{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:3HZU3V2VFWVOITVNJD6SHGTFC2","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":"7f24f7816db0f5319d38d3b65abbcfc8576b063d39c94585d892fca29fb11864","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-05-23T15:13:56Z","title_canon_sha256":"dda1d75b21b839e8f362bfd36d591292aae73ef4266047d1d1e8958e4f0655b6"},"schema_version":"1.0","source":{"id":"1805.09214","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.09214","created_at":"2026-05-18T00:15:08Z"},{"alias_kind":"arxiv_version","alias_value":"1805.09214v1","created_at":"2026-05-18T00:15:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.09214","created_at":"2026-05-18T00:15:08Z"},{"alias_kind":"pith_short_12","alias_value":"3HZU3V2VFWVO","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"3HZU3V2VFWVOITVN","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"3HZU3V2V","created_at":"2026-05-18T12:32:02Z"}],"graph_snapshots":[{"event_id":"sha256:5fc0ab0a20f00ba05e18ef860794432a61f1a3281464cb3d9802e2f412bb568d","target":"graph","created_at":"2026-05-18T00:15:08Z","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":"The lack of mathematical tractability of Deep Neural Networks (DNNs) has hindered progress towards having a unified convergence analysis of training algorithms, in the general setting. We propose a unified optimization framework for training different types of DNNs, and establish its convergence for arbitrary loss, activation, and regularization functions, assumed to be smooth. We show that framework generalizes well-known first- and second-order training methods, and thus allows us to show the convergence of these methods for various DNN architectures and learning tasks, as a special case of ","authors_text":"Carlo Fischione, Hadi Ghauch, Hossein Shokri-Ghadikolaei, Mikael Skoglund","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-05-23T15:13:56Z","title":"A Unified Framework for Training Neural Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.09214","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:b4b624ad385f2ab3d258259f058ad661e09b62829158e351617c1e5f868cb9b4","target":"record","created_at":"2026-05-18T00:15:08Z","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":"7f24f7816db0f5319d38d3b65abbcfc8576b063d39c94585d892fca29fb11864","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-05-23T15:13:56Z","title_canon_sha256":"dda1d75b21b839e8f362bfd36d591292aae73ef4266047d1d1e8958e4f0655b6"},"schema_version":"1.0","source":{"id":"1805.09214","kind":"arxiv","version":1}},"canonical_sha256":"d9f34dd7552daae44ead48fd239a65168348a8c23557d9ded999bf087eafee4b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d9f34dd7552daae44ead48fd239a65168348a8c23557d9ded999bf087eafee4b","first_computed_at":"2026-05-18T00:15:08.220699Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:08.220699Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7ODKo0JBvL+GZKXofX4vvu/ApeSilBlUYEuMh5U+HDk5BBZpqbjX9udGxhjTFqUsbqvl8eE0eiwDT36RbqqXAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:08.221248Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.09214","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b4b624ad385f2ab3d258259f058ad661e09b62829158e351617c1e5f868cb9b4","sha256:5fc0ab0a20f00ba05e18ef860794432a61f1a3281464cb3d9802e2f412bb568d"],"state_sha256":"fa2f0362def5ef9183a68bf8da2437423507db69f1ff8c60717703c14d1ac2c5"}