Related papers: SDE approximations of GANs training and its long-r…

Neural Stochastic Differential Equations (Neural SDEs) provide a principled framework for modeling continuous-time stochastic processes and have been widely adopted in fields ranging from physics to finance. Recent advances suggest that…

We present a theoretical analysis of the training process for a single-layer GAN fed by high-dimensional input data. The training dynamics of the proposed model at both microscopic and macroscopic scales can be exactly analyzed in the…

Generative adversarial networks (GANs) have shown promising results when applied on partial differential equations and financial time series generation. We investigate if GANs can also be used to approximate one-dimensional Ito stochastic…

Generative Adversarial Networks (GANs) are powerful generative models that achieved strong results, mainly in the image domain. However, the training of GANs is not trivial, presenting some challenges tackled by different strategies.…

Training generative adversarial networks (GANs) is known to be difficult, especially for financial time series. This paper first analyzes the well-posedness problem in GANs minimax games and the convexity issue in GANs objective functions.…

Understanding the behavior of stochastic gradient methods is a central problem in modern machine learning. Recent work has highlighted diagonal linear networks as a simplified yet expressive setting for analyzing the optimization and…

We consider the filtering and prediction problem for a diffusion process. The signal and observation are modeled by stochastic differential equations (SDEs) driven by correlated Wiener processes. In classical estimation theory,…

The Latent Stochastic Differential Equation (SDE) is a powerful tool for time series and sequence modeling. However, training Latent SDEs typically relies on adjoint sensitivity methods, which depend on simulation and backpropagation…

Generative adversarial networks, or GANs, commonly display unstable behavior during training. In this work, we develop a principled theoretical framework for understanding the stability of various types of GANs. In particular, we derive…

In this paper, we carry out numerical analysis to prove convergence of a novel sample-wise back-propagation method for training a class of stochastic neural networks (SNNs). The structure of the SNN is formulated as discretization of a…

Ever since its debut, generative adversarial networks (GANs) have attracted tremendous amount of attention. Over the past years, different variations of GANs models have been developed and tailored to different applications in practice.…

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…

Stochastic differential equations (SDEs) have been widely used to model real world random phenomena. Existing works mainly focus on the case where the time series is modeled by a single SDE, which might be restrictive for modeling time…

Generative Adversarial Networks (GANs) have become one of the dominant methods for deep generative modeling. Despite their demonstrated success on multiple vision tasks, GANs are difficult to train and much research has been dedicated…

Stochastic differential equations (SDEs) have been shown recently to characterize well the dynamics of training machine learning models with SGD. When the generalization error of the SDE approximation closely aligns with that of SGD in…

The instability of Generative Adversarial Network (GAN) training has frequently been attributed to gradient descent. Consequently, recent methods have aimed to tailor the models and training procedures to stabilise the discrete updates. In…

Continuous-time models provide important insights into the training dynamics of optimization algorithms in deep learning. In this work, we establish a non-asymptotic convergence analysis of stochastic gradient Langevin dynamics (SGLD),…

We investigate neural ordinary and stochastic differential equations (neural ODEs and SDEs) to model stochastic dynamics in fully and partially observed environments within a model-based reinforcement learning (RL) framework. Through a…

Generative adversarial networks (GANs) have been extremely effective in approximating complex distributions of high-dimensional, input data samples, and substantial progress has been made in understanding and improving GAN performance in…

Generative adversarial networks (GANs) have attracted intense interest in the field of generative models. However, few investigations focusing either on the theoretical analysis or on algorithm design for the approximation ability of the…