Uncertainty quantification (UQ) is important for reliability assessment and enhancement of machine learning models.

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We establish Central Limit Theorems (CLT) for the derivatives of 2-layers NN models in(2) when n,p,d + in the proportional asymptotic regime(6). A weighted average of the gradients of the trained NN, up to an explicit additive correction, is proved to be asymptotically normal, where the variance of the limit can be estimatedexplicitly.

Weshowthatforpolynomial alignment, there is anover-aligned regime, in which TKRR can achieve a faster rate than what is achievable by full KRR.

It is a commonly held belief that enforcing invariance improves generalisation.

Despite being powerful and well-understood, the kernel ridge regression suffers from the costly computation when dealing with large datasets, since generally implementation of Eq. (1) requires O(n3) running time.