{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:ZJESJEZG6OX4Q6OU4QTDU2VLD3","short_pith_number":"pith:ZJESJEZG","canonical_record":{"source":{"id":"1708.06633","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-08-22T14:25:55Z","cross_cats_sorted":["cs.LG","stat.ML","stat.TH"],"title_canon_sha256":"62727f5ce5942e569bd8d53ee884a80566b27a24ae994dbc46b9363f01617e84","abstract_canon_sha256":"b30e8b08a86aa30d71f8520ebd6c797c59b5665a807875cc4403a2e218d18242"},"schema_version":"1.0"},"canonical_sha256":"ca49249326f3afc879d4e4263a6aab1ec17b745105bbe0915e9264fdff05180a","source":{"kind":"arxiv","id":"1708.06633","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.06633","created_at":"2026-07-05T01:34:46Z"},{"alias_kind":"arxiv_version","alias_value":"1708.06633v5","created_at":"2026-07-05T01:34:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.06633","created_at":"2026-07-05T01:34:46Z"},{"alias_kind":"pith_short_12","alias_value":"ZJESJEZG6OX4","created_at":"2026-07-05T01:34:46Z"},{"alias_kind":"pith_short_16","alias_value":"ZJESJEZG6OX4Q6OU","created_at":"2026-07-05T01:34:46Z"},{"alias_kind":"pith_short_8","alias_value":"ZJESJEZG","created_at":"2026-07-05T01:34:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:ZJESJEZG6OX4Q6OU4QTDU2VLD3","target":"record","payload":{"canonical_record":{"source":{"id":"1708.06633","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-08-22T14:25:55Z","cross_cats_sorted":["cs.LG","stat.ML","stat.TH"],"title_canon_sha256":"62727f5ce5942e569bd8d53ee884a80566b27a24ae994dbc46b9363f01617e84","abstract_canon_sha256":"b30e8b08a86aa30d71f8520ebd6c797c59b5665a807875cc4403a2e218d18242"},"schema_version":"1.0"},"canonical_sha256":"ca49249326f3afc879d4e4263a6aab1ec17b745105bbe0915e9264fdff05180a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:34:46.954809Z","signature_b64":"eYTUkCtYWD3rB8wzUls233Ecid5/aANkFdGB1PELvW0pFaT7vutNP5RbzIIKI8xwYFdd1WdnMbWzZ7diqeA7Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ca49249326f3afc879d4e4263a6aab1ec17b745105bbe0915e9264fdff05180a","last_reissued_at":"2026-07-05T01:34:46.954466Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:34:46.954466Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.06633","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T01:34:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YMPw77z8GyMvTH0Ow0EIxk9VUv+FVE0JhTawkdlik0jC6LXmxgrnQmUt6EigguyeQ+166yXA+f54/E1GVhzxAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T01:29:49.848903Z"},"content_sha256":"960a020868e37faa09447e9e9c71ad515d581af13bfb2672b6a99631efad505c","schema_version":"1.0","event_id":"sha256:960a020868e37faa09447e9e9c71ad515d581af13bfb2672b6a99631efad505c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:ZJESJEZG6OX4Q6OU4QTDU2VLD3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nonparametric regression using deep neural networks with ReLU activation function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Johannes Schmidt-Hieber","submitted_at":"2017-08-22T14:25:55Z","abstract_excerpt":"Consider the multivariate nonparametric regression model. It is shown that estimators based on sparsely connected deep neural networks with ReLU activation function and properly chosen network architecture achieve the minimax rates of convergence (up to $\\log n$-factors) under a general composition assumption on the regression function. The framework includes many well-studied structural constraints such as (generalized) additive models. While there is a lot of flexibility in the network architecture, the tuning parameter is the sparsity of the network. Specifically, we consider large networks"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.06633","kind":"arxiv","version":5},"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/1708.06633/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":"2026-07-05T01:34:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sPFJ5GvXr3Sg/DPCbn+GVK1WXXUBUCgPN+aRhQGt1hSM/j5b8ZxW1PQHlDfkD6vb9tq1li3lB1YzxzgtzGRcCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T01:29:49.849792Z"},"content_sha256":"2cc90ae3f8f6b48132e5b4f227c77253062989eaf180801ba9f041358db39827","schema_version":"1.0","event_id":"sha256:2cc90ae3f8f6b48132e5b4f227c77253062989eaf180801ba9f041358db39827"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZJESJEZG6OX4Q6OU4QTDU2VLD3/bundle.json","state_url":"https://pith.science/pith/ZJESJEZG6OX4Q6OU4QTDU2VLD3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZJESJEZG6OX4Q6OU4QTDU2VLD3/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":"2026-08-05T01:29:49Z","links":{"resolver":"https://pith.science/pith/ZJESJEZG6OX4Q6OU4QTDU2VLD3","bundle":"https://pith.science/pith/ZJESJEZG6OX4Q6OU4QTDU2VLD3/bundle.json","state":"https://pith.science/pith/ZJESJEZG6OX4Q6OU4QTDU2VLD3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZJESJEZG6OX4Q6OU4QTDU2VLD3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ZJESJEZG6OX4Q6OU4QTDU2VLD3","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":"b30e8b08a86aa30d71f8520ebd6c797c59b5665a807875cc4403a2e218d18242","cross_cats_sorted":["cs.LG","stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-08-22T14:25:55Z","title_canon_sha256":"62727f5ce5942e569bd8d53ee884a80566b27a24ae994dbc46b9363f01617e84"},"schema_version":"1.0","source":{"id":"1708.06633","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.06633","created_at":"2026-07-05T01:34:46Z"},{"alias_kind":"arxiv_version","alias_value":"1708.06633v5","created_at":"2026-07-05T01:34:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.06633","created_at":"2026-07-05T01:34:46Z"},{"alias_kind":"pith_short_12","alias_value":"ZJESJEZG6OX4","created_at":"2026-07-05T01:34:46Z"},{"alias_kind":"pith_short_16","alias_value":"ZJESJEZG6OX4Q6OU","created_at":"2026-07-05T01:34:46Z"},{"alias_kind":"pith_short_8","alias_value":"ZJESJEZG","created_at":"2026-07-05T01:34:46Z"}],"graph_snapshots":[{"event_id":"sha256:2cc90ae3f8f6b48132e5b4f227c77253062989eaf180801ba9f041358db39827","target":"graph","created_at":"2026-07-05T01:34:46Z","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/1708.06633/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Consider the multivariate nonparametric regression model. It is shown that estimators based on sparsely connected deep neural networks with ReLU activation function and properly chosen network architecture achieve the minimax rates of convergence (up to $\\log n$-factors) under a general composition assumption on the regression function. The framework includes many well-studied structural constraints such as (generalized) additive models. While there is a lot of flexibility in the network architecture, the tuning parameter is the sparsity of the network. Specifically, we consider large networks","authors_text":"Johannes Schmidt-Hieber","cross_cats":["cs.LG","stat.ML","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-08-22T14:25:55Z","title":"Nonparametric regression using deep neural networks with ReLU activation function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.06633","kind":"arxiv","version":5},"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":"sha256:960a020868e37faa09447e9e9c71ad515d581af13bfb2672b6a99631efad505c","target":"record","created_at":"2026-07-05T01:34:46Z","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":"b30e8b08a86aa30d71f8520ebd6c797c59b5665a807875cc4403a2e218d18242","cross_cats_sorted":["cs.LG","stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-08-22T14:25:55Z","title_canon_sha256":"62727f5ce5942e569bd8d53ee884a80566b27a24ae994dbc46b9363f01617e84"},"schema_version":"1.0","source":{"id":"1708.06633","kind":"arxiv","version":5}},"canonical_sha256":"ca49249326f3afc879d4e4263a6aab1ec17b745105bbe0915e9264fdff05180a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ca49249326f3afc879d4e4263a6aab1ec17b745105bbe0915e9264fdff05180a","first_computed_at":"2026-07-05T01:34:46.954466Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:34:46.954466Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eYTUkCtYWD3rB8wzUls233Ecid5/aANkFdGB1PELvW0pFaT7vutNP5RbzIIKI8xwYFdd1WdnMbWzZ7diqeA7Aw==","signature_status":"signed_v1","signed_at":"2026-07-05T01:34:46.954809Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.06633","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:960a020868e37faa09447e9e9c71ad515d581af13bfb2672b6a99631efad505c","sha256:2cc90ae3f8f6b48132e5b4f227c77253062989eaf180801ba9f041358db39827"],"state_sha256":"e1c1a68137e9c26cfd5eaae61fe4e1c00ee515be6598481ee20f8a6f006ef783"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LRfYzkvbIAZ/AvJVtFGbRg4DPIcFod0l6i6F6LpcfFLMk94D1ZrLcDmXz0JDTrgFT1z24g8TkOS7zOO9xJeTBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T01:29:49.862563Z","bundle_sha256":"a5e6d62cb1c7e9ed78dffc80bdbb5e5084e024ab6a1c09f961d2bafed87fc89e"}}