The population loss of trained deep neural networks often follows precise power-law scaling
relations with either the size of the training dataset or the number of parameters in the …

The practical success of overparameterized neural networks has motivated the recent
scientific study of\emph {interpolating methods}--learning methods which are able fit their …

Of theories for why large-scale machine learning models generalize despite being vastly
overparameterized, which of their assumptions are needed to capture the qualitative …

This manuscript considers the problem of learning a random Gaussian network function
using a fully connected network with frozen intermediate layers and trainable readout layer …

We consider the problem of learning a target function corresponding to a deep, extensive-
width, non-linear neural network with random Gaussian weights. We consider the asymptotic …

We investigate theoretically how the features of a two-layer neural network adapt to the
structure of the target function through a few large batch gradient descent steps, leading to …

The widely observed'benign overfitting phenomenon'in the neural network literature raises
the challenge to thebias-variance trade-off'doctrine in the statistical learning theory. Since …

In this manuscript we consider the problem of generalized linear estimation on Gaussian
mixture data with labels given by a single-index model. Our first result is a sharp asymptotic …

In the misspecified kernel ridge regression problem, researchers usually assume the
underground true function $ f_ {\rho}^{\star}\in [\mathcal {H}]^{s} $, a less-smooth …

We study the spectrum of inner-product kernel matrices, ie, $ n\times n $ matrices with
entries $ h (\langle\textbf {x} _i,\textbf {x} _j\rangle/d) $ where the $(\textbf {x} _i) _ {i\leq n} …