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核岭回归预测误差的置信上界：基于高斯重拟合AI 解读

Assessing a single model fit requires a computable upper confidence bound for the gap between the fit and the unknown truth, as mean estimates ignore realization variance. Standard cross-validation margins are bottlenecked at order $n^{-1/2}$ by noise fluctuations, even when the true error shrinks faster. While wild refitting cancels this noise level, existing Rademacher sign methods degenerate for kernel ridge regression and rely on unobservable quantities. We propose a…

带动量与非收敛自适应预条件的 SA-Adam 的 Polyak-Ruppert 中心极限定理AI 解读

Adaptive optimizers combining preconditioning, momentum, and weight decay (Adam and AdamW) are, under Polyak-Ruppert averaging, candidate engines for one-pass inference. Does the averaged iterate keep the classical Polyak-Ruppert central limit theorem (CLT), with sandwich covariance $H^{-1}SH^{-1}$ (Hessian $H$, gradient covariance $S$), under momentum and non-convergent preconditioning? The preconditioner-only analysis does not carry over: with momentum the canonical…