Related papers: Generative Modeling of Discrete Data Using Geometr…

This paper focuses on Geodesic Principal Component Analysis (GPCA) on a collection of probability distributions using the Otto-Wasserstein geometry. The goal is to identify geodesic curves in the space of probability measures that best…

Evaluating the quality of learned representations without relying on a downstream task remains one of the challenges in representation learning. In this work, we present Geometric Component Analysis (GeomCA) algorithm that evaluates…

Deep generative models such as flow and diffusion models have proven to be effective in modeling high-dimensional and complex data types such as videos or proteins, and this has motivated their use in different data modalities, such as…

Variables in many massive high-dimensional data sets are structured, arising for example from measurements on a regular grid as in imaging and time series or from spatial-temporal measurements as in climate studies. Classical multivariate…

Despite strong performance in data-rich regimes, deep learning often underperforms in the data-scarce settings common in practice. While foundation models (FMs) trained on massive datasets demonstrate strong generalization by extracting…

Diffusion models recently developed for generative AI tasks can produce high-quality samples while still maintaining diversity among samples to promote mode coverage, providing a promising path for learning stochastic closure models.…

Latent variable models (LVMs) learn probabilistic models of data manifolds lying in an \emph{ambient} Euclidean space. In a number of applications, a priori known spatial constraints can shrink the ambient space into a considerably smaller…

Modern generative models can produce realistic samples, however, balancing memorisation and generalisation remains an open problem. We approach this challenge from a Bayesian perspective by focusing on the parameter space of flow matching…

Many real-world problems require reasoning across multiple scales, demanding models which operate not on single data points, but on entire distributions. We introduce generative distribution embeddings (GDE), a framework that lifts…

The graph-based variational autoencoder represents an architecture that can handle the uncertainty of different geological scenarios, such as depositional or structural, through the concept of a lowerdimensional latent space. The main…

In a number of disciplines, the data (e.g., graphs, manifolds) to be analyzed are non-Euclidean in nature. Geometric deep learning corresponds to techniques that generalize deep neural network models to such non-Euclidean spaces. Several…

The ability to accurately model random fields plays a critical role in science and engineering for problems involving uncertain, spatially-varying quantities such as heterogeneous material properties and turbulent flows. Deep generative…

This report presents some fundamental mathematical results towards elucidating the information-geometric underpinnings of evolutionary modelling schemes for (quasi-)stationary discrete stochastic processes. The model class under…

The increasing prevalence of relational data describing interactions among a target population has motivated a wide literature on statistical network analysis. In many applications, interactions may involve more than two members of the…

High-dimensional biological data often exhibit a severe mismatch between feature dimensionality and sample size, making reliable classification difficult in extremely small-data regimes. In these settings, kernel methods can lose…

Augmentation by generative modelling yields a promising alternative to the accumulation of surgical data, where ethical, organisational and regulatory aspects must be considered. Yet, the joint synthesis of (image, mask) pairs for…

We present an architecture which lets us train deep, directed generative models with many layers of latent variables. We include deterministic paths between all latent variables and the generated output, and provide a richer set of…

Representing 3D shape is a fundamental problem in artificial intelligence, which has numerous applications within computer vision and graphics. One avenue that has recently begun to be explored is the use of latent representations of…

Despite the success of diffusion models (DMs), we still lack a thorough understanding of their latent space. While image editing with GANs builds upon latent space, DMs rely on editing the conditions such as text prompts. We present an…

Symbolic Regression (SR) tries to reveal the hidden equations behind observed data. However, most methods search within a discrete equation space, where the structural modifications of equations rarely align with their numerical behavior,…