{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:YXGOBFKD6XIXDAESBSP62F5KVM","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":"a21f18a51ef17265ef565484c64f11acd80dc39931629468058663536f3cf342","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-04-15T11:02:22Z","title_canon_sha256":"dd56ea39b06e0f2f5b03ccde57301a88e61f77a680a25b49c4654a62f1247e53"},"schema_version":"1.0","source":{"id":"1904.06963","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.06963","created_at":"2026-07-05T01:16:38Z"},{"alias_kind":"arxiv_version","alias_value":"1904.06963v5","created_at":"2026-07-05T01:16:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.06963","created_at":"2026-07-05T01:16:38Z"},{"alias_kind":"pith_short_12","alias_value":"YXGOBFKD6XIX","created_at":"2026-07-05T01:16:38Z"},{"alias_kind":"pith_short_16","alias_value":"YXGOBFKD6XIXDAES","created_at":"2026-07-05T01:16:38Z"},{"alias_kind":"pith_short_8","alias_value":"YXGOBFKD","created_at":"2026-07-05T01:16:38Z"}],"graph_snapshots":[{"event_id":"sha256:2820156924d18c03251ba8fb698646b49d624403aaea1263f14172b5cd7c95fb","target":"graph","created_at":"2026-07-05T01:16:38Z","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/1904.06963/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper studies how neural network architecture affects the speed of training. We introduce a simple concept called gradient confusion to help formally analyze this. When gradient confusion is high, stochastic gradients produced by different data samples may be negatively correlated, slowing down convergence. But when gradient confusion is low, data samples interact harmoniously, and training proceeds quickly. Through theoretical and experimental results, we demonstrate how the neural network architecture affects gradient confusion, and thus the efficiency of training. Our results show that","authors_text":"Karthik A. Sankararaman, Soham De, Tom Goldstein, W. Ronny Huang, Zheng Xu","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-04-15T11:02:22Z","title":"The Impact of Neural Network Overparameterization on Gradient Confusion and Stochastic Gradient Descent"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.06963","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":"sha256:031be66e6ac88f6ef8595d28992a84b91af156c4da7a7e0359dfec7075a385d8","target":"record","created_at":"2026-07-05T01:16:38Z","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":"a21f18a51ef17265ef565484c64f11acd80dc39931629468058663536f3cf342","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-04-15T11:02:22Z","title_canon_sha256":"dd56ea39b06e0f2f5b03ccde57301a88e61f77a680a25b49c4654a62f1247e53"},"schema_version":"1.0","source":{"id":"1904.06963","kind":"arxiv","version":5}},"canonical_sha256":"c5cce09543f5d17180920c9fed17aaab22621bae61e972370ad7de5b9ac0d2a8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c5cce09543f5d17180920c9fed17aaab22621bae61e972370ad7de5b9ac0d2a8","first_computed_at":"2026-07-05T01:16:38.677695Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:16:38.677695Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VR6LMXrRshO0TlA94oisMaw9ZDYuWbGWuu1ZxVrLi+jt1wxTAPAxrENylqDeIns3zp5VpaUcIL/VmolyKMnTBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T01:16:38.678100Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.06963","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:031be66e6ac88f6ef8595d28992a84b91af156c4da7a7e0359dfec7075a385d8","sha256:2820156924d18c03251ba8fb698646b49d624403aaea1263f14172b5cd7c95fb"],"state_sha256":"56ddac10f8edca38db30fb3bc3d6faa85a3a0011d2c893de3052f02f4a96ac33"}