Related papers: Exploring Data Geometry for Continual Learning

The enduring legacy of Euclidean geometry underpins classical machine learning, which, for decades, has been primarily developed for data lying in Euclidean space. Yet, modern machine learning increasingly encounters richly structured data…

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,…

Mapping complex input data into suitable lower dimensional manifolds is a common procedure in machine learning. This step is beneficial mainly for two reasons: (1) it reduces the data dimensionality and (2) it provides a new data…

Current practice in parameter space exploration in euclidean space is dominated by randomized sampling or design of experiment methods. The biggest issue with these methods is not keeping track of what part of parameter space has been…

Continual learning~(CL) is a field concerned with learning a series of inter-related task with the tasks typically defined in the sense of either regression or classification. In recent years, CL has been studied extensively when these…

In this work, we develop new generalization bounds for neural networks trained on data supported on Riemannian manifolds. Existing generalization theories often rely on complexity measures derived from Euclidean geometry, which fail to…

Recently, continual graph learning has been increasingly adopted for diverse graph-structured data processing tasks in non-stationary environments. Despite its promising learning capability, current studies on continual graph learning…

Deep learning has achieved a remarkable performance breakthrough in several fields, most notably in speech recognition, natural language processing, and computer vision. In particular, convolutional neural network (CNN) architectures…

Continual learning on graph data has recently attracted paramount attention for its aim to resolve the catastrophic forgetting problem on existing tasks while adapting the sequentially updated model to newly emerged graph tasks. While there…

Graph representation learning in Euclidean space, despite its widespread adoption and proven utility in many domains, often struggles to effectively capture the inherent hierarchical and complex relational structures prevalent in real-world…

We investigate learning of the differential geometric structure of a data manifold embedded in a high-dimensional Euclidean space. We first analyze kernel-based algorithms and show that under the usual regularizations, non-probabilistic…

Modern machine learning systems are increasingly trained on large amounts of data embedded in high-dimensional spaces. Often this is done without analyzing the structure of the dataset. In this work, we propose a framework to study the…

Mathematical descriptions of dynamical systems are deeply rooted in topological spaces defined by non-Euclidean geometry. This paper proposes leveraging structure-rich geometric spaces for machine learning to achieve structural…

Continual learning is an emerging paradigm in machine learning, wherein a model is exposed in an online fashion to data from multiple different distributions (i.e. environments), and is expected to adapt to the distribution change.…

Supervised manifold learning methods learn data representations by preserving the geometric structure of data while enhancing the separation between data samples from different classes. In this work, we propose a theoretical study of…

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…

This article proposes an active learning method for high dimensional data, based on intrinsic data geometries learned through diffusion processes on graphs. Diffusion distances are used to parametrize low-dimensional structures on the…

Real-world graphs naturally exhibit hierarchical or cyclical structures that are unfit for the typical Euclidean space. While there exist graph neural networks that leverage hyperbolic or spherical spaces to learn representations that embed…

Geometric data analysis and learning has emerged as a distinct and rapidly developing research area, increasingly recognized for its effectiveness across diverse applications. At the heart of this field lies curvature, a powerful and…

Learning a latent embedding to understand the underlying nature of data distribution is often formulated in Euclidean spaces with zero curvature. However, the success of the geometry constraints, posed in the embedding space, indicates that…