{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:FHXPVUW7Y4LYFIU2FJTUATXQTR","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":"c0488ad553ac2023956c7c4a020d79eff86c503e35ba88d54bb5164e8c731c0d","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2021-06-30T09:34:05Z","title_canon_sha256":"38930fbf67221358248ad7c6b9badbf4834e81303a1b9d11b63996c210cb83cf"},"schema_version":"1.0","source":{"id":"2106.15933","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2106.15933","created_at":"2026-07-05T03:52:29Z"},{"alias_kind":"arxiv_version","alias_value":"2106.15933v2","created_at":"2026-07-05T03:52:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.15933","created_at":"2026-07-05T03:52:29Z"},{"alias_kind":"pith_short_12","alias_value":"FHXPVUW7Y4LY","created_at":"2026-07-05T03:52:29Z"},{"alias_kind":"pith_short_16","alias_value":"FHXPVUW7Y4LYFIU2","created_at":"2026-07-05T03:52:29Z"},{"alias_kind":"pith_short_8","alias_value":"FHXPVUW7","created_at":"2026-07-05T03:52:29Z"}],"graph_snapshots":[{"event_id":"sha256:6fd0154e980ca80db06b03e59652631d14e491e3f6e5fea624b51c02890b2537","target":"graph","created_at":"2026-07-05T03:52:29Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2106.15933/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The dynamics of Deep Linear Networks (DLNs) is dramatically affected by the variance $\\sigma^2$ of the parameters at initialization $\\theta_0$. For DLNs of width $w$, we show a phase transition w.r.t. the scaling $\\gamma$ of the variance $\\sigma^2=w^{-\\gamma}$ as $w\\to\\infty$: for large variance ($\\gamma<1$), $\\theta_0$ is very close to a global minimum but far from any saddle point, and for small variance ($\\gamma>1$), $\\theta_0$ is close to a saddle point and far from any global minimum. While the first case corresponds to the well-studied NTK regime, the second case is less understood. This","authors_text":"Arthur Jacot, Berfin \\c{S}im\\c{s}ek, Cl\\'ement Hongler, Fran\\c{c}ois Ged, Franck Gabriel","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2021-06-30T09:34:05Z","title":"Saddle-to-Saddle Dynamics in Deep Linear Networks: Small Initialization Training, Symmetry, and Sparsity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.15933","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:ad1c562d017743d4092d6b69de03e16386b61a13249246685867c02b93863afe","target":"record","created_at":"2026-07-05T03:52:29Z","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":"c0488ad553ac2023956c7c4a020d79eff86c503e35ba88d54bb5164e8c731c0d","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2021-06-30T09:34:05Z","title_canon_sha256":"38930fbf67221358248ad7c6b9badbf4834e81303a1b9d11b63996c210cb83cf"},"schema_version":"1.0","source":{"id":"2106.15933","kind":"arxiv","version":2}},"canonical_sha256":"29eefad2dfc71782a29a2a67404ef09c75040e6c8ac595c3ccf586268298c658","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"29eefad2dfc71782a29a2a67404ef09c75040e6c8ac595c3ccf586268298c658","first_computed_at":"2026-07-05T03:52:29.620354Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:52:29.620354Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rCUXbvAI/khEzZXZRudu/5aX1htJKjPkOQN2ncvurVt3ySIQOgQt9YkwN+Sxjf2OKx+vKe+dQBM0jjX94i6uDA==","signature_status":"signed_v1","signed_at":"2026-07-05T03:52:29.620818Z","signed_message":"canonical_sha256_bytes"},"source_id":"2106.15933","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ad1c562d017743d4092d6b69de03e16386b61a13249246685867c02b93863afe","sha256:6fd0154e980ca80db06b03e59652631d14e491e3f6e5fea624b51c02890b2537"],"state_sha256":"7b00534277f0c93ddefcd1f3431c2ac0f9b9d86b273e60414cbea647660fbbf9"}