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We present evidence that $\\alpha$ depends systematically on the optimizer. In controlled random-feature regression experiments -- the canonical theoretical framework for neural scaling -- we measure $\\alpha$ across five optimizer variants and six spectral conditions. Preconditioned optimizers consistently yield steeper scaling (larger $\\alpha$), with the $\\alpha$-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 $\\alpha \\approx 0.31$ versus $\\alpha \\approx 0.12$ 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 sh","title":"On the Optimizer Dependence of Neural Scaling Laws","url":"https://arxiv.org/abs/2605.29387","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.29387v1 Announce Type: cross \nAbstract: The scaling exponent $\\alpha$ in neural scaling laws $L(N) \\propto N^{-\\alpha}$ is commonly treated as a fixed constant set by architecture and data. We present evidence that $\\alpha$ depends systematically on the optimizer. In controlled random-feature regression experiments -- the canonical theoretical framework for neural scaling -- we measure $\\alpha$ across five optimizer variants and six spectral conditions. Preconditioned optimizers consistently yield steeper scaling (larger $\\alpha$), with the $\\alpha$-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 $\\alpha \\approx 0.31$ versus $\\alpha \\approx 0.12$ for gradient descent -- a $2.6\\times$ larger fitted exponent that, within the random-feature model, compounds with each model-size doubling. 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