Related papers: A Simple and Universal Rotation Equivariant Point-…
This paper proposes a convolution structure for learning SE(3)-equivariant features from 3D point clouds. It can be viewed as an equivariant version of kernel point convolutions (KPConv), a widely used convolution form to process point…
Recent progresses in 3D deep learning has shown that it is possible to design special convolution operators to consume point cloud data. However, a typical drawback is that rotation invariance is often not guaranteed, resulting in networks…
Graph Neural Networks (GNN) come in many flavors, but should always be either invariant (permutation of the nodes of the input graph does not affect the output) or equivariant (permutation of the input permutes the output). In this paper,…
Many learning tasks, including learning potential energy surfaces from ab initio calculations, involve global spatial symmetries and permutational symmetry between atoms or general particles. Equivariant graph neural networks are a standard…
In many computer vision tasks, we expect a particular behavior of the output with respect to rotations of the input image. If this relationship is explicitly encoded, instead of treated as any other variation, the complexity of the problem…
3D point clouds deep learning is a promising field of research that allows a neural network to learn features of point clouds directly, making it a robust tool for solving 3D scene understanding tasks. While recent works show that point…
The rising adoption of machine learning in high energy physics and lattice field theory necessitates the re-evaluation of common methods that are widely used in computer vision, which, when applied to problems in physics, can lead to…
Equivariant neural networks are neural networks with symmetry. Motivated by the theory of group representations, we decompose the layers of an equivariant neural network into simple representations. The nonlinear activation functions lead…
There has been enormous progress in the last few years in designing neural networks that respect the fundamental symmetries and coordinate freedoms of physical law. Some of these frameworks make use of irreducible representations, some make…
In the recent application of scientific modeling, machine learning models are largely applied to facilitate computational simulations of fluid systems. Rotation symmetry is a general property for most symmetric fluid systems. However, in…
Point cloud normal estimation is a fundamental task in 3D geometry processing. While recent learning-based methods achieve notable advancements in normal prediction, they often overlook the critical aspect of equivariance. This results in…
The simplicity and effectiveness of the UNet architecture makes it ubiquitous in image restoration, image segmentation, and diffusion models. They are often assumed to be equivariant to translations, yet they traditionally consist of layers…
The set of functions parameterized by a linear fully-connected neural network is a determinantal variety. We investigate the subvariety of functions that are equivariant or invariant under the action of a permutation group. Examples of such…
Rotation equivariance is a desirable property in many practical applications such as motion forecasting and 3D perception, where it can offer benefits like sample efficiency, better generalization, and robustness to input perturbations.…
We prove an impossibility result, which in the context of function learning says the following: under certain conditions, it is impossible to simultaneously learn symmetries and functions equivariant under them using an ansatz consisting of…
We introduce a novel architecture for graph networks which is equivariant to any transformation in the coordinate embeddings that preserves the distance between neighbouring nodes. In particular, it is equivariant to the Euclidean and…
Invariant and equivariant networks are useful in learning data with symmetry, including images, sets, point clouds, and graphs. In this paper, we consider invariant and equivariant networks for symmetries of finite groups. Invariant and…
Many applications require robustness, or ideally invariance, of neural networks to certain transformations of input data. Most commonly, this requirement is addressed by training data augmentation, using adversarial training, or defining…
The design of convolutional neural architectures that are exactly equivariant to continuous translations is an active field of research. It promises to benefit scientific computing, notably by making existing imaging systems more physically…
Constraining linear layers in neural networks to respect symmetry transformations from a group $G$ is a common design principle for invariant networks that has found many applications in machine learning. In this paper, we consider a…