{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:BEYFNEPY7773RQZBXGVHCB77BU","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":"dd97312c4184078426f999f2435d225acc90144365b6bb0e62d6b8ad005c9323","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-09-29T05:16:43Z","title_canon_sha256":"acdd84abb1a6e1c7a7101f1c285c803b11f6dce0e28a87427c5687946f2acf4c"},"schema_version":"1.0","source":{"id":"1810.00150","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.00150","created_at":"2026-05-17T23:59:43Z"},{"alias_kind":"arxiv_version","alias_value":"1810.00150v2","created_at":"2026-05-17T23:59:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.00150","created_at":"2026-05-17T23:59:43Z"},{"alias_kind":"pith_short_12","alias_value":"BEYFNEPY7773","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"BEYFNEPY7773RQZB","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"BEYFNEPY","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:bf8e2a02ce1a6c932f39403fa4a7ff66296ff5c32f18b1af6b9eba59af6f6877","target":"graph","created_at":"2026-05-17T23:59:43Z","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":"Although stochastic gradient descent (SGD) is a driving force behind the recent success of deep learning, our understanding of its dynamics in a high-dimensional parameter space is limited. In recent years, some researchers have used the stochasticity of minibatch gradients, or the signal-to-noise ratio, to better characterize the learning dynamics of SGD. Inspired from these work, we here analyze SGD from a geometrical perspective by inspecting the stochasticity of the norms and directions of minibatch gradients. We propose a model of the directional concentration for minibatch gradients thro","authors_text":"Cheolhyoung Lee, Kyunghyun Cho, Wanmo Kang","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-09-29T05:16:43Z","title":"Directional Analysis of Stochastic Gradient Descent via von Mises-Fisher Distributions in Deep learning"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.00150","kind":"arxiv","version":2},"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":"sha256:36c7536fb148a3453920c15b6eaa89e7e57445678e3ee54c96762de0f68fbeb1","target":"record","created_at":"2026-05-17T23:59:43Z","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":"dd97312c4184078426f999f2435d225acc90144365b6bb0e62d6b8ad005c9323","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-09-29T05:16:43Z","title_canon_sha256":"acdd84abb1a6e1c7a7101f1c285c803b11f6dce0e28a87427c5687946f2acf4c"},"schema_version":"1.0","source":{"id":"1810.00150","kind":"arxiv","version":2}},"canonical_sha256":"09305691f8ffffb8c321b9aa7107ff0d1f7fbbab7a10c613e460d2fd7a2921e4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"09305691f8ffffb8c321b9aa7107ff0d1f7fbbab7a10c613e460d2fd7a2921e4","first_computed_at":"2026-05-17T23:59:43.351839Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:43.351839Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"h2jfTofm6hTpmyttu9pp6/FlqNXIpDFhrrddJn9W+qrTah5AOlhrFJhJIHkgrPuh5b8zWj8hAK1F/iagolceDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:43.352332Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.00150","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:36c7536fb148a3453920c15b6eaa89e7e57445678e3ee54c96762de0f68fbeb1","sha256:bf8e2a02ce1a6c932f39403fa4a7ff66296ff5c32f18b1af6b9eba59af6f6877"],"state_sha256":"cd3621066cf43407306b1503366384f06bdc1defad4117d9a73dd1e00a2f5c28"}