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Despite the large success of deep neural networks (DNN) in recent years, most neural networks still lack mathematical guarantees in terms of stability. For instance, DNNs are vulnerable to small or even imperceptible input perturbations, so…

The generalized Gauss-Newton (GGN) optimization method incorporates curvature estimates into its solution steps, and provides a good approximation to the Newton method for large-scale optimization problems. GGN has been found particularly…

We consider hierarchical variational inequality problems, or more generally, variational inequalities defined over the set of zeros of a monotone operator. This framework includes convex optimization over equilibrium constraints and…

Both generative adversarial networks (GAN) in unsupervised learning and actor-critic methods in reinforcement learning (RL) have gained a reputation for being difficult to optimize. Practitioners in both fields have amassed a large number…

Generative Adversarial Networks (GANs) learn an implicit generative model from data samples through a two-player game. In this paper, we study the existence of Nash equilibrium of the game which is consistent as the number of data samples…

Existing models for unsupervised image translation with Generative Adversarial Networks (GANs) can learn the mapping from the source domain to the target domain using a cycle-consistency loss. However, these methods always adopt a symmetric…

The successful training of deep neural networks requires addressing challenges such as overfitting, numerical instabilities leading to divergence, and increasing variance in the residual stream. A common solution is to apply regularization…

Generative Adversarial Networks (GANs) enjoy great success at image generation, but have proven difficult to train in the domain of natural language. Challenges with gradient estimation, optimization instability, and mode collapse have lead…

We study sequential decision-making when the agent's internal model class is misspecified. Within the infinite-horizon Berk-Nash framework, stable behavior arises as a fixed point: the agent acts optimally relative to a subjective model,…

Generative adversarial networks have been very successful in generative modeling, however they remain relatively challenging to train compared to standard deep neural networks. In this paper, we propose new visualization techniques for the…

Generative adversarial network (GAN) has gotten wide re-search interest in the field of deep learning. Variations of GAN have achieved competitive results on specific tasks. However, the stability of training and diversity of generated…

We tackle the problem of building adaptive estimation procedures for ill-posed inverse problems. For general regularization methods depending on tuning parameters, we construct a penalized method that selects the optimal smoothing sequence…

The training of Generative Adversarial Networks is a difficult task mainly due to the nature of the networks. One such issue is when the generator and discriminator start oscillating, rather than converging to a fixed point. Another case…

Classical model-based imaging methods for ultrasound elasticity inverse problem require prior constraints about the underlying elasticity patterns, while finding the appropriate hand-crafted prior for each tissue type is a challenge. In…

In this paper, we develop a novel regularization method for deep neural networks by penalizing the trace of Hessian. This regularizer is motivated by a recent guarantee bound of the generalization error. We explain its benefits in finding…

Although the \emph{residual method}, or \emph{constrained regularization}, is frequently used in applications, a detailed study of its properties is still missing. This sharply contrasts the progress of the theory of Tikhonov…

We consider the problem of computing an equilibrium in a class of \textit{nonlinear generalized Nash equilibrium problems (NGNEPs)} in which the strategy sets for each player are defined by equality and inequality constraints that may…

Generative Adversarial Networks (GANs) have shown immense potential in fields such as text and image generation. Only very recently attempts to exploit GANs to statistical-mechanics models have been reported. Here we quantitatively test…

The paper presents a fully explicit algorithm for monotone variational inequalities. The method uses variable stepsizes that are computed using two previous iterates as an approximation of the local Lipschitz constant without running a…

Generative adversarial networks (GANs) were initially proposed to generate images by learning from a large number of samples. Recently, GANs have been used to emulate complex physical systems such as turbulent flows. However, a critical…