相关论文: Equivariant Networks for Pixelized Spheres

Convolutional neural networks (CNNs) constructed natively on the sphere have been developed recently and shown to be highly effective for the analysis of spherical data. While an efficient framework has been formulated, spherical CNNs are…

Learning depth from spherical panoramas is becoming a popular research topic because a panorama has a full field-of-view of the environment and provides a relatively complete description of a scene. However, applying well-studied CNNs for…

Omni-directional cameras have many advantages overconventional cameras in that they have a much wider field-of-view (FOV). Accordingly, several approaches have beenproposed recently to apply convolutional neural networks(CNNs) to…

Semantic segmentation for spherical data is a challenging problem in machine learning since conventional planar approaches require projecting the spherical image to the Euclidean plane. Representing the signal on a fundamentally different…

The Euclidean scattering transform was introduced nearly a decade ago to improve the mathematical understanding of the success of convolutional neural networks (ConvNets) in image data analysis and other tasks. Inspired by recent interest…

Convolutional Neural Networks (CNNs) are a cornerstone of the Deep Learning toolbox and have led to many breakthroughs in Artificial Intelligence. These networks have mostly been developed for regular Euclidean domains such as those…

Designing a convolution for a spherical neural network requires a delicate tradeoff between efficiency and rotation equivariance. DeepSphere, a method based on a graph representation of the sampled sphere, strikes a controllable balance…

Translating or rotating an input image should not affect the results of many computer vision tasks. Convolutional neural networks (CNNs) are already translation equivariant: input image translations produce proportionate feature map…

Modeling the energy and forces of atomic systems is a fundamental problem in computational chemistry with the potential to help address many of the world's most pressing problems, including those related to energy scarcity and climate…

Convolutional Neural Networks (CNNs) have been providing the state-of-the-art performance for learning-related problems involving 2D/3D images in Euclidean space. However, unlike in the Euclidean space, the shapes of many structures in…

We develop a theory of category-equivariant neural networks (CENNs) that unifies group/groupoid-equivariant networks, poset/lattice-equivariant networks, graph and sheaf neural networks. Equivariance is formulated as naturality in a…

Group invariant and equivariant Multilayer Perceptrons (MLP), also known as Equivariant Networks, have achieved remarkable success in learning on a variety of data structures, such as sequences, images, sets, and graphs. Using tools from…

Symmetries and equivariance are fundamental to the generalization of neural networks on domains such as images, graphs, and point clouds. Existing work has primarily focused on a small number of groups, such as the translation, rotation,…

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…

Many successful deep learning architectures are equivariant to certain transformations in order to conserve parameters and improve generalization: most famously, convolution layers are equivariant to shifts of the input. This approach only…

Efficiently processing structured point cloud data while preserving multiscale information is a key challenge across domains, from graphics to atomistic modeling. Using a curated dataset of simulated galaxy positions and properties,…

Identifying symmetries in data sets is generally difficult, but knowledge about them is crucial for efficient data handling. Here we present a method how neural networks can be used to identify symmetries. We make extensive use of the…

From early image processing to modern computational imaging, successful models and algorithms have relied on a fundamental property of natural signals: symmetry. Here symmetry refers to the invariance property of signal sets to…

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…

Developing deep learning techniques for geometric data is an active and fruitful research area. This paper tackles the problem of sphere-type surface learning by developing a novel surface-to-image representation. Using this representation…