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 …

A common lens to theoretically study neural net architectures is to analyze the functions they
can approximate. However, the constructions from approximation theory often have …

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 …

Abstract Deep Neural Networks and Reinforcement Learning methods have empirically
shown great promise in tackling challenging combinatorial problems. In those methods a …

Universal approximation capability, also referred to as universality, is an important property
of deep neural networks, endowing them with the potency to accurately represent the …

Depth separation results propose a possible theoretical explanation for the benefits of deep
neural networks over shallower architectures, establishing that the former possess superior …

We solve an open question from Lu et al.(2017), by showing that any target network with
inputs in $\mathbb {R}^ d $ can be approximated by a width $ O (d) $ network (independent …

When studying the expressive power of neural networks, a main challenge is to understand
how the size and depth of the network affect its ability to approximate real functions …

High-dimensional depth separation results for neural networks show that certain functions
can be efficiently approximated by two-hidden-layer networks but not by one-hidden-layer …

Despite the immense success of deep learning in reinforcement learning and control, few
theoretical guarantees for neural networks exist for these problems. Deriving performance …