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Point clouds are versatile representations of 3D objects and have found widespread application in science and engineering. Many successful deep-learning models have been proposed that use them as input. The domain of chemical and materials…
We introduce tensor field neural networks, which are locally equivariant to 3D rotations, translations, and permutations of points at every layer. 3D rotation equivariance removes the need for data augmentation to identify features in…
Defining and reliably finding a canonical orientation for 3D surfaces is key to many Computer Vision and Robotics applications. This task is commonly addressed by handcrafted algorithms exploiting geometric cues deemed as distinctive and…
Symmetry-aware architectures are central to geometric deep learning. We present a systematic approach for constructing continuous rotationally invariant and equivariant functions using symmetric tensor networks. The proposed framework…
Learning functions on point clouds has applications in many fields, including computer vision, computer graphics, physics, and chemistry. Recently, there has been a growing interest in neural architectures that are invariant or equivariant…
Objects' rigid motions in 3D space are described by rotations and translations of a highly-correlated set of points, each with associated $x,y,z$ coordinates that real-valued networks consider as separate entities, losing information.…
Learning 3D representations that generalize well to arbitrarily oriented inputs is a challenge of practical importance in applications varying from computer vision to physics and chemistry. We propose a novel multi-resolution convolutional…
Statistical learning methods show great promise in providing an accurate prediction of materials and molecular properties, while minimizing the need for computationally demanding electronic structure calculations. The accuracy and…
Recent developments in the field of quantum machine learning have promoted the idea of incorporating physical symmetries in the structure of quantum circuits. A crucial milestone in this area is the realization of $S_{n}$-permutation…
Tensors are a fundamental data structure for many scientific contexts, such as time series analysis, materials science, and physics, among many others. Improving our ability to produce and handle tensors is essential to efficiently address…
Symmetry considerations are at the core of the major frameworks used to provide an effective mathematical representation of atomic configurations that is then used in machine-learning models to predict the properties associated with each…
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…
State-of-the-art deep learning systems often require large amounts of data and computation. For this reason, leveraging known or unknown structure of the data is paramount. Convolutional neural networks (CNNs) are successful examples of…
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…
This paper proposes a set of rules to revise various neural networks for 3D point cloud processing to rotation-equivariant quaternion neural networks (REQNNs). We find that when a neural network uses quaternion features under certain…
Features that are equivariant to a larger group of symmetries have been shown to be more discriminative and powerful in recent studies. However, higher-order equivariant features often come with an exponentially-growing computational cost.…
Embedding molecular symmetries into machine-learning models is key for efficient learning of chemico-physical scalar properties, but little evidence on how to extend the same strategy to tensorial quantities exists. Here we formulate a…
Spherical convolutional networks have been introduced recently as tools to learn powerful feature representations of 3D shapes. Spherical CNNs are equivariant to 3D rotations making them ideally suited to applications where 3D data may be…
We address the problem of 3D rotation equivariance in convolutional neural networks. 3D rotations have been a challenging nuisance in 3D classification tasks requiring higher capacity and extended data augmentation in order to tackle it. We…
Extending the translation equivariance property of convolutional neural networks to larger symmetry groups has been shown to reduce sample complexity and enable more discriminative feature learning. Further, exploiting additional symmetries…