Related papers: Geometric deep learning: going beyond Euclidean da…

Thanks to the availability of large scale digital datasets and massive amounts of computational power, deep learning algorithms can learn representations of data by exploiting multiple levels of abstraction. These machine learning methods…

Graphs provide a powerful means for representing complex interactions between entities. Recently, deep learning approaches are emerging for representing and modeling graph-structured data, although the conventional deep learning methods…

This paper is the first attempt to use geometric deep learning and Sobolev training to incorporate non-Euclidean microstructural data such that anisotropic hyperelastic material machine learning models can be trained in the finite…

Recently, there has been a rising surge of momentum for deep representation learning in hyperbolic spaces due to theirhigh capacity of modeling data like knowledge graphs or synonym hierarchies, possessing hierarchical structure. We refer…

Convolutional Neural Networks (CNNs) have been very successful at solving a variety of computer vision tasks such as object classification and detection, semantic segmentation, activity understanding, to name just a few. One key enabling…

Latent space geometry provides a rigorous and empirically valuable framework for interacting with the latent variables of deep generative models. This approach reinterprets Euclidean latent spaces as Riemannian through a pull-back metric,…

Hyperbolic geometry has emerged as a powerful tool for modeling complex, structured data, particularly where hierarchical or tree-like relationships are present. By enabling embeddings with lower distortion, hyperbolic neural networks offer…

Learning low-dimensional numerical representations from symbolic data, e.g., embedding the nodes of a graph into a geometric space, is an important concept in machine learning. While embedding into Euclidean space is common, recent…

Embedding nodes of a large network into a metric (e.g., Euclidean) space has become an area of active research in statistical machine learning, which has found applications in natural and social sciences. Generally, a representation of a…

Networks are a powerful tool to model complex systems, and the definition of many Graph Neural Networks (GNN), Deep Learning algorithms that can handle networks, has opened a new way to approach many real-world problems that would be hardly…

Deep neural networks are workhorse models in machine learning with multiple layers of non-linear functions composed in series. Their loss function is highly non-convex, yet empirically even gradient descent minimisation is sufficient to…

The history-dependent behaviors of classical plasticity models are often driven by internal variables evolved according to phenomenological laws. The difficulty to interpret how these internal variables represent a history of deformation,…

Modern information processing relies on the axiom that high-dimensional data lie near low-dimensional geometric structures. This paper revisits the problem of data-driven learning of these geometric structures and puts forth two new…

Graph Neural Networks (GNNs) have significant advantages in handling non-Euclidean data and have been widely applied across various areas, thus receiving increasing attention in recent years. The framework of GNN models mainly includes the…

The data sciences revolution is poised to transform the way photonic systems are simulated and designed. Photonics are in many ways an ideal substrate for machine learning: the objective of much of computational electromagnetics is the…

One of the most prominent attributes of Neural Networks (NNs) constitutes their capability of learning to extract robust and descriptive features from high dimensional data, like images. Hence, such an ability renders their exploitation as…

A complete understanding of the widely used over-parameterized deep networks is a key step for AI. In this work we try to give a geometric picture of over-parameterized deep networks using our geometrization scheme. We show that the…

Difficulties in replication and reproducibility of empirical evidences in machine learning research have become a prominent topic in recent years. Ensuring that machine learning research results are sound and reliable requires…

Deep learning, a branch of artificial intelligence, is a data-driven method that uses multiple layers of interconnected units or neurons to learn intricate patterns and representations directly from raw input data. Empowered by this…

Unstructured grid data are essential for modelling complex geometries and dynamics in computational physics. Yet, their inherent irregularity presents significant challenges for conventional machine learning (ML) techniques. This paper…