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      "statement": "# Sophia: clipped diagonal-curvature stochastic optimization\n\nPreconditioned momentum gradients with moving averages of infrequently estimated Hessian diagonals and clipped coordinate updates, comparing two inexpensive curvature estimators.\n\n## Scientific scope\n\nSecond-order estimates and clipping have additional costs; reported twofold gains concern125M–770M GPT2/OpenWebText settings. Source theoretical results have assumptions not certified here and do not establish global convergence or universal condition-number independence.\n\n## Reading status\n\nThis is a source-linked WRS catalogue note. A full explanatory guide and independent scientific reconstruction have not been completed for this entry. Read the identified original work for its complete narrative and arguments.\n\n## People and systems\n\nHong Liu; Zhiyuan Li; David Hall; Percy Liang; Tengyu Ma\n\nSource-listed authors or explicitly credited technical contributors for the cited versions. Family entries retain source-specific attribution; a combined list is not one original-paper byline or equal individual work. Names alone do not establish resolved identities.\n\n\n\n## Original sources\n\n- [Sophia: A Scalable Stochastic Second-order Optimizer for Language Model Pre-training](https://arxiv.org/abs/2305.14342v1)\n",
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