Related papers: Implicit Bias of Linear Equivariant Networks
Quantum Neural Networks (QNNs) are suggested as one of the quantum algorithms which can be efficiently simulated with a low depth on near-term quantum hardware in the presence of noises. However, their performance highly relies on choosing…
Group convolutional neural networks (G-CNNs) can be used to improve classical CNNs by equipping them with the geometric structure of groups. Central in the success of G-CNNs is the lifting of feature maps to higher dimensional disentangled…
Currently, increasingly deeper neural networks have been applied to improve their accuracy. In contrast, We propose a novel wider Convolutional Neural Networks (CNN) architecture, motivated by the Multi-column Deep Neural Networks and the…
Equivariances provide useful inductive biases in neural network modeling, with the translation equivariance of convolutional neural networks being a canonical example. Equivariances can be embedded in architectures through weight-sharing…
Group convolutional neural networks (G-CNNs) have been shown to increase parameter efficiency and model accuracy by incorporating geometric inductive biases. In this work, we investigate the properties of representations learned by regular…
The rising adoption of machine learning in high energy physics and lattice field theory necessitates the re-evaluation of common methods that are widely used in computer vision, which, when applied to problems in physics, can lead to…
The recent success of neural network models has shone light on a rather surprising statistical phenomenon: statistical models that perfectly fit noisy data can generalize well to unseen test data. Understanding this phenomenon of…
Understanding the asymptotic behavior of gradient-descent training of deep neural networks is essential for revealing inductive biases and improving network performance. We derive the infinite-time training limit of a mathematically…
Group equivariant neural networks have been explored in the past few years and are interesting from theoretical and practical standpoints. They leverage concepts from group representation theory, non-commutative harmonic analysis and…
Many scientific and geometric problems exhibit general linear symmetries, yet most equivariant neural networks are built for compact groups or simple vector features, limiting their reuse on matrix-valued data such as covariances, inertias,…
Many data symmetries can be described in terms of group equivariance and the most common way of encoding group equivariances in neural networks is by building linear layers that are group equivariant. In this work we investigate whether…
We propose a novel class of neural network-like parametrized functions, i.e., general transformation neural networks (GTNNs), for high-dimensional approximation. Conventional deep neural networks sometimes perform less accurately on…
Neural functional networks (NFNs) have recently gained significant attention due to their diverse applications, ranging from predicting network generalization and network editing to classifying implicit neural representation. Previous NFN…
Many learning problems involve symmetries, and while invariance can be built into neural architectures, it can also emerge implicitly when training on group-structured data. We study this phenomenon in classical Hopfield networks and show…
The translational equivariant nature of Convolutional Neural Networks (CNNs) is a reason for its great success in computer vision. However, networks do not enjoy more general equivariance properties such as rotation or scaling, ultimately…
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…
We introduce a general method for achieving robust group-invariance in group-equivariant convolutional neural networks ($G$-CNNs), which we call the $G$-triple-correlation ($G$-TC) layer. The approach leverages the theory of the…
The Symmetric group $S_{n}$ manifests itself in large classes of quantum systems as the invariance of certain characteristics of a quantum state with respect to permuting the qubits. The subgroups of $S_{n}$ arise, among many other…
Equivariant networks are specifically designed to ensure consistent behavior with respect to a set of input transformations, leading to higher sample efficiency and more accurate and robust predictions. However, redesigning each component…
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…