On the Optimizer Dependence of Neural Scaling Laws

• URL: http://arxiv.org/abs/2605.29387v1
• Date: Thu, 28 May 2026 05:41:36 GMT
• Title: On the Optimizer Dependence of Neural Scaling Laws
• Abstract summary: scaling exponent $$ in neural scaling laws $L(N) propto N-$ is commonly treated as a fixed constant set by architecture and data.<n>We present evidence that $$ depends systematically on the scale.
• Score: 0.8594140167290097
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The scaling exponent $α$ in neural scaling laws $L(N) \propto N^{-α}$ is commonly treated as a fixed constant set by architecture and data. We present evidence that $α$ depends systematically on the optimizer. In controlled random-feature regression experiments -- the canonical theoretical framework for neural scaling -- we measure $α$ across five optimizer variants and six spectral conditions. Preconditioned optimizers consistently yield steeper scaling (larger $α$), with the $α$-shift increasing across most of the tested spectral range, peaking near $s = 1.5$, and remaining large at $s = 2.0$. At $s \approx 1.0$ (characteristic of natural language), the full natural gradient achieves $α\approx 0.31$ versus $α\approx 0.12$ for gradient descent -- a $2.6\times$ larger fitted exponent that, within the random-feature model, compounds with each model-size doubling. Whether and how this exponent shift transfers to large-scale LLM training -- where recent evidence suggests the advantage may attenuate with scale -- remains an important open question. Our results imply that scaling-law forecasts should account for optimizer choice, and we provide a spectral diagnostic predicting when advanced optimizers will pay off.

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