Related papers: Generative Modeling through Koopman Spectral Analy…
Generating realistic graph-structured data is challenging due to discrete structures, variable sizes, and class-specific connectivity patterns that resist conventional generative modelling. While recent graph generation methods employ…
Generative Adversarial Networks (GANs) have been successful in producing outstanding results in areas as diverse as image, video, and text generation. Building on these successes, a large number of empirical studies have validated the…
Koopman operator recently gained increasing attention in the control systems community for its abilities to bridge linear and nonlinear systems. Data driven Koopman operator approximations have established themselves as key enablers for…
Stream stochastic gradient descent (SGD) is a simple and efficient method for solving online optimization problems in operations research (OR), where data is generated by parameter-dependent Markov chains. Unlike traditional approaches…
Gaussian process (GP) regression is a popular surrogate modeling tool for computer simulations in engineering and scientific domains. However, it often struggles with high computational costs and low prediction accuracy when the simulation…
Latent-variable energy-based models (LVEBMs) assign a single normalized energy to joint pairs of observed data and latent variables, offering expressive generative modeling while capturing hidden structure. We recast maximum-likelihood…
We consider the minimization of a function defined on a Riemannian manifold $\mathcal{M}$ accessible only through unbiased estimates of its gradients. We develop a geometric framework to transform a sequence of slowly converging iterates…
Stochastic weather generators (SWGs) are digital twins of complex weather processes and widely used in agriculture and urban design. Due to improved measuring instruments, an accurate SWG for high-frequency precipitation is now possible.…
Particle-based deep generative models, such as gradient flows and score-based diffusion models, have recently gained traction thanks to their striking performance. Their principle of displacing particle distributions using differential…
Stochastic gradient descent (SGD) is widely used in deep learning due to its computational efficiency, but a complete understanding of why SGD performs so well remains a major challenge. It has been observed empirically that most…
We propose a novel distributed inference algorithm for continuous graphical models, by extending Stein variational gradient descent (SVGD) to leverage the Markov dependency structure of the distribution of interest. Our approach combines…
In deep learning, stochastic gradient descent (SGD) and its momentum-based variants are widely used for optimization. However, the internal dynamics of these methods remain underexplored. In this paper, we analyze gradient behavior through…
We propose kernel-gradient drifting, a one-step generative modeling framework that replaces the fixed Euclidean displacement direction in drifting models with directions induced by the kernel itself. Standard drifting is attractive because…
This paper explores the problem of generative modeling, aiming to simulate diverse examples from an unknown distribution based on observed examples. While recent studies have focused on quantifying the statistical precision of popular…
Kolmogorov--Arnold Networks (KANs), a recently proposed neural network architecture, have gained significant attention in the deep learning community, due to their potential as a viable alternative to multi-layer perceptrons (MLPs) and…
Solving inverse problems without the use of derivatives or adjoints of the forward model is highly desirable in many applications arising in science and engineering. In this paper, we propose a new version of such a methodology, a framework…
Generative models based on latent variables, such as generative adversarial networks (GANs) and variational auto-encoders (VAEs), have gained lots of interests due to their impressive performance in many fields. However, many data such as…
The projected gradient descent (PGD) method has shown to be effective in recovering compressed signals described in a data-driven way by a generative model, i.e., a generator which has learned the data distribution. Further reconstruction…
The shape of an object is an important characteristic for many vision problems such as segmentation, detection and tracking. Being independent of appearance, it is possible to generalize to a large range of objects from only small amounts…
In this paper, we propose projected gradient descent (PGD) algorithms for signal estimation from noisy nonlinear measurements. We assume that the unknown $p$-dimensional signal lies near the range of an $L$-Lipschitz continuous generative…