{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:7ENGHTO462KM5HICIS45ZQ6LWY","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":"39f5f9bb9083604a90d4ad13688484a2bfad73fb08191515fe675e22484ade90","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2019-05-17T15:24:33Z","title_canon_sha256":"f3e3330b1d5a95afbf3705aac4a748d7bf9bbde01d69040f2bc973c59101e5ad"},"schema_version":"1.0","source":{"id":"1905.07325","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.07325","created_at":"2026-05-17T23:45:55Z"},{"alias_kind":"arxiv_version","alias_value":"1905.07325v1","created_at":"2026-05-17T23:45:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.07325","created_at":"2026-05-17T23:45:55Z"},{"alias_kind":"pith_short_12","alias_value":"7ENGHTO462KM","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"7ENGHTO462KM5HIC","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"7ENGHTO4","created_at":"2026-05-18T12:33:12Z"}],"graph_snapshots":[{"event_id":"sha256:a04c132bb7b2bcf58c61d6e546db066d00f326f2020d2584e250761200c02933","target":"graph","created_at":"2026-05-17T23:45:55Z","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":"With an eye toward understanding complexity control in deep learning, we study how infinitesimal regularization or gradient descent optimization lead to margin maximizing solutions in both homogeneous and non-homogeneous models, extending previous work that focused on infinitesimal regularization only in homogeneous models. To this end we study the limit of loss minimization with a diverging norm constraint (the \"constrained path\"), relate it to the limit of a \"margin path\" and characterize the resulting solution. For non-homogeneous ensemble models, which output is a sum of homogeneous sub-mo","authors_text":"Daniel Soudry, Jason D. Lee, Mor Shpigel Nacson, Nathan Srebro, Suriya Gunasekar","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2019-05-17T15:24:33Z","title":"Lexicographic and Depth-Sensitive Margins in Homogeneous and Non-Homogeneous Deep Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.07325","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":"sha256:8694d83bcb6bd13b7dd4346822cc7bce0996a2c7a016355b1474e1e7bc25b7d0","target":"record","created_at":"2026-05-17T23:45:55Z","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":"39f5f9bb9083604a90d4ad13688484a2bfad73fb08191515fe675e22484ade90","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2019-05-17T15:24:33Z","title_canon_sha256":"f3e3330b1d5a95afbf3705aac4a748d7bf9bbde01d69040f2bc973c59101e5ad"},"schema_version":"1.0","source":{"id":"1905.07325","kind":"arxiv","version":1}},"canonical_sha256":"f91a63cddcf694ce9d0244b9dcc3cbb60977231e32c33045b2307bd82fffdd4d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f91a63cddcf694ce9d0244b9dcc3cbb60977231e32c33045b2307bd82fffdd4d","first_computed_at":"2026-05-17T23:45:55.880595Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:55.880595Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZBaNRNw5jw/B884s/FIc5d6BAKZ83ogvolp5WCY6LU7ETDaH4Fs45KhzAXqAT2+SQcuTqJWr05iK+mWNeMYECg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:55.881212Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.07325","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8694d83bcb6bd13b7dd4346822cc7bce0996a2c7a016355b1474e1e7bc25b7d0","sha256:a04c132bb7b2bcf58c61d6e546db066d00f326f2020d2584e250761200c02933"],"state_sha256":"169834881e02f53cd0a28fd611ac060f4ba010b666ebf4a7777a081cf75ebf91"}