Related papers: Riemannian Archetypal Analysis: Interpretable non-…

Efficient topology optimization based on the adaptive auxiliary reduced model reanalysis (AARMR) is proposed to improve computational efficiency and scale. In this method, a projection auxiliary reduced model (PARM) is integrated into the…

We study the properties of stochastic approximation applied to a tame nondifferentiable function subject to constraints defined by a Riemannian manifold. The objective landscape of tame functions, arising in o-minimal topology extended to a…

Riemannian neural networks, which extend deep learning techniques to Riemannian spaces, have gained significant attention in machine learning. To better classify the manifold-valued features, researchers have started extending Euclidean…

We construct a derived enhancement of Hom spaces between rigid analytic spaces. It encodes the hidden deformation-theoretic informations of the underlying classical moduli space. The main tool in our construction is the representability…

Variational regularization is a classical technique to solve statistical inference tasks and inverse problems, with modern data-driven approaches parameterizing regularizers via deep neural networks showcasing impressive empirical…

Methods based on Riemannian geometry have proven themselves to be good models for decoding in brain-computer interfacing (BCI). However, one major drawback of these methods is that it is not possible to determine what aspect of the signal…

In this paper, we present an adaptive gradient descent method for geodesically convex optimization on a Riemannian manifold with nonnegative sectional curvature. The method automatically adapts to the local geometry of the function and does…

Generative machine learning models offer a powerful framework for therapeutic design by efficiently exploring large spaces of biological sequences enriched for desirable properties. Unlike supervised learning methods, which require both…

Inferring time-varying graph structures from high-dimensional nodal observations is a fundamental problem arising in neuroscience, finance, climatology, and beyond. Two intrinsic challenges govern this problem: maintaining the…

"Deep Archetypal Analysis" generates latent representations of high-dimensional datasets in terms of fractions of intuitively understandable basic entities called archetypes. The proposed method is an extension of linear "Archetypal…

The advent of integral field data has revolutionised the study of galaxy evolution. A key component of this is dynamical modelling methods which have allowed for crucial insights to be made from kinematic data. Despite this importance, most…

Capsule Networks (CapsNets) show exceptional graph representation capacity via dynamic routing and vectorized hierarchical representations, but they model the complex geometries of real\-world graphs poorly by fixed\-curvature space due to…

Multi-domain graph pre-training integrates knowledge from diverse domains to enhance performance in the target domains, which is crucial for building graph foundation models. Despite initial success, existing solutions often fall short of…

Archetypal analysis is an unsupervised machine learning method that summarizes data using a convex polytope. In its original formulation, for fixed k, the method finds a convex polytope with k vertices, called archetype points, such that…

This paper analyzes the convergence for a large class of Riemannian stochastic approximation (SA) schemes, which aim at tackling stochastic optimization problems. In particular, the recursions we study use either the exponential map of the…

Various statistical tasks, including sampling or computing Wasserstein barycenters, can be reformulated as fixed-point problems for operators on probability distributions. Accelerating standard fixed-point iteration schemes provides a…

Data encoded as symmetric positive definite (SPD) matrices frequently arise in many areas of computer vision and machine learning. While these matrices form an open subset of the Euclidean space of symmetric matrices, viewing them through…

Deep generative models provide a systematic way to learn nonlinear data distributions, through a set of latent variables and a nonlinear "generator" function that maps latent points into the input space. The nonlinearity of the generator…

Direct search methods represent a robust and reliable class of algorithms for solving black-box optimization problems. In this paper, we explore the application of those strategies to Riemannian optimization, wherein minimization is to be…

Learning the distribution of data on Riemannian manifolds is crucial for modeling data from non-Euclidean space, which is required by many applications in diverse scientific fields. Yet, existing generative models on manifolds suffer from…