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Relational representation learning transforms relational data into continuous and low-dimensional vector representations. However, vector-based representations fall short in capturing crucial properties of relational data that are complex…

Deep learning on point clouds has made a lot of progress recently. Many point cloud dedicated deep learning frameworks, such as PointNet and PointNet++, have shown advantages in accuracy and speed comparing to those using traditional 3D…

Geometric deep learning (GDL), which is based on neural network architectures that incorporate and process symmetry information, has emerged as a recent paradigm in artificial intelligence. GDL bears particular promise in molecular modeling…

Point cloud stands as the most widely adopted format for representing 3D shapes and scenes due to its simplicity and geometric fidelity. However, its inherent unordered and irregular nature, exacerbated by sensor noise and occlusions,…

Recent advances in computational modelling of atomic systems, spanning molecules, proteins, and materials, represent them as geometric graphs with atoms embedded as nodes in 3D Euclidean space. In these graphs, the geometric attributes…

Equivariance has been a long-standing concern in various fields ranging from computer vision to physical modeling. Most previous methods struggle with generality, simplicity, and expressiveness -- some are designed ad hoc for specific data…

Transformers achieve strong performance across diverse domains but implicitly assume Euclidean geometry in their attention mechanisms, limiting their effectiveness on data with non-Euclidean structure. While recent extensions to hyperbolic…

Recently, many deep neural networks were designed to process 3D point clouds, but a common drawback is that rotation invariance is not ensured, leading to poor generalization to arbitrary orientations. In this paper, we introduce a new…

Conformal symmetries, i.e.\ coordinate transformations that preserve angles, play a key role in many fields, including physics, mathematics, computer vision and (geometric) machine learning. Here we build a neural network that is…

The use of geometric and symmetry techniques in quantum and classical information processing has a long tradition across the physical sciences as a means of theoretical discovery and applied problem solving. In the modern era, the emergent…

In this chapter, we identify fundamental geometric structures that underlie the problems of sampling, optimisation, inference and adaptive decision-making. Based on this identification, we derive algorithms that exploit these geometric…

Recent developments in the field of quantum machine learning have promoted the idea of incorporating physical symmetries in the structure of quantum circuits. A crucial milestone in this area is the realization of $S_{n}$-permutation…

Geometric relational embeddings map relational data as geometric objects that combine vector information suitable for machine learning and structured/relational information for structured/relational reasoning, typically in low dimensions.…

Deep Neural Networks achieve state-of-the-art results in many different problem settings by exploiting vast amounts of training data. However, collecting, storing and - in the case of supervised learning - labelling the data is expensive…

Recent attempts at introducing rotation invariance or equivariance in 3D deep learning approaches have shown promising results, but these methods still struggle to reach the performances of standard 3D neural networks. In this work we study…

Deep learning has proven to yield fast and accurate predictions of quantum-chemical properties to accelerate the discovery of novel molecules and materials. As an exhaustive exploration of the vast chemical space is still infeasible, we…

Recently, the advancement of 3D point clouds in deep learning has attracted intensive research in different application domains such as computer vision and robotic tasks. However, creating feature representation of robust, discriminative…

Many anatomical structures can be described by surface or volume meshes. Machine learning is a promising tool to extract information from these 3D models. However, high-fidelity meshes often contain hundreds of thousands of vertices, which…

Recent advances in image clustering typically focus on learning better deep representations. In contrast, we present an orthogonal approach that does not rely on abstract features but instead learns to predict image transformations and…

Symmetry considerations are at the core of the major frameworks used to provide an effective mathematical representation of atomic configurations that is then used in machine-learning models to predict the properties associated with each…