Related papers: Learning to Normalize on the SPD Manifold under Bu…

Manifold-valued measurements exist in numerous applications within computer vision and machine learning. Recent studies have extended Deep Neural Networks (DNNs) to manifolds, and concomitantly, normalization techniques have also been…

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…

Essential characteristics of signal data can be captured by the autocovariance matrix, which, in the stationary scenarios, is Toeplitz Hermitian positive definite (HPD). In this paper, several well-known Riemannian geometric structures of…

Despite its long history, Bayesian neural networks (BNNs) and variational training remain underused in practice: standard Gaussian posteriors misalign with network geometry, KL terms can be brittle in high dimensions, and implementations…

Recent progress in geometric deep learning has drawn increasing attention from the machine learning community toward domain adaptation on symmetric positive definite (SPD) manifolds, especially for neuroimaging data that often suffer from…

Symmetric Positive Definite (SPD) matrices have become popular to encode image information. Accounting for the geometry of the Riemannian manifold of SPD matrices has proven key to the success of many algorithms. However, most existing…

Batch normalization (BN) has become a critical component across diverse deep neural networks. The network with BN is invariant to positively linear re-scale transformation, which makes there exist infinite functionally equivalent networks…

Scientific machine learning increasingly uses spectral methods to understand physical systems. Current spectral learning approaches provide only point estimates without uncertainty quantification, limiting their use in safety-critical…

Deep neural networks for learning Symmetric Positive Definite (SPD) matrices are gaining increasing attention in machine learning. Despite the significant progress, most existing SPD networks use traditional Euclidean classifiers on an…

Optimizing deep neural networks (DNNs) often suffers from the ill-conditioned problem. We observe that the scaling-based weight space symmetry property in rectified nonlinear network will cause this negative effect. Therefore, we propose to…

An increasing number of machine learning tasks deal with learning representations from set-structured data. Solutions to these problems involve the composition of permutation-equivariant modules (e.g., self-attention, or individual…

Boltzmann Machines (BMs) are graphical models with interconnected binary units, employed for the unsupervised modeling of data distributions. When trained on real data, BMs show the tendency to behave like critical systems, displaying a…

Modern machine learning increasingly leverages the insight that high-dimensional data often lie near low-dimensional, non-linear manifolds, an idea known as the manifold hypothesis. By explicitly modeling the geometric structure of data…

Deep learning methods achieve great success recently on many computer vision problems, with image classification and object detection as the prominent examples. In spite of these practical successes, optimization of deep networks remains an…

Machine learning representations of many-body quantum states have recently been introduced as an ansatz to describe the ground states and unitary evolutions of many-body quantum systems. We explore one of the most important representations,…

This paper proposes new algorithms for the metric learning problem. We start by noticing that several classical metric learning formulations from the literature can be viewed as modified covariance matrix estimation problems. Leveraging…

The Restricted Boltzmann Machine (RBM), an important tool used in machine learning in particular for unsupervized learning tasks, is investigated from the perspective of its spectral properties. Starting from empirical observations, we…

Deep neural networks (DNNs) on Riemannian manifolds have garnered increasing interest in various applied areas. For instance, DNNs on spherical and hyperbolic manifolds have been designed to solve a wide range of computer vision and nature…

Matrix-valued optimization tasks, including those involving symmetric positive definite (SPD) matrices, arise in a wide range of applications in machine learning, data science and statistics. Classically, such problems are solved via…

Symmetric positive definite (SPD) matrix has been demonstrated to be an effective feature descriptor in many scientific areas, as it can encode spatiotemporal statistics of the data adequately on a curved Riemannian manifold, i.e., SPD…