{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:3HYT534D4MED65JFT2DA624D7F","short_pith_number":"pith:3HYT534D","canonical_record":{"source":{"id":"1806.07808","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-06-20T15:52:43Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"e2e38cea472089207075e2192ffa4ac98ec9796c2e7665f7868e3fbf656029cb","abstract_canon_sha256":"0e5b0cc8081803e70b9f7822f45ffc85db5849ed7e0671bab3bfbdc3cdee248d"},"schema_version":"1.0"},"canonical_sha256":"d9f13eef83e3083f75259e860f6b83f9722a6d8d741cf5c6d02a1456aa1e4e06","source":{"kind":"arxiv","id":"1806.07808","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.07808","created_at":"2026-05-18T00:12:46Z"},{"alias_kind":"arxiv_version","alias_value":"1806.07808v1","created_at":"2026-05-18T00:12:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.07808","created_at":"2026-05-18T00:12:46Z"},{"alias_kind":"pith_short_12","alias_value":"3HYT534D4MED","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"3HYT534D4MED65JF","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"3HYT534D","created_at":"2026-05-18T12:32:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:3HYT534D4MED65JFT2DA624D7F","target":"record","payload":{"canonical_record":{"source":{"id":"1806.07808","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-06-20T15:52:43Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"e2e38cea472089207075e2192ffa4ac98ec9796c2e7665f7868e3fbf656029cb","abstract_canon_sha256":"0e5b0cc8081803e70b9f7822f45ffc85db5849ed7e0671bab3bfbdc3cdee248d"},"schema_version":"1.0"},"canonical_sha256":"d9f13eef83e3083f75259e860f6b83f9722a6d8d741cf5c6d02a1456aa1e4e06","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:46.572416Z","signature_b64":"oZhtUaD15X5z2s9bBkAF+T+G4eatJs0Y2sf7yEdqRb3oNnXZzszqwSDiXwwCF4L5K9Lp4/gpAeT6EBhpAGCsCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d9f13eef83e3083f75259e860f6b83f9722a6d8d741cf5c6d02a1456aa1e4e06","last_reissued_at":"2026-05-18T00:12:46.571679Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:46.571679Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.07808","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:12:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DbvttsmO5VUyeoTcVdIDq2rR1vJV74KDENjUf66kQPIdY2yMEVKPP3ixnwchtMD5YHQ+62gBSOymluTUtnwYAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T08:03:45.167583Z"},"content_sha256":"1828855d65a4073f6da96c3f9f7b868cb1e10acc7560de32b9a63c501e2341cc","schema_version":"1.0","event_id":"sha256:1828855d65a4073f6da96c3f9f7b868cb1e10acc7560de32b9a63c501e2341cc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:3HYT534D4MED65JFT2DA624D7F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Learning One-hidden-layer ReLU Networks via Gradient Descent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Lingxiao Wang, Quanquan Gu, Xiao Zhang, Yaodong Yu","submitted_at":"2018-06-20T15:52:43Z","abstract_excerpt":"We study the problem of learning one-hidden-layer neural networks with Rectified Linear Unit (ReLU) activation function, where the inputs are sampled from standard Gaussian distribution and the outputs are generated from a noisy teacher network. We analyze the performance of gradient descent for training such kind of neural networks based on empirical risk minimization, and provide algorithm-dependent guarantees. In particular, we prove that tensor initialization followed by gradient descent can converge to the ground-truth parameters at a linear rate up to some statistical error. To the best "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.07808","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T00:12:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fPT4WtudOO8s0t3vlB7FcMqLFWBkntnBTTv1HbQTScXCCXHJjREgievVrs85i1VODGbscUBZa0KMNq0zyTlnCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T08:03:45.168337Z"},"content_sha256":"52a32c011056d3ee17c23227249b5333d06286e0c5c21b490860c80d4007cbd6","schema_version":"1.0","event_id":"sha256:52a32c011056d3ee17c23227249b5333d06286e0c5c21b490860c80d4007cbd6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3HYT534D4MED65JFT2DA624D7F/bundle.json","state_url":"https://pith.science/pith/3HYT534D4MED65JFT2DA624D7F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3HYT534D4MED65JFT2DA624D7F/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":"2026-05-25T08:03:45Z","links":{"resolver":"https://pith.science/pith/3HYT534D4MED65JFT2DA624D7F","bundle":"https://pith.science/pith/3HYT534D4MED65JFT2DA624D7F/bundle.json","state":"https://pith.science/pith/3HYT534D4MED65JFT2DA624D7F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3HYT534D4MED65JFT2DA624D7F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:3HYT534D4MED65JFT2DA624D7F","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":"0e5b0cc8081803e70b9f7822f45ffc85db5849ed7e0671bab3bfbdc3cdee248d","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-06-20T15:52:43Z","title_canon_sha256":"e2e38cea472089207075e2192ffa4ac98ec9796c2e7665f7868e3fbf656029cb"},"schema_version":"1.0","source":{"id":"1806.07808","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.07808","created_at":"2026-05-18T00:12:46Z"},{"alias_kind":"arxiv_version","alias_value":"1806.07808v1","created_at":"2026-05-18T00:12:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.07808","created_at":"2026-05-18T00:12:46Z"},{"alias_kind":"pith_short_12","alias_value":"3HYT534D4MED","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"3HYT534D4MED65JF","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"3HYT534D","created_at":"2026-05-18T12:32:02Z"}],"graph_snapshots":[{"event_id":"sha256:52a32c011056d3ee17c23227249b5333d06286e0c5c21b490860c80d4007cbd6","target":"graph","created_at":"2026-05-18T00:12:46Z","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"},"paper":{"abstract_excerpt":"We study the problem of learning one-hidden-layer neural networks with Rectified Linear Unit (ReLU) activation function, where the inputs are sampled from standard Gaussian distribution and the outputs are generated from a noisy teacher network. We analyze the performance of gradient descent for training such kind of neural networks based on empirical risk minimization, and provide algorithm-dependent guarantees. In particular, we prove that tensor initialization followed by gradient descent can converge to the ground-truth parameters at a linear rate up to some statistical error. To the best ","authors_text":"Lingxiao Wang, Quanquan Gu, Xiao Zhang, Yaodong Yu","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-06-20T15:52:43Z","title":"Learning One-hidden-layer ReLU Networks via Gradient Descent"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.07808","kind":"arxiv","version":1},"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":"sha256:1828855d65a4073f6da96c3f9f7b868cb1e10acc7560de32b9a63c501e2341cc","target":"record","created_at":"2026-05-18T00:12:46Z","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":"0e5b0cc8081803e70b9f7822f45ffc85db5849ed7e0671bab3bfbdc3cdee248d","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-06-20T15:52:43Z","title_canon_sha256":"e2e38cea472089207075e2192ffa4ac98ec9796c2e7665f7868e3fbf656029cb"},"schema_version":"1.0","source":{"id":"1806.07808","kind":"arxiv","version":1}},"canonical_sha256":"d9f13eef83e3083f75259e860f6b83f9722a6d8d741cf5c6d02a1456aa1e4e06","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d9f13eef83e3083f75259e860f6b83f9722a6d8d741cf5c6d02a1456aa1e4e06","first_computed_at":"2026-05-18T00:12:46.571679Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:46.571679Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oZhtUaD15X5z2s9bBkAF+T+G4eatJs0Y2sf7yEdqRb3oNnXZzszqwSDiXwwCF4L5K9Lp4/gpAeT6EBhpAGCsCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:46.572416Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.07808","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1828855d65a4073f6da96c3f9f7b868cb1e10acc7560de32b9a63c501e2341cc","sha256:52a32c011056d3ee17c23227249b5333d06286e0c5c21b490860c80d4007cbd6"],"state_sha256":"325d8c8f2eacafabd7fdbe043607f392fb30688521e11dfb6797401156eba9a1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Vxct4oqR3sG0aukwIyTTVDP/ycQ3XCncj9J3Ak1P55Cz3x5FOWTBLSYD3WBSx578wJypNLf/WbF3MwrLK2bSCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T08:03:45.172198Z","bundle_sha256":"4052e97adf734c039149fff7c4a04e32a678d3ef2d1efce3babe62bafca411e6"}}