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 …

A recent line of work in high-dimensional statistics working under the Gaussian mixture
hypothesis has led to a number of results in the context of empirical risk minimization …

We investigate the spectral properties of linear-width feed-forward neural networks, where
the sample size is asymptotically proportional to network width. Empirically, we show that the …

Uncertainty quantification is a central challenge in reliable and trustworthy machine
learning. Naive measures such as last-layer scores are well-known to yield overconfident …

In this manuscript we investigate the problem of how two-layer neural networks learn
features from data, and improve over the kernel regime, after being trained with a single …

Many recent works have studied the eigenvalue spectrum of the Conjugate Kernel (CK)
defined by the nonlinear feature map of a feedforward neural network. However, existing …

Feature learning, or the ability of deep neural networks to automatically learn relevant
features from raw data, underlies their exceptional capability to solve complex tasks …

In recent years, significant attention in deep learning theory has been devoted to analyzing
when models that interpolate their training data can still generalize well to unseen …

Maximum margin binary classification is one of the most fundamental algorithms in machine
learning, yet the role of featurization maps and the high-dimensional asymptotics of the …

For a large class of feature maps we provide a tight asymptotic characterisation of the test
error associated with learning the readout layer, in the high-dimensional limit where the …