Let Ω=[0, 1] d be the unit cube in ℝ d. We study the problem of how efficiently, in terms of the
number of parameters, deep neural networks with the ReLU activation function can …

Abstract We present Polarity Sampling, a theoretically justified plug-and-play method for
controlling the generation quality and diversity of any pre-trained deep generative network …

For second-order general nonlinear systems with uncertainties, a control scheme combining
fractional-order fast terminal sliding mode control (FOFTSMC) and self-organizing emotional …

In industrial applications where computational resources are finite and data noises are
prevalent, the representation power of deep neural networks (DNNs) is crucial. Traditional …

We analyze the structure of a one-dimensional deep ReLU neural network (ReLU DNN) in
comparison to the model of continuous piecewise linear (CPL) spline functions with arbitrary …

We develop new theoretical results on matrix perturbation to shed light on the impact of
architecture on the performance of a deep network. In particular, we explain analytically …

Wasserstein generative adversarial networks are minimax optimal distribution estimators
Page 1 The Annals of Statistics 2024, Vol. 52, No. 5, 2167–2193 https://doi.org/10.1214/24-AOS2430 …

We consider neural network approximation spaces that classify functions according to the
rate at which they can be approximated (with error measured in L p) by ReLU neural …

We develop Scalable Latent Exploration Score (ScaLES) to mitigate over-exploration in
Latent Space Optimization (LSO), a popular method for solving black-box discrete …

Let $\Omega=[0, 1]^ d $ be the unit cube in $\mathbb {R}^ d $. We study the problem of how
efficiently, in terms of the number of parameters, deep neural networks with the ReLU …