc2da6d8639177bf6749157e52106b49443f658ffeeac572a5c","first_computed_at":"2026-07-05T02:34:41.637408Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:34:41.637408Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/eqBX4bZ6hohC4QO9DhI2Jk1AI3YNl3ZLyUHRYfnY28VVep1HS0wm9LSCok3gIage23+Exl3b5UZjLlpED07Dw==","signature_status":"signed_v1","signed_at":"2026-07-05T02:34:41.637879Z","signed_message":"canonical_sha256_bytes"},"source_id":"2008.02545","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cf9f53ecea563dfd1392510e9958dea106d25f7407aff6ce3dc9b3ee711360d3","sha256:c0d216f92bc50f48734c3740243efab78f376c4ac4a9f90f365ac6bb4744efed"],"state_sha256":"9506ecaa60f93b451f148d74efb9f109c644adc079aa8f605c7f3f93e07d1c15"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"giS5hSTTUHrT789eRdJhB3SSRqwmNAbBA9rp4Wsa9yUn+DLLSawQPZbIHK2GozGyFTNSEcha2w47nVUbAdoGDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T04:27:24.766131Z","bundle_sha256":"08c9d340b5b68ea469b049491190efbf6e59ed4b6a49e197d6db2bd7c4f7c944"}}