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

Representations are a foundational component of any modelling protocol, including on molecules and molecular solids. For tasks that depend on knowledge of both molecular conformation and 3D orientation, such as the modelling of molecular…

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…

This paper presents a novel framework combining group equivariant convolutional neural networks (G-CNNs) with equivariant-aware structured pruning to produce compact, transformation-invariant models for resource-constrained environments.…

The task of human pose estimation (HPE) deals with the ill-posed problem of estimating the 3D position of human joints directly from images and videos. In recent literature, most of the works tackle the problem mostly by using convolutional…

A wide range of techniques have been proposed in recent years for designing neural networks for 3D data that are equivariant under rotation and translation of the input. Most approaches for equivariance under the Euclidean group…

This work introduces E3x, a software package for building neural networks that are equivariant with respect to the Euclidean group $\mathrm{E}(3)$, consisting of translations, rotations, and reflections of three-dimensional space. Compared…

Spatial and channel re-calibration have become powerful concepts in computer vision. Their ability to capture long-range dependencies is especially useful for those networks that extract local features, such as CNNs. While re-calibration…

Incorporating symmetries can lead to highly data-efficient and generalizable models by defining equivalence classes of data samples related by transformations. However, characterizing how transformations act on input data is often…

Neural networks that incorporate geometric relationships respecting SE(3) group transformations (e.g. rotations and translations) are increasingly important in molecular applications, such as molecular property prediction, protein structure…

Equivariance has gained strong interest as a desirable network property that inherently ensures robust generalization. However, when dealing with complex systems such as articulated objects or multi-object scenes, effectively capturing…

Based on the theory of homogeneous spaces we derive geometrically optimal edge attributes to be used within the flexible message-passing framework. We formalize the notion of weight sharing in convolutional networks as the sharing of…

Many problems in computer vision require dealing with sparse, unordered data in the form of point clouds. Permutation-equivariant networks have become a popular solution-they operate on individual data points with simple perceptrons and…

Physics-Informed Neural Networks (PINNs) have emerged as a tool for approximating the solution of Partial Differential Equations (PDEs) in both forward and inverse problems. PINNs minimize a loss function which includes the PDE residual…

In industrial defect segmentation tasks, while pixel accuracy and Intersection over Union (IoU) are commonly employed metrics to assess segmentation performance, the output consistency (also referred to equivalence) of the model is often…

In this paper, we propose a similarity-aware fusion network (SAFNet) to adaptively fuse 2D images and 3D point clouds for 3D semantic segmentation. Existing fusion-based methods achieve remarkable performances by integrating information…

Scanning real-life scenes with modern registration devices typically gives incomplete point cloud representations, primarily due to the limitations of partial scanning, 3D occlusions, and dynamic light conditions. Recent works on processing…

Point cloud completion is the task of predicting complete geometry from partial observations using a point set representation for a 3D shape. Previous approaches propose neural networks to directly estimate the whole point cloud through…

Invariance and equivariance to the rotation group have been widely discussed in the 3D deep learning community for pointclouds. Yet most proposed methods either use complex mathematical tools that may limit their accessibility, or are tied…

The application of deep learning to 3D point clouds is challenging due to its lack of order. Inspired by the point embeddings of PointNet and the edge embeddings of DGCNNs, we propose three improvements to the task of point cloud analysis.…

Graph neural networks that model 3D data, such as point clouds or atoms, are typically desired to be $SO(3)$ equivariant, i.e., equivariant to 3D rotations. Unfortunately equivariant convolutions, which are a fundamental operation for…