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Shazeer and Stern: Adafactor factored optimizer state

Contribution grade

Optimization and large-model systems · Human-designed research method or resource

Reference score125,000Provisional editorial estimate of this exact contribution; its grade is assessed separately.

What changed

Approximated matrix-valued second-moment accumulators from row and column statistics and combined update clipping, decay scheduling and relative-step scaling for low-memory adaptive optimization.

Scientific scope

Approximated matrix-valued second-moment accumulators from row and column statistics and combined update clipping, decay scheduling and relative-step scaling for low-memory adaptive optimization. The O(n+m) auxiliary-state saving refers to a matrix's factored second moment, not all training memory. Translation experiments do not guarantee Adam-equivalent behavior for arbitrary models; no dense nonconvex convergence proof is claimed.

Evidence

The linked original sources describe the stated contribution and its evidence limits. WRS has not independently rerun the experiments or certified a proof. The O(n+m) auxiliary-state saving refers to a matrix's factored second moment, not all training memory. Translation experiments do not guarantee Adam-equivalent behavior for arbitrary models; no dense nonconvex convergence proof is claimed.

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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