Related papers: Enabling equivariance for arbitrary Lie groups
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…
In this paper, we introduce group convolutional neural networks (GCNNs) equivariant to color variation. GCNNs have been designed for a variety of geometric transformations from 2D and 3D rotation groups, to semi-groups such as scale.…
Transformation groups, such as translations or rotations, effectively express part of the variability observed in many recognition problems. The group structure enables the construction of invariant signal representations with appealing…
The principle of equivariance to symmetry transformations enables a theoretically grounded approach to neural network architecture design. Equivariant networks have shown excellent performance and data efficiency on vision and medical…
3D Convolutional Neural Networks are sensitive to transformations applied to their input. This is a problem because a voxelized version of a 3D object, and its rotated clone, will look unrelated to each other after passing through to the…
Lattice gauge equivariant convolutional neural networks (L-CNNs) are a framework for convolutional neural networks that can be applied to non-Abelian lattice gauge theories without violating gauge symmetry. We demonstrate how L-CNNs can be…
Next-generation radio surveys will yield an unprecedented amount of data, warranting analysis by use of machine learning techniques. Convolutional neural networks are the deep learning technique that has proven to be the most successful in…
Neural networks are a promising tool for simulating quantum many body systems. Recently, it has been shown that neural network-based models describe quantum many body systems more accurately when they are constrained to have the correct…
In this paper, we propose a novel network design mechanism for efficient embedded computing. Inspired by the limited computing patterns, we propose to fix the number of channels in a group convolution, instead of the existing practice that…
Capsule Networks face a critical problem in computer vision in the sense that the image background can challenge its performance, although they learn very well on training data. In this work, we propose to improve Capsule Networks'…
In this work we investigate how to achieve equivariance to input transformations in deep networks, purely from data, without being given a model of those transformations. Convolutional Neural Networks (CNNs), for example, are equivariant to…
Convolutional neural networks (CNNs) have been established as the main workhorse in image data processing; nonetheless, they require large amounts of data to train, often produce overconfident predictions, and frequently lack the ability to…
We propose Lattice gauge equivariant Convolutional Neural Networks (L-CNNs) for generic machine learning applications on lattice gauge theoretical problems. At the heart of this network structure is a novel convolutional layer that…
Convolutional neural networks (CNNs) have enabled the state-of-the-art performance in many computer vision tasks. However, little effort has been devoted to establishing convolution in non-linear space. Existing works mainly leverage on the…
In recent years, the CNNs have achieved great successes in the image processing tasks, e.g., image recognition and object detection. Unfortunately, traditional CNN's classification is found to be easily misled by increasingly complex image…
In convolutional neural networks (CNNs), the filter grouping in convolution layers is known to be useful to reduce the network parameter size. In this paper, we propose a new logarithmic filter grouping which can capture the nonlinearity of…
Depthwise convolution and grouped convolution has been successfully applied to improve the efficiency of convolutional neural network (CNN). We suggest that these models can be considered as special cases of a generalized convolution…
We review a novel neural network architecture called lattice gauge equivariant convolutional neural networks (L-CNNs), which can be applied to generic machine learning problems in lattice gauge theory while exactly preserving gauge…
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…
In many machine learning tasks it is desirable that a model's prediction transforms in an equivariant way under transformations of its input. Convolutional neural networks (CNNs) implement translational equivariance by construction; for…