Related papers: Group invariant machine learning by fundamental do…

Quantum neural network architectures that have little-to-no inductive biases are known to face trainability and generalization issues. Inspired by a similar problem, recent breakthroughs in machine learning address this challenge by…

Data with geometric structure is ubiquitous in machine learning often arising from fundamental symmetries in a domain, such as permutation-invariance in graphs and translation-invariance in images. Group-convolutional architectures, which…

In recent years, deep learning techniques have shown great success in various tasks related to inverse problems, where a target quantity of interest can only be observed through indirect measurements by a forward operator. Common approaches…

This paper presents a mathematical framework for analyzing machine learning models through the geometry of their induced partitions. By representing partitions as Riemannian simplicial complexes, we capture not only adjacency relationships…

We address the problem of determining correspondences between two images in agreement with a geometric model such as an affine or thin-plate spline transformation, and estimating its parameters. The contributions of this work are…

Despite significant advances in the field of deep learning in applications to various fields, explaining the inner processes of deep learning models remains an important and open question. The purpose of this article is to describe and…

The problem of identifying geometric structure in data is a cornerstone of (unsupervised) learning. As a result, Geometric Representation Learning has been widely applied across scientific and engineering domains. In this work, we…

Group equivariance has emerged as a valuable inductive bias in deep learning, enhancing generalization, data efficiency, and robustness. Classically, group equivariant methods require the groups of interest to be known beforehand, which may…

In the field of medical image, deep convolutional neural networks(ConvNets) have achieved great success in the classification, segmentation, and registration tasks thanks to their unparalleled capacity to learn image features. However,…

In this chapter, we identify fundamental geometric structures that underlie the problems of sampling, optimisation, inference and adaptive decision-making. Based on this identification, we derive algorithms that exploit these geometric…

Equivariant network architectures are a well-established tool for predicting invariant or equivariant quantities. However, almost all learning problems considered in this context feature a global symmetry, i.e. each point of the underlying…

Bayesian learning with Gaussian processes demonstrates encouraging regression and classification performances in solving computer vision tasks. However, Bayesian methods on 3D manifold-valued vision data, such as meshes and point clouds,…

Group equivariance (e.g. SE(3) equivariance) is a critical physical symmetry in science, from classical and quantum physics to computational biology. It enables robust and accurate prediction under arbitrary reference transformations. In…

Geophysical inversion should ideally produce geologically realistic subsurface models that explain the available data. Multiple-point statistics is a geostatistical approach to construct subsurface models that are consistent with…

We introduce a novel co-learning paradigm for manifolds naturally equipped with a group action, motivated by recent developments on learning a manifold from attached fibre bundle structures. We utilize a representation theoretic mechanism…

Fitting an unknown number of hyperplanes to data is a fundamental yet challenging problem in machine learning, characterized by its non-convexity, non-differentiability, and unknown model order. Existing approaches often struggle with local…

Equivariance is a powerful prior for learning physical dynamics, yet exact group equivariance can degrade performance if the symmetries are broken. We propose object-centric world models built with geometric algebra neural networks,…

Incorporating group symmetries via equivariance into neural networks has emerged as a robust approach for overcoming the efficiency and data demands of modern deep learning. While most existing approaches, such as group convolutions and…

Many scientific fields study data with an underlying structure that is a non-Euclidean space. Some examples include social networks in computational social sciences, sensor networks in communications, functional networks in brain imaging,…

Learning to predict agent motions with relationship reasoning is important for many applications. In motion prediction tasks, maintaining motion equivariance under Euclidean geometric transformations and invariance of agent interaction is a…