Related papers: Toward a Unified Geometry Understanding: Riemannia…

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…

Graphs are ubiquitous, and learning on graphs has become a cornerstone in artificial intelligence and data mining communities. Unlike pixel grids in images or sequential structures in language, graphs exhibit a typical non-Euclidean…

We introduce novel estimators for computing the curvature, tangent spaces, and dimension of data from manifolds, using tools from diffusion geometry. Although classical Riemannian geometry is a rich source of inspiration for geometric data…

We propose two graph neural network layers for graphs with features in a Riemannian manifold. First, based on a manifold-valued graph diffusion equation, we construct a diffusion layer that can be applied to an arbitrary number of nodes and…

We introduce diffusion geometry as a new framework for geometric and topological data analysis. Diffusion geometry uses the Bakry-Emery $\Gamma$-calculus of Markov diffusion operators to define objects from Riemannian geometry on a wide…

Graphs are typical non-Euclidean data of complex structures. In recent years, Riemannian graph representation learning has emerged as an exciting alternative to Euclidean ones. However, Riemannian methods are still in an early stage: most…

Modern generative modeling methods have demonstrated strong performance in learning complex data distributions from clean samples. In many scientific and imaging applications, however, clean samples are unavailable, and only noisy or…

A generative modeling framework is proposed that combines diffusion models and manifold learning to efficiently sample data densities on manifolds. The approach utilizes Diffusion Maps to uncover possible low-dimensional underlying (latent)…

Euclidean representations distort data with intrinsic non-Euclidean structure. While Riemannian representation learning offers a solution by embedding data onto matching manifolds, it typically relies on an encoder to estimate densities on…

Real-world graphs have inherently complex and diverse topological patterns, known as topological heterogeneity. Most existing works learn graph representation in a single constant curvature space that is insufficient to match the complex…

In this paper, we propose the first framework that enables solving graph learning tasks of all levels (node, edge and graph) and all types (generation, regression and classification) using one formulation. We first formulate prediction…

Deep generative models learn a mapping from a low dimensional latent space to a high-dimensional data space. Under certain regularity conditions, these models parameterize nonlinear manifolds in the data space. In this paper, we investigate…

In recent years, manifold learning has become increasingly popular as a tool for performing non-linear dimensionality reduction. This has led to the development of numerous algorithms of varying degrees of complexity that aim to recover man…

Non-Euclidean constraints are inherent in many kinds of data in computer vision and machine learning, typically as a result of specific invariance requirements that need to be respected during high-level inference. Often, these geometric…

Generation of graphs is a major challenge for real-world tasks that require understanding the complex nature of their non-Euclidean structures. Although diffusion models have achieved notable success in graph generation recently, they are…

Recent advances in diffusion models have demonstrated their remarkable ability to capture complex image distributions, but the geometric properties of the learned data manifold remain poorly understood. We address this gap by introducing a…

Graph data often exhibits complex geometric heterogeneity, where structures with varying local curvature, such as tree-like hierarchies and dense communities, coexist within a single network. Existing geometric GNNs, which embed graphs into…

Recently, studies on machine learning have focused on methods that use symmetry implicit in a specific manifold as an inductive bias. Grassmann manifolds provide the ability to handle fundamental shapes represented as shape spaces, enabling…

Diffusion models have made significant contributions to computer vision, sparking a growing interest in the community recently regarding the application of them to graph generation. Existing discrete graph diffusion models exhibit…

Recent breakthroughs and rapid integration of generative models (GMs) have sparked interest in the problem of model attribution and their fingerprints. For instance, service providers need reliable methods of authenticating their models to…