{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:WVTPM2BAJ72ZBC657WU3WO7GI7","short_pith_number":"pith:WVTPM2BA","schema_version":"1.0","canonical_sha256":"b566f668204ff5908bddfda9bb3be647d59cc9e889fe7f5d2a41f51f8b481103","source":{"kind":"arxiv","id":"1803.05999","version":2},"attestation_state":"computed","paper":{"title":"Escaping Saddles with Stochastic Gradients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC","stat.ML"],"primary_cat":"cs.LG","authors_text":"Aurelien Lucchi, Hadi Daneshmand, Jonas Kohler, Thomas Hofmann","submitted_at":"2018-03-15T20:48:06Z","abstract_excerpt":"We analyze the variance of stochastic gradients along negative curvature directions in certain non-convex machine learning models and show that stochastic gradients exhibit a strong component along these directions. Furthermore, we show that - contrary to the case of isotropic noise - this variance is proportional to the magnitude of the corresponding eigenvalues and not decreasing in the dimensionality. Based upon this observation we propose a new assumption under which we show that the injection of explicit, isotropic noise usually applied to make gradient descent escape saddle points can su"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1803.05999","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-03-15T20:48:06Z","cross_cats_sorted":["math.OC","stat.ML"],"title_canon_sha256":"6cac2cfacc4aad2e5deeea9797089044f9b2ad1d23121541cc7174493c14936f","abstract_canon_sha256":"e231826950576d89104fadff68a784526225644a112567eb360139ff6dfcebf1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:39.306954Z","signature_b64":"n3HO+TSwmoCwAidPDil/ZASMnU17M05o32yeR/EpLE36daWrI/eRim06GYzMx5MDSJYmGagOTvIm3ZyNzT6UDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b566f668204ff5908bddfda9bb3be647d59cc9e889fe7f5d2a41f51f8b481103","last_reissued_at":"2026-05-18T00:05:39.306502Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:39.306502Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Escaping Saddles with Stochastic Gradients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC","stat.ML"],"primary_cat":"cs.LG","authors_text":"Aurelien Lucchi, Hadi Daneshmand, Jonas Kohler, Thomas Hofmann","submitted_at":"2018-03-15T20:48:06Z","abstract_excerpt":"We analyze the variance of stochastic gradients along negative curvature directions in certain non-convex machine learning models and show that stochastic gradients exhibit a strong component along these directions. Furthermore, we show that - contrary to the case of isotropic noise - this variance is proportional to the magnitude of the corresponding eigenvalues and not decreasing in the dimensionality. Based upon this observation we propose a new assumption under which we show that the injection of explicit, isotropic noise usually applied to make gradient descent escape saddle points can su"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.05999","kind":"arxiv","version":2},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1803.05999","created_at":"2026-05-18T00:05:39.306568+00:00"},{"alias_kind":"arxiv_version","alias_value":"1803.05999v2","created_at":"2026-05-18T00:05:39.306568+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.05999","created_at":"2026-05-18T00:05:39.306568+00:00"},{"alias_kind":"pith_short_12","alias_value":"WVTPM2BAJ72Z","created_at":"2026-05-18T12:33:01.666342+00:00"},{"alias_kind":"pith_short_16","alias_value":"WVTPM2BAJ72ZBC65","created_at":"2026-05-18T12:33:01.666342+00:00"},{"alias_kind":"pith_short_8","alias_value":"WVTPM2BA","created_at":"2026-05-18T12:33:01.666342+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":3,"internal_anchor_count":2,"sample":[{"citing_arxiv_id":"1907.01848","citing_title":"Distributed Learning in Non-Convex Environments -- Part I: Agreement at a Linear Rate","ref_index":24,"is_internal_anchor":true},{"citing_arxiv_id":"1907.01849","citing_title":"Distributed Learning in Non-Convex Environments -- Part II: Polynomial Escape from Saddle-Points","ref_index":27,"is_internal_anchor":true},{"citing_arxiv_id":"2605.09331","citing_title":"Dimension-Free Saddle-Point Escape in Muon","ref_index":5,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WVTPM2BAJ72ZBC657WU3WO7GI7","json":"https://pith.science/pith/WVTPM2BAJ72ZBC657WU3WO7GI7.json","graph_json":"https://pith.science/api/pith-number/WVTPM2BAJ72ZBC657WU3WO7GI7/graph.json","events_json":"https://pith.science/api/pith-number/WVTPM2BAJ72ZBC657WU3WO7GI7/events.json","paper":"https://pith.science/paper/WVTPM2BA"},"agent_actions":{"view_html":"https://pith.science/pith/WVTPM2BAJ72ZBC657WU3WO7GI7","download_json":"https://pith.science/pith/WVTPM2BAJ72ZBC657WU3WO7GI7.json","view_paper":"https://pith.science/paper/WVTPM2BA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1803.05999&json=true","fetch_graph":"https://pith.science/api/pith-number/WVTPM2BAJ72ZBC657WU3WO7GI7/graph.json","fetch_events":"https://pith.science/api/pith-number/WVTPM2BAJ72ZBC657WU3WO7GI7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WVTPM2BAJ72ZBC657WU3WO7GI7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WVTPM2BAJ72ZBC657WU3WO7GI7/action/storage_attestation","attest_author":"https://pith.science/pith/WVTPM2BAJ72ZBC657WU3WO7GI7/action/author_attestation","sign_citation":"https://pith.science/pith/WVTPM2BAJ72ZBC657WU3WO7GI7/action/citation_signature","submit_replication":"https://pith.science/pith/WVTPM2BAJ72ZBC657WU3WO7GI7/action/replication_record"}},"created_at":"2026-05-18T00:05:39.306568+00:00","updated_at":"2026-05-18T00:05:39.306568+00:00"}