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

Training deep learning models for point cloud prediction tasks such as shape completion and generation depends critically on loss functions that measure discrepancies between predicted and ground-truth point sets. Commonly used functions…

Neural networks that are equivariant to rotations, translations, reflections, and permutations on n-dimensional geometric space have shown promise in physical modeling for tasks such as accurately but inexpensively modeling complex…

Graph neural networks excel at modeling pairwise interactions, but they cannot flexibly accommodate higher-order interactions and features. Topological deep learning (TDL) has emerged recently as a promising tool for addressing this issue.…

Machine learning, especially physics-informed neural networks (PINNs) and their neural network variants, has been widely used to solve problems involving partial differential equations (PDEs). The successful deployment of such methods…

Image restoration is an inherently ill posed inverse problem. Equivariant networks that embed geometric symmetry priors can mitigate this ill posedness and improve performance. However, current understanding of the relationship between…

This paper introduces E(n) Equivariant Message Passing Cellular Networks (EMPCNs), an extension of E(n) Equivariant Graph Neural Networks to CW-complexes. Our approach addresses two aspects of geometric message passing networks: 1)…

Shape completion, the problem of estimating the complete geometry of objects from partial observations, lies at the core of many vision and robotics applications. In this work, we propose Point Completion Network (PCN), a novel…

Convolutional Neural Networks (CNNs) have performed extremely well on data represented by regularly arranged grids such as images. However, directly leveraging the classic convolution kernels or parameter sharing mechanisms on sparse 3D…

Incorporating geometric invariance into neural networks enhances parameter efficiency but typically increases computational costs. This paper introduces new equivariant neural networks that preserve symmetry while maintaining a comparable…

Point cloud completion is a vital task focused on reconstructing complete point clouds and addressing the incompleteness caused by occlusion and limited sensor resolution. Traditional methods relying on fixed local region partitioning, such…

Geometric deep learning enables the encoding of physical symmetries in modeling 3D objects. Despite rapid progress in encoding 3D symmetries into Graph Neural Networks (GNNs), a comprehensive evaluation of the expressiveness of these…

Partition of unity networks (POU-Nets) have been shown capable of realizing algebraic convergence rates for regression and solution of PDEs, but require empirical tuning of training parameters. We enrich POU-Nets with a Gaussian noise model…

Group Convolutional Neural Networks (G-CNNs) constrain learned features to respect the symmetries in the selected group, and lead to better generalization when these symmetries appear in the data. If this is not the case, however,…

Incomplete point clouds captured by 3D sensors often result in the loss of both geometric and semantic information. Most existing point cloud completion methods are built on rotation-variant frameworks trained with data in canonical poses,…

Equivariance is a powerful inductive bias in neural networks, improving generalisation and physical consistency. Recently, however, non-equivariant models have regained attention, due to their better runtime performance and imperfect…

In spite of the recent progresses on classifying 3D point cloud with deep CNNs, large geometric transformations like rotation and translation remain challenging problem and harm the final classification performance. To address this…

Solving partial differential equations (PDEs) by numerical methods meet computational cost challenge for getting the accurate solution since fine grids and small time steps are required. Machine learning can accelerate this process, but…

Invariance under symmetry is an important problem in machine learning. Our paper looks specifically at equivariant neural networks where transformations of inputs yield homomorphic transformations of outputs. Here, steerable CNNs have…

Incorporating inductive bias by embedding geometric entities (such as rays) as input has proven successful in multi-view learning. However, the methods adopting this technique typically lack equivariance, which is crucial for effective 3D…

Knowledge of 3D properties of objects is a necessity in order to build effective computer vision systems. However, lack of large scale 3D datasets can be a major constraint for data-driven approaches in learning such properties. We consider…