Related papers: Mathematical Foundations of Geometric Deep Learnin…
Particle physics is a branch of science aiming at discovering the fundamental laws of matter and forces. Graph neural networks are trainable functions which operate on graphs---sets of elements and their pairwise relations---and are a…
This draft summarizes some basics about geometric computer vision needed to implement efficient computer vision algorithms for applications that use measurements from at least one digital camera mounted on a moving platform with a special…
The characterization of dynamical processes in living systems provides important clues for their mechanistic interpretation and link to biological functions. Thanks to recent advances in microscopy techniques, it is now possible to…
In recent years, Deep Learning has become the go-to solution for a broad range of applications, often outperforming state-of-the-art. However, it is important, for both theoreticians and practitioners, to gain a deeper understanding of the…
Evaluating the quality of learned representations without relying on a downstream task remains one of the challenges in representation learning. In this work, we present Geometric Component Analysis (GeomCA) algorithm that evaluates…
This book introduces the mathematical foundations and techniques that lead to the development and analysis of many of the algorithms that are used in machine learning. It starts with an introductory chapter that describes notation used…
Learning representations on Grassmann manifolds is popular in quite a few visual recognition tasks. In order to enable deep learning on Grassmann manifolds, this paper proposes a deep network architecture by generalizing the Euclidean…
This paper introduces deep Gaussian processes (DGPs) for geophysical parameter retrieval. Unlike the standard full GP model, the DGP accounts for complicated (modular, hierarchical) processes, provides an efficient solution that scales well…
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…
The study of geometric extremes, where extremal dependence properties are inferred from the deterministic limiting shapes of scaled sample clouds, provides an exciting approach to modelling the extremes of multivariate data. These shapes,…
Deep learning, despite its remarkable achievements, is still a young field. Like the early stages of many scientific disciplines, it is marked by the discovery of new phenomena, ad-hoc design decisions, and the lack of a uniform and…
Geometric aspects play an important role in the construction and analysis of structure-preserving numerical methods for a wide variety of ordinary and partial differential equations. Here we review the development and theory of symplectic…
The application of deep learning in robotics leads to very specific problems and research questions that are typically not addressed by the computer vision and machine learning communities. In this paper we discuss a number of…
This chapter gives an overview of the core concepts of machine learning (ML) -- the use of algorithms that learn from data, identify patterns, and make predictions or decisions without being explicitly programmed -- that are relevant to…
Machine learning is finding increasingly broad application in the physical sciences. This most often involves building a model relationship between a dependent, measurable output and an associated set of controllable, but complicated,…
Topological data analysis asks when balls in a metric space $(X,d)$ intersect. Geometric data analysis asks how much balls have to be enlarged to intersect. We connect this principle to the traditional core geometric concept of curvature.…
Geometric ability is a significant challenge for large language models (LLMs) due to the need for advanced spatial comprehension and abstract thinking. Existing datasets primarily evaluate LLMs on their final answers, but they cannot truly…
Researchers have now achieved great success on dealing with 2D images using deep learning. In recent years, 3D computer vision and Geometry Deep Learning gain more and more attention. Many advanced techniques for 3D shapes have been…
Surface-based geodesic topology provides strong cues for object semantic analysis and geometric modeling. However, such connectivity information is lost in point clouds. Thus we introduce GeoNet, the first deep learning architecture trained…
During a geosteering operation the well path is intentionally adjusted in response to the new data acquired while drilling. To achieve consistent high-quality decisions, especially when drilling in complex environments, decision support…