On the Optimizer Dependence of Neural Scaling Laws

ArXi:2605.29387v1 Announce Type: cross 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.