Generative Adversarial Networks (GANs) are commonly used for modeling complex
distributions of data. Both the generators and discriminators of GANs are often modeled by …

Threshold activation functions are highly preferable in neural networks due to their efficiency
in hardware implementations. Moreover, their mode of operation is more interpretable and …

The calculation of the direction of the Wasserstein gradient is vital for addressing problems
related to posterior sampling and scientific computing. To approximate the Wasserstein …

Training deep neural networks is a challenging non-convex optimization problem. Recent
work has proven that the strong duality holds (which means zero duality gap) for regularized …

We study non-convex subgradient flows for training two-layer ReLU neural networks from a
convex geometry and duality perspective. We characterize the implicit bias of unregularized …

We develop a decomposition method based on the augmented Lagrangian framework to
solve a broad family of semidefinite programming problems, possibly with nonlinear …

Neural networks (NNs) have been extremely successful across many tasks in machine
learning. Quantization of NN weights has become an important topic due to its impact on …

The practice of deep learning has shown that neural networks generalize remarkably well
even with an extreme number of learned parameters. This appears to contradict traditional …

Abstract Fisher's Linear Discriminant Analysis (FLDA) is a statistical analysis method that
linearly embeds data points to a lower dimensional space to maximize a discrimination …

This letter proposes convex formulations of system identification and control for nonlinear
systems using two layer quadratic neural networks. The results in this letter cast system …