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Predictive geometric models deliver excellent results for many Machine Learning use cases. Despite their undoubted performance, neural predictive algorithms can show unexpected degrees of instability and variance, particularly when applied…

In this report we discuss the concepts of geometric memory align- ment, geometric memory allocation and geometric memory mapping. We introduce block trees as an efficient data structure for representing geo- metrically aligned block…

Deep learning is having a tremendous impact in many areas of computer science and engineering. Motivated by this success, deep neural networks are attracting an increasing attention in many other disciplines, including physical sciences. In…

Deep learning is changing many areas in molecular physics, and it has shown great potential to deliver new solutions to challenging molecular modeling problems. Along with this trend arises the increasing demand of expressive and versatile…

Point cloud analysis is a fundamental task in 3D computer vision. Most previous works have conducted experiments on synthetic datasets with well-aligned data; while real-world point clouds are often not pre-aligned. How to achieve rotation…

We present a novel deep learning framework for flow field predictions in irregular domains when the solution is a function of the geometry of either the domain or objects inside the domain. Grid vertices in a computational fluid dynamics…

Previous studies have demonstrated the effectiveness of point-based neural models on the point cloud analysis task. However, there remains a crucial issue on producing the efficient input embedding for raw point coordinates. Moreover,…

The difficult problem of relating the static structure of glassy liquids and their dynamics is a good target for Machine Learning, an approach which excels at finding complex patterns hidden in data. Indeed, this approach is currently a hot…

Point clouds are a popular representation for 3D shapes. However, they encode a particular sampling without accounting for shape priors or non-local information. We advocate for the use of a hierarchical Gaussian mixture model (hGMM), which…

In many real-world applications of regression, conditional probability estimation, and uncertainty quantification, exploiting symmetries rooted in physics or geometry can dramatically improve generalization and sample efficiency. While…

Many scientific and geometric problems exhibit general linear symmetries, yet most equivariant neural networks are built for compact groups or simple vector features, limiting their reuse on matrix-valued data such as covariances, inertias,…

We propose Geometric Neural Parametric Models (GNPM), a learned parametric model that takes into account the local structure of data to learn disentangled shape and pose latent spaces of 4D dynamics, using a geometric-aware architecture on…

Point clouds are a basic data type that is increasingly of interest as 3D content becomes more ubiquitous. Applications using point clouds include virtual, augmented, and mixed reality and autonomous driving. We propose a more efficient…

Real algebraic geometry adapts the methods and ideas from (complex) algebraic geometry to study the real solutions to systems of polynomial equations and polynomial inequalities. As it is the real solutions to such systems modeling…

Learning meaningful local and global information remains a challenge in point cloud segmentation tasks. When utilizing local information, prior studies indiscriminately aggregates neighbor information from different classes to update query…

We present a lightweight network that infers grouping and boundaries, including curves, corners and junctions. It operates in a bottom-up fashion, analogous to classical methods for sub-pixel edge localization and edge-linking, but with a…

This paper develops a novel mathematical framework for collaborative learning by means of geometrically inspired kernel machines which includes statements on the bounds of generalisation and approximation errors, and sample complexity. For…

Convolutional networks are successful due to their equivariance/invariance under translations. However, rotatable data such as images, volumes, shapes, or point clouds require processing with equivariance/invariance under rotations in cases…

Processing global geometric context while preserving equivariance is crucial when modeling biological, chemical, and physical systems. Yet, this is challenging due to the computational demands of equivariance and global context at scale.…

Continual Learning aims to learn multiple incoming new tasks continually, and to keep the performance of learned tasks at a consistent level. However, existing research on continual learning assumes the pose of the object is pre-defined and…