Related papers: Infinite dimensional generative sensing

Generative models, such as GANs, learn an explicit low-dimensional representation of a particular class of images, and so they may be used as natural image priors for solving inverse problems such as image restoration and compressive…

Modern datasets across many disciplines increasingly consist of time-evolving, potentially infinite-dimensional random objects, such as dynamic functional data, which are naturally modeled in Hilbert spaces. In these settings,…

Compressed sensing deals with the reconstruction of sparse signals using a small number of linear measurements. One of the main challenges in compressed sensing is to find the support of a sparse signal. In the literature, several bounds on…

Recent advances in semi-supervised learning with deep generative models have shown promise in generalizing from small labeled datasets ($\mathbf{x},\mathbf{y}$) to large unlabeled ones ($\mathbf{x}$). In the case where the codomain has…

Deep latent generative models have attracted increasing attention due to the capacity of combining the strengths of deep learning and probabilistic models in an elegant way. The data representations learned with the models are often…

Building on the remarkable achievements in generative sampling of natural images, we propose an innovative challenge, potentially overly ambitious, which involves generating samples of entire multivariate time series that resemble images.…

We study the asymptotic stability of a dissipative evolution in a Hilbert space subject to intermittent damping. We observe that, even if the intermittence satisfies a persistent excitation condition, if the Hilbert space is…

Recent deep generative models are able to provide photo-realistic images as well as visual or textual content embeddings useful to address various tasks of computer vision and natural language processing. Their usefulness is nevertheless…

Deep generative models produce data according to a learned representation, e.g. diffusion models, through a process of approximation computing possible samples. Approximation can be understood as reconstruction and the large datasets used…

Speech super-resolution (SR) is the task that restores high-resolution speech from low-resolution input. Existing models employ simulated data and constrained experimental settings, which limit generalization to real-world SR. Predictive…

Two-dimensional array-based datasets are pervasive in a variety of domains. Current approaches for generative modeling have typically been limited to conventional image datasets and performed in the pixel domain which do not explicitly…

Deep generative models are becoming widely used across science and industry for a variety of purposes. A common challenge is achieving a precise implicit or explicit representation of the data probability density. Recent proposals have…

The construction of highly incoherent frames, sequences of vectors placed on the unit hyper sphere of a finite dimensional Hilbert space with low correlation between them, has proven very difficult. Algorithms proposed in the past have…

In deep learning it is common to overparameterize neural networks, that is, to use more parameters than training samples. Quite surprisingly training the neural network via (stochastic) gradient descent leads to models that generalize very…

We propose a novel approach for solving inverse-problems with high-dimensional inputs and an expensive forward mapping. It leverages joint deep generative modelling to transfer the original problem spaces to a lower dimensional latent…

Modeling uncertainty in deep neural networks, despite recent important advances, is still an open problem. Bayesian neural networks are a powerful solution, where the prior over network weights is a design choice, often a normal…

Scientific measurements are often bottlenecked by suboptimal conditions, whether that be noise, incomplete spatial coverage, or limited resolution, rendering accurate field reconstruction a difficult task. We introduce LatentPDE, a latent…

Generative modeling within constrained sets is essential for scientific and engineering applications involving physical, geometric, or safety requirements (e.g., molecular generation, robotics). We present a unified framework for…

We address data-driven learning of the infinitesimal generator of stochastic diffusion processes, essential for understanding numerical simulations of natural and physical systems. The unbounded nature of the generator poses significant…

Local climate information is crucial for impact assessment and decision-making, yet coarse global climate simulations cannot capture small-scale phenomena. Current statistical downscaling methods infer these phenomena as temporally…