Related papers: Geometric Deep Learning and Equivariant Neural Net…
State-of-the-art deep learning systems often require large amounts of data and computation. For this reason, leveraging known or unknown structure of the data is paramount. Convolutional neural networks (CNNs) are successful examples of…
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…
Recent advances in deep learning and Transformers have driven major breakthroughs in robotics by employing techniques such as imitation learning, reinforcement learning, and LLM-based multimodal perception and decision-making. However,…
Learning and reasoning about 3D molecular structures with varying size is an emerging and important challenge in machine learning and especially in drug discovery. Equivariant Graph Neural Networks (GNNs) can simultaneously leverage the…
Invariant models, one important class of geometric deep learning models, are capable of generating meaningful geometric representations by leveraging informative geometric features in point clouds. These models are characterized by their…
The scattering transform is a multilayered wavelet-based deep learning architecture that acts as a model of convolutional neural networks. Recently, several works have introduced generalizations of the scattering transform for non-Euclidean…
Most current deep learning models equivariant to $O(n)$ or $SO(n)$ either consider mostly scalar information such as distances and angles or have a very high computational complexity. In this work, we test a few novel message passing graph…
Deep learning has achieved a remarkable performance breakthrough in several fields, most notably in speech recognition, natural language processing, and computer vision. In particular, convolutional neural network (CNN) architectures…
The translation equivariance of convolutions can make convolutional neural networks translation equivariant or invariant. Equivariance to other transformations (e.g. rotations, affine transformations, scalings) may also be desirable as soon…
Tractably modelling distributions over manifolds has long been an important goal in the natural sciences. Recent work has focused on developing general machine learning models to learn such distributions. However, for many applications…
This paper introduces a new model to learn graph neural networks equivariant to rotations, translations, reflections and permutations called E(n)-Equivariant Graph Neural Networks (EGNNs). In contrast with existing methods, our work does…
Training a Convolutional Neural Network (CNN) to be robust against rotation has mostly been done with data augmentation. In this paper, another progressive vision of research direction is highlighted to encourage less dependence on data…
In this paper, we utilize hyperspheres and regular $n$-simplexes and propose an approach to learning deep features equivariant under the transformations of $n$D reflections and rotations, encompassed by the powerful group of O$(n)$. Namely,…
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…
In recent years the use of convolutional layers to encode an inductive bias (translational equivariance) in neural networks has proven to be a very fruitful idea. The successes of this approach have motivated a line of research into…
Group equivariant neural networks have proven effective in modelling a wide range of tasks where the data lives in a classical geometric space and exhibits well-defined group symmetries. However, these networks are not suitable for learning…
We propose a novel approach for performing convolution of signals on curved surfaces and show its utility in a variety of geometric deep learning applications. Key to our construction is the notion of directional functions defined on the…
Group equivariance (e.g. SE(3) equivariance) is a critical physical symmetry in science, from classical and quantum physics to computational biology. It enables robust and accurate prediction under arbitrary reference transformations. In…
Soft, porous mechanical metamaterials exhibit pattern transformations that may have important applications in soft robotics, sound reduction and biomedicine. To design these innovative materials, it is important to be able to simulate them…
Incorporating group symmetries via equivariance into neural networks has emerged as a robust approach for overcoming the efficiency and data demands of modern deep learning. While most existing approaches, such as group convolutions and…