相关论文: E(2)-Equivariant Features in Machine Learning for …

Classifying the morphologies of galaxies is an important step in understanding their physical properties and evolutionary histories. The advent of large-scale surveys has hastened the need to develop techniques for automated morphological…

The morphological classification of radio sources is important to gain a full understanding of galaxy evolution processes and their relation with local environmental properties. Furthermore, the complex nature of the problem, its appeal for…

Deep learning based on deep neural networks has been very successful in many practical applications, but it lacks enough theoretical understanding due to the network architectures and structures. In this paper we establish some analysis for…

We train three convolutional neural networks (CNNs) to classify galaxies with Galaxy Zoo 2 dataset and extract the activations from the last fully connected layer or the last average pooling layer of CNNs to study the high-dimensional…

Classifying the morphologies of radio galaxies is important to understand their physical properties and evolutionary histories. A galaxy's morphology is often determined by visual inspection, but as survey size increases robust automated…

Convolutional neural networks (CNNs) allow for parameter sharing and translational equivariance by using convolutional kernels in their linear layers. By restricting these kernels to be SO(3)-steerable, CNNs can further improve parameter…

Equivariant machine learning methods have shown wide success at 3D learning applications in recent years. These models explicitly build in the reflection, translation and rotation symmetries of Euclidean space and have facilitated large…

Classification of EEG signals using shallow Convolutional Neural Networks (CNNs) is a prevalent and successful approach across a variety of fields. Most of these models use independent one-dimensional (1D) convolutional layers along the…

Analyzing scalar and vector fields on the sphere, such as temperature or wind speed and direction on Earth, is a difficult task. Models should respect both the rotational symmetries of the sphere and the inherent symmetries of the vector…

Histology images are inherently symmetric under rotation, where each orientation is equally as likely to appear. However, this rotational symmetry is not widely utilised as prior knowledge in modern Convolutional Neural Networks (CNNs),…

Many problems across computer vision and the natural sciences require the analysis of spherical data, for which representations may be learned efficiently by encoding equivariance to rotational symmetries. We present a generalized spherical…

The automated segmentation of cortical areas has been a long-standing challenge in medical image analysis. The complex geometry of the cortex is commonly represented as a polygon mesh, whose segmentation can be addressed by graph-based…

The K-means algorithm is among the most commonly used data clustering methods. However, the regular K-means can only be applied in the input space and it is applicable when clusters are linearly separable. The kernel K-means, which extends…

We present a convolutional network that is equivariant to rigid body motions. The model uses scalar-, vector-, and tensor fields over 3D Euclidean space to represent data, and equivariant convolutions to map between such representations.…

Including covariant information, such as position, force, velocity or spin is important in many tasks in computational physics and chemistry. We introduce Steerable E(3) Equivariant Graph Neural Networks (SEGNNs) that generalise equivariant…

We analyze the role of rotational equivariance in convolutional neural networks (CNNs) applied to spherical images. We compare the performance of the group equivariant networks known as S2CNNs and standard non-equivariant CNNs trained with…

There is an increasing interest in applying deep learning to 3D mesh segmentation. We observe that 1) existing feature-based techniques are often slow or sensitive to feature resizing, 2) there are minimal comparative studies and 3)…

Convolutional neural networks are ubiquitous in Machine Learning applications for solving a variety of problems. They however can not be used in their native form when the domain of the data is commonly encountered manifolds such as the…

Learning and reasoning about 3D molecular structures with varying size is an emerging and important challenge in machine learning and especially in drug discovery. Equivariant Graph Neural Networks (GNNs) can simultaneously leverage the…

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…