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Object segmentation is a key component in the visual system of a robot that performs tasks like grasping and object manipulation, especially in presence of occlusions. Like many other computer vision tasks, the adoption of deep…

Group equivariant convolutional networks (GCNNs) endow classical convolutional networks with additional symmetry priors, which can lead to a considerably improved performance. Recent advances in the theoretical description of GCNNs revealed…

Quantum kernels are reproducing kernel functions built using quantum-mechanical principles and are studied with the aim of outperforming their classical counterparts. The enthusiasm for quantum kernel machines has been tempered by recent…

Motivation: A branching processes model yields an unevenly stochastically distributed dataset that consists of sparse and dense regions. This work addresses the problem of precisely evaluating parameters for such a model. Applying a…

The universality properties of kernels characterize the class of functions that can be approximated in the associated reproducing kernel Hilbert space and are of fundamental importance in the theoretical underpinning of kernel methods in…

We present a geometric formulation of the Multiple Kernel Learning (MKL) problem. To do so, we reinterpret the problem of learning kernel weights as searching for a kernel that maximizes the minimum (kernel) distance between two convex…

Kernel methods in Quantum Machine Learning (QML) have recently gained significant attention as a potential candidate for achieving a quantum advantage in data analysis. Among other attractive properties, when training a kernel-based model…

Kernel methods are used extensively in classical machine learning, especially in the field of pattern analysis. In this paper, we propose a kernel-based quantum machine learning algorithm that can be implemented on a near-term, intermediate…

We focus on the problem of efficient sampling and learning of probability densities by incorporating symmetries in probabilistic models. We first introduce Equivariant Stein Variational Gradient Descent algorithm -- an equivariant sampling…

Computing atomic-scale properties of chemically disordered materials requires an efficient exploration of their vast configuration space. Traditional approaches such as Monte Carlo or Special Quasirandom Structures either entail sampling an…

A linear-complexity algorithm for computing the Wasserstein-1 distance on non-uniform meshes is proposed. This work extends the fast Sinkhorn algorithms from [Q. Liao et al., Commun. Math. Sci., 20(2022)] and [Q. Liao et al., J. Sci.…

We survey the mathematical foundations of geometric deep learning, focusing on group equivariant and gauge equivariant neural networks. We develop gauge equivariant convolutional neural networks on arbitrary manifolds $\mathcal{M}$ using…

In this paper we revisit the kernel density estimation problem: given a kernel $K(x, y)$ and a dataset of $n$ points in high dimensional Euclidean space, prepare a data structure that can quickly output, given a query $q$, a…

Motivated by the growing interest in representation learning approaches that uncover the latent structure of high-dimensional data, this work proposes new algorithms for reconstruction-based manifold learning within Reproducing-Kernel…

In this paper, we address the challenge of obtaining a comprehensive and symmetric representation of point particle groups, such as atoms in a molecule, which is crucial in physics and theoretical chemistry. The problem has become even more…

Determining the stability of molecules and condensed phases is the cornerstone of atomistic modelling, underpinning our understanding of chemical and materials properties and transformations. Here we show that a machine learning model,…

Advances in machine learning have led to the development of foundation models for atomistic materials chemistry, enabling quantum-accurate descriptions of interatomic forces across chemically diverse compounds at reduced computational cost.…

In this abstract paper, we introduce a new kernel learning method by a nonparametric density estimator. The estimator consists of a group of k-centroids clusterings. Each clustering randomly selects data points with randomly selected…

This paper generalizes recent advances on quadratic manifold (QM) dimensionality reduction by developing kernel methods-based nonlinear-augmentation dimensionality reduction. QMs, and more generally feature map-based nonlinear corrections,…

The importance of wild video based image set recognition is becoming monotonically increasing. However, the contents of these collected videos are often complicated, and how to efficiently perform set modeling and feature extraction is a…