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Sophia: clipped diagonal-curvature stochastic optimization

Contribution grade

Language-model training optimization · Human-designed research method or resource

Reference score105,000Provisional editorial estimate of this exact contribution; its grade is assessed separately.

What changed

Preconditioned momentum gradients with moving averages of infrequently estimated Hessian diagonals and clipped coordinate updates, comparing two inexpensive curvature estimators.

Scientific scope

Preconditioned momentum gradients with moving averages of infrequently estimated Hessian diagonals and clipped coordinate updates, comparing two inexpensive curvature estimators. Second-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.

Evidence

The linked original sources describe the stated contribution and its evidence limits. WRS has not independently rerun the experiments or certified a proof. Second-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.

Contributors

Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.

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