Single-index models are a class of functions given by an unknown univariate``link''function
applied to an unknown one-dimensional projection of the input. These models are …

We investigate the time complexity of SGD learning on fully-connected neural networks with
isotropic data. We put forward a complexity measure,{\it the leap}, which measures how …

One of the central questions in the theory of deep learning is to understand how neural
networks learn hierarchical features. The ability of deep networks to extract salient features …

We study the problem of learning hierarchical polynomials over the standard Gaussian
distribution with three-layer neural networks. We specifically consider target functions of the …

This work characterizes the effect of depth on the optimization landscape of linear
regression, showing that, despite their nonconvexity, deeper models have more desirable …

Transformers have demonstrated exceptional in-context learning capabilities, yet the
theoretical understanding of the underlying mechanisms remain limited. A recent work …

We study the size of a neural network needed to approximate the maximum function over d
inputs, in the most basic setting of approximating with respect to the L 2 norm, for continuous …

To understand the training dynamics of neural networks (NNs), prior studies have
considered the infinite-width mean-field (MF) limit of two-layer NN, establishing theoretical …

This work characterizes the effect of depth on the optimization landscape of linear
regression, showing that, despite their nonconvexity, deeper models have more desirable …

We study separations between two fundamental models (or\emph {Ans\" atze}) of
antisymmetric functions, that is, functions $ f $ of the form $ f (x_ {\sigma (1)},\ldots, x …