Related papers: Generative Modeling through Koopman Spectral Analy…

Diffusion models are commonly interpreted as learning the score function, i.e., the gradient of the log-density of noisy data. However, this assumption implies that the target of learning is a conservative vector field, which is not…

A new approach in stochastic optimization via the use of stochastic gradient Langevin dynamics (SGLD) algorithms, which is a variant of stochastic gradient decent (SGD) methods, allows us to efficiently approximate global minimizers of…

We study policy gradient methods for continuous-action, entropy-regularized reinforcement learning through the lens of Wasserstein geometry. Starting from a Wasserstein proximal update, we derive Wasserstein Proximal Policy Gradient (WPPG)…

Koopman operators are infinite-dimensional operators that globally linearize nonlinear dynamical systems, making their spectral information valuable for understanding dynamics. However, Koopman operators can have continuous spectra and…

Koopman operators linearize nonlinear dynamical systems, making their spectral information of crucial interest. Numerous algorithms have been developed to approximate these spectral properties, and Dynamic Mode Decomposition (DMD) stands…

We introduce a novel training principle for probabilistic models that is an alternative to maximum likelihood. The proposed Generative Stochastic Networks (GSN) framework is based on learning the transition operator of a Markov chain whose…

Conditional distribution is a fundamental quantity for describing the relationship between a response and a predictor. We propose a Wasserstein generative approach to learning a conditional distribution. The proposed approach uses a…

By building upon the recent theory that established the connection between implicit generative modeling (IGM) and optimal transport, in this study, we propose a novel parameter-free algorithm for learning the underlying distributions of…

Continuous Normalizing Flows (CNFs) enable elegant generative modeling but remain bottlenecked by slow sampling: producing a single sample requires solving a nonlinear ODE with hundreds of function evaluations. Recent approaches such as…

In this paper, we propose a quasi-periodic parallel WaveGAN (QPPWG) waveform generative model, which applies a quasi-periodic (QP) structure to a parallel WaveGAN (PWG) model using pitch-dependent dilated convolution networks (PDCNNs). PWG…

With the rapidly growing model complexity and data volume, training deep generative models (DGMs) for better performance has becoming an increasingly more important challenge. Previous research on this problem has mainly focused on…

Generative Control Policies (GCPs) show immense promise in robotic manipulation but struggle to simultaneously model stable global motions and high-frequency local corrections. While modern architectures extract multi-scale spatial…

Optimising probabilistic models is a well-studied field in statistics. However, its connection with the training of generative models remains largely under-explored. In this paper, we show that the evolution of time-varying generative…

We consider the geometric ergodicity of the Stochastic Gradient Langevin Dynamics (SGLD) algorithm under nonconvexity settings. Via the technique of reflection coupling, we prove the Wasserstein contraction of SGLD when the target…

We develop a new generalization of Koopman operator theory that incorporates the effects of inputs and control. Koopman spectral analysis is a theoretical tool for the analysis of nonlinear dynamical systems. Moreover, Koopman is intimately…

Generative Modeling via Drifting has recently achieved state-of-the-art one-step image generation through a kernel-based drift operator, yet the success is largely empirical and its theoretical foundations remain poorly understood. In this…

The study of quantum generative models is well-motivated, not only because of its importance in quantum machine learning and quantum chemistry but also because of the perspective of its implementation on near-term quantum machines. Inspired…

The analysis of parametric and non-parametric uncertainties of very large dynamical systems requires the construction of a stochastic model of said system. Linear approaches relying on random matrix theory and principal componant analysis…

Gradient Descent (GD) and its variants are the primary tool for enabling efficient training of recurrent dynamical systems such as Recurrent Neural Networks (RNNs), Neural ODEs and Gated Recurrent units (GRUs). The dynamics that are formed…

Generative Adversarial Networks (GANs) have been impactful on many problems and applications but suffer from unstable training. The Wasserstein GAN (WGAN) leverages the Wasserstein distance to avoid the caveats in the minmax two-player…