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Rotational symmetry plays a central role in physics, providing an elegant framework to describe how the properties of 3D objects -- from atoms to the macroscopic scale -- transform under the action of rigid rotations. Equivariant models of…
We propose Equiangular Basis Vectors (EBVs) for classification tasks. In deep neural networks, models usually end with a k-way fully connected layer with softmax to handle different classification tasks. The learning objective of these…
Modeling the complex three-dimensional (3D) dynamics of relational systems is an important problem in the natural sciences, with applications ranging from molecular simulations to particle mechanics. Machine learning methods have achieved…
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…
The accurate prediction of changes in protein stability under multiple amino acid substitutions is essential for realising true in-silico protein re-design. To this purpose, we propose improvements to state-of-the-art Deep learning (DL)…
Exploiting symmetries and invariance in data is a powerful, yet not fully exploited, way to achieve better generalisation with more efficiency. In this paper, we introduce two graph network architectures that are equivariant to several…
Learning about the three-dimensional world from two-dimensional images is a fundamental problem in computer vision. An ideal neural network architecture for such tasks would leverage the fact that objects can be rotated and translated in…
Graphs are one of the most important data structures for representing pairwise relations between objects. Specifically, a graph embedded in a Euclidean space is essential to solving real problems, such as physical simulations. A crucial…
In robotic tasks, changes in reference frames typically do not influence the underlying physical properties of the system, which has been known as invariance of physical laws.These changes, which preserve distance, encompass isometric…
Deep learning architectures such as convolutional neural networks are the standard in computer vision for image processing tasks. Their accuracy however often comes at the cost of long and computationally expensive training, the need for…
Regular group convolutional neural networks (G-CNNs) have been shown to increase model performance and improve equivariance to different geometrical symmetries. This work addresses the problem of SE(3), i.e., roto-translation equivariance,…
We present a PDE-based framework that generalizes Group equivariant Convolutional Neural Networks (G-CNNs). In this framework, a network layer is seen as a set of PDE-solvers where geometrically meaningful PDE-coefficients become the…
Rotation equivariance has recently become a strongly desired property in the 3D deep learning community. Yet most existing methods focus on equivariance regarding a global input rotation while ignoring the fact that rotation symmetry has…
This work seeks to improve the generalization and robustness of existing neural networks for 3D point clouds by inducing group equivariance under general group transformations. The main challenge when designing equivariant models for point…
Convolution is an integral operation that defines how the shape of one function is modified by another function. This powerful concept forms the basis of hierarchical feature learning in deep neural networks. Although performing convolution…
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…
Molecular 3D conformations play a key role in determining how molecules interact with other molecules or protein surfaces. Recent deep learning advancements have improved conformation prediction, but slow training speeds and difficulties in…
We introduce Group equivariant Convolutional Neural Networks (G-CNNs), a natural generalization of convolutional neural networks that reduces sample complexity by exploiting symmetries. G-CNNs use G-convolutions, a new type of layer that…
Crystal structure optimization is fundamental to materials modeling but remains computationally expensive when performed with density-functional theory (DFT). Machine-learning (ML) approaches offer substantial acceleration, yet existing…
In hierarchal order of molecular geometry, we compare the performances of Geometric Quantum Machine Learning models. Two molecular datasets are considered: the simplistic linear shaped LiH-molecule and the trigonal pyramidal molecule NH3.…