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Many scientific problems require to process data in the form of geometric graphs. Unlike generic graph data, geometric graphs exhibit symmetries of translations, rotations, and/or reflections. Researchers have leveraged such inductive bias…
Generative adversarial network (GAN) is widely used for generalized and robust learning on graph data. However, for non-Euclidean graph data, the existing GAN-based graph representation methods generate negative samples by random walk or…
Latent variable models are powerful tools for learning low-dimensional manifolds from high-dimensional data. However, when dealing with constrained data such as unit-norm vectors or symmetric positive-definite matrices, existing approaches…
Representation learning on temporal graphs has drawn considerable research attention owing to its fundamental importance in a wide spectrum of real-world applications. Though a number of studies succeed in obtaining time-dependent…
Deep neural networks have enabled researchers to create powerful generalized frameworks, such as transformers, that can be used to solve well-studied problems in various application domains, such as text and image. However, such generalized…
We exploit the structure of geometric graphs on Riemannian manifolds to analyze strategic dynamic graphs at the limit, when the number of nodes tends to infinity. This framework allows to preserve intrinsic geometrical information about the…
One of the main challenges in modern deep learning is to understand why such over-parameterized models perform so well when trained on finite data. A way to analyze this generalization concept is through the properties of the associated…
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…
This work proposes a geometric insight into equivariant message passing on Riemannian manifolds. As previously proposed, numerical features on Riemannian manifolds are represented as coordinate-independent feature fields on the manifold. To…
Graph learning has become essential in various domains, including recommendation systems and social network analysis. Graph Neural Networks (GNNs) have emerged as promising techniques for encoding structural information and improving…
Graphs represent interconnected structures prevalent in a myriad of real-world scenarios. Effective graph analytics, such as graph learning methods, enables users to gain profound insights from graph data, underpinning various tasks…
Hyperbolic geometry, a Riemannian manifold endowed with constant sectional negative curvature, has been considered an alternative embedding space in many learning scenarios, \eg, natural language processing, graph learning, \etc, as a…
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…
Graph Neural Networks (GNNs) have emerged as a powerful and flexible framework for representation learning on irregular data. As they generalize the operations of classical CNNs on grids to arbitrary topologies, GNNs also bring much of the…
The fundamental laws of physics are intrinsically geometric, dictating the evolution of systems through principles of symmetry and conservation. While modern machine learning offers powerful tools for modeling complex dynamics from data,…
Graphs are a natural representation for systems based on relations between connected entities. Combinatorial optimization problems, which arise when considering an objective function related to a process of interest on discrete structures,…
Recent progress in research on Deep Graph Networks (DGNs) has led to a maturation of the domain of learning on graphs. Despite the growth of this research field, there are still important challenges that are yet unsolved. Specifically,…
Embedding graphs in continous spaces is a key factor in designing and developing algorithms for automatic information extraction to be applied in diverse tasks (e.g., learning, inferring, predicting). The reliability of graph embeddings…
Graphs representation learning has been a very active research area in recent years. The goal of graph representation learning is to generate graph representation vectors that capture the structure and features of large graphs accurately.…
Graph learning is a popular approach for performing machine learning on graph-structured data. It has revolutionized the machine learning ability to model graph data to address downstream tasks. Its application is wide due to the…