{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:I7RESVSR76WKF3PT2TBV7NXYMK","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":"04833327b518ecb8a6c6e22b2a5cb0e293e21008e7f82f7fcf0930a4039e0000","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-12-13T13:35:27Z","title_canon_sha256":"6839721524047ece06fd3412e70a452882101ab85a6416d8258d205fbe7e91d1"},"schema_version":"1.0","source":{"id":"1712.04755","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.04755","created_at":"2026-05-18T00:00:22Z"},{"alias_kind":"arxiv_version","alias_value":"1712.04755v4","created_at":"2026-05-18T00:00:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.04755","created_at":"2026-05-18T00:00:22Z"},{"alias_kind":"pith_short_12","alias_value":"I7RESVSR76WK","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"I7RESVSR76WKF3PT","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"I7RESVSR","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:31578a6493336fa56f887266a3e7495c6a9aeab6f982e24ef673672635bdbb51","target":"graph","created_at":"2026-05-18T00:00:22Z","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 consider binary classification problems with positive definite kernels and square loss, and study the convergence rates of stochastic gradient methods. We show that while the excess testing loss (squared loss) converges slowly to zero as the number of observations (and thus iterations) goes to infinity, the testing error (classification error) converges exponentially fast if low-noise conditions are assumed.","authors_text":"Alessandro Rudi (SIERRA), Francis Bach (SIERRA), Loucas Pillaud-Vivien (SIERRA)","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-12-13T13:35:27Z","title":"Exponential convergence of testing error for stochastic gradient methods"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.04755","kind":"arxiv","version":4},"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":"sha256:4377c6e2dff3bb8893cfeb9b85dc45c24c56fdbc10a5a944b54072e88c9804f9","target":"record","created_at":"2026-05-18T00:00:22Z","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":"04833327b518ecb8a6c6e22b2a5cb0e293e21008e7f82f7fcf0930a4039e0000","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-12-13T13:35:27Z","title_canon_sha256":"6839721524047ece06fd3412e70a452882101ab85a6416d8258d205fbe7e91d1"},"schema_version":"1.0","source":{"id":"1712.04755","kind":"arxiv","version":4}},"canonical_sha256":"47e2495651ffaca2edf3d4c35fb6f86290316922c24072c7f2251413f58ec751","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"47e2495651ffaca2edf3d4c35fb6f86290316922c24072c7f2251413f58ec751","first_computed_at":"2026-05-18T00:00:22.213254Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:22.213254Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oq4sXK0QeMZGazSVFQH77eTHu9SrdOFLL8jaWGNIAZKNL/J2vW2/DjRWFNgTVDLy/e6Ery1APcwTteCUWElZCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:22.213867Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.04755","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4377c6e2dff3bb8893cfeb9b85dc45c24c56fdbc10a5a944b54072e88c9804f9","sha256:31578a6493336fa56f887266a3e7495c6a9aeab6f982e24ef673672635bdbb51"],"state_sha256":"7affe9b178db887a621809255f56c915b3041ef2bc6544cd365f54e5308f9a87"}