Related papers: Approximately Piecewise E(3) Equivariant Point Net…

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,…

Transformer-based networks have achieved impressive performance in 3D point cloud understanding. However, most of them concentrate on aggregating local features, but neglect to directly model global dependencies, which results in a limited…

Deep learning for predicting the electronic-structure Hamiltonian of quantum systems necessitates satisfying the covariance laws, among which achieving SO(3)-equivariance without sacrificing the non-linear expressive capability of networks…

Anatomical mesh segmentation requires models that operate directly on irregular surface geometry while remaining robust to arbitrary patient pose and mesh resolution variation. Existing task-specific mesh and point-cloud methods are not…

3D Convolutional Neural Networks are sensitive to transformations applied to their input. This is a problem because a voxelized version of a 3D object, and its rotated clone, will look unrelated to each other after passing through to the…

Among 2D convolutional networks on point clouds, point-based approaches consume point clouds of fixed size directly. By analysis of PointNet, a pioneer in introducing deep learning into point sets, we reveal that current point-based methods…

Nowadays, the number of emerging embedded systems rapidly grows in many application domains, due to recent advances in artificial intelligence and internet of things. The main inherent specification of these application-specific systems is…

Point clouds, being the simple and compact representation of surface geometry of 3D objects, have gained increasing popularity with the evolution of deep learning networks for classification and segmentation tasks. Unlike human, teaching…

Research has shown that deep networks tend to be overly optimistic about their predictions, leading to an underestimation of prediction errors. Due to the limited nature of data, existing studies have proposed various methods based on model…

3D scanning is a complex multistage process that generates a point cloud of an object typically containing damaged parts due to occlusions, reflections, shadows, scanner motion, specific properties of the object surface, imperfect…

Many machine learning tasks involve learning functions that are known to be invariant or equivariant to certain symmetries of the input data. However, it is often challenging to design neural network architectures that respect these…

Given a graph G where each node is associated with a set of attributes, attributed network embedding (ANE) maps each node v in G to a compact vector Xv, which can be used in downstream machine learning tasks. Ideally, Xv should capture node…

Network Embeddings (NEs) map the nodes of a given network into $d$-dimensional Euclidean space $\mathbb{R}^d$. Ideally, this mapping is such that `similar' nodes are mapped onto nearby points, such that the NE can be used for purposes such…

Image segmentation is a popular area of research in computer vision that has many applications in automated image processing. A recent technique called piecewise flat embeddings (PFE) has been proposed for use in image segmentation; PFE…

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…

Antibody design is valuable for therapeutic usage and biological research. Existing deep-learning-based methods encounter several key issues: 1) incomplete context for Complementarity-Determining Regions (CDRs) generation; 2) incapability…

This paper presents a novel framework for non-linear equivariant neural network layers on homogeneous spaces. The seminal work of Cohen et al. on equivariant $G$-CNNs on homogeneous spaces characterized the representation theory of such…

Using neural networks to solve variational problems, and other scientific machine learning tasks, has been limited by a lack of consistency and an inability to exactly integrate expressions involving neural network architectures. We address…

This paper presents $\mathrm{E}(n)$ Equivariant Message Passing Simplicial Networks (EMPSNs), a novel approach to learning on geometric graphs and point clouds that is equivariant to rotations, translations, and reflections. EMPSNs can…

This paper presents Point Convolutional Neural Networks (PCNN): a novel framework for applying convolutional neural networks to point clouds. The framework consists of two operators: extension and restriction, mapping point cloud functions…