Related papers: Representing spherical tensors with scalar-based m…

We introduce the SE(3)-Transformer, a variant of the self-attention module for 3D point clouds and graphs, which is equivariant under continuous 3D roto-translations. Equivariance is important to ensure stable and predictable performance in…

In this article, we introduce and study the concept of $\textit{spherical-vectors}$, which can be perceived as a natural extension of the arguments of complex numbers in the context of quaternions. We initially establish foundational…

Spherical convolutional neural networks (Spherical CNNs) learn nonlinear representations from 3D data by exploiting the data structure and have shown promising performance in shape analysis, object classification, and planning among others.…

Much attention has been devoted to the use of machine learning to approximate physical concepts. Yet, due to challenges in interpretability of machine learning techniques, the question of what physics machine learning models are able to…

In this paper, we study the approximate orthogonal diagonalization problem of third order symmetric tensors. We define several classes of approximately diagonal tensors, including the ones corresponding to the stationary points of this…

Three dimensional (3D) object recognition is becoming a key desired capability for many computer vision systems such as autonomous vehicles, service robots and surveillance drones to operate more effectively in unstructured environments.…

A current challenge in atomistic machine learning is that of efficiently predicting the response of the electron density under electric fields. We address this challenge with symmetry-adapted kernel functions that are specifically derived…

Discrete translational symmetry plays a fundamental role in condensed matter physics and lattice gauge theories, enabling the analysis of systems that would otherwise be intractable. Despite this, many open problems remain. Quantum…

Learning from unordered sets is a fundamental learning setup, recently attracting increasing attention. Research in this area has focused on the case where elements of the set are represented by feature vectors, and far less emphasis has…

Point clouds obtained from photogrammetry are noisy and incomplete models of reality. We propose an evolutionary optimization methodology that is able to approximate the underlying object geometry on such point clouds. This approach assumes…

Self-supervised learning has emerged as a promising approach for acquiring transferable 3D representations from unlabeled 3D point clouds. Unlike 2D images, which are widely accessible, acquiring 3D assets requires specialized expertise or…

Point clouds are unstructured and unordered in the embedded 3D space. In order to produce consistent responses under different permutation layouts, most existing methods aggregate local spatial points through maximum or summation operation.…

Structure-informed protein representation learning is essential for effective protein function annotation and \textit{de novo} design. However, the presence of inherent noise in both crystal and AlphaFold-predicted structures poses…

Recent years have witnessed the surge of learned representations that directly build upon point clouds. Though becoming increasingly expressive, most existing representations still struggle to generate ordered point sets. Inspired by…

Accurate simulations of atomistic systems from first principles are limited by computational cost. In high-throughput settings, machine learning can reduce these costs significantly by accurately interpolating between reference…

Learning equivariant representations is a promising way to reduce sample and model complexity and improve the generalization performance of deep neural networks. The spherical CNNs are successful examples, producing SO(3)-equivariant…

Analyzing the geometric and semantic properties of 3D point clouds through the deep networks is still challenging due to the irregularity and sparsity of samplings of their geometric structures. This paper presents a new method to define…

Point cloud analysis (such as 3D segmentation and detection) is a challenging task, because of not only the irregular geometries of many millions of unordered points, but also the great variations caused by depth, viewpoint, occlusion, etc.…

We propose a fast and accurate surface reconstruction algorithm for unorganized point clouds using an implicit representation. Recent learning methods are either single-object representations with small neural models that allow for high…

A general machine learning architecture is introduced that uses wavelet scattering coefficients of an inputted three dimensional signal as features. Solid harmonic wavelet scattering transforms of three dimensional signals were previously…