Related papers: Theory for Equivariant Quantum Neural Networks

Quantum Machine Learning (QML) models are aimed at learning from data encoded in quantum states. Recently, it has been shown that models with little to no inductive biases (i.e., with no assumptions about the problem embedded in the model)…

Quantum machine learning models based on parametrized quantum circuits, also called quantum neural networks (QNNs), are considered to be among the most promising candidates for applications on near-term quantum devices. Here we explore the…

Artificial neural networks have achieved great success in many fields ranging from image recognition to video understanding. However, its high requirements for computing and memory resources have limited further development on processing…

In this paper, we present a novel framework for enhancing the performance of Quanvolutional Neural Networks (QuNNs) by introducing trainable quanvolutional layers and addressing the critical challenges associated with them. Traditional…

Employing equivariance in neural networks leads to greater parameter efficiency and improved generalization performance through the encoding of domain knowledge in the architecture; however, the majority of existing approaches require an a…

Incorporating symmetry as an inductive bias into neural network architecture has led to improvements in generalization, data efficiency, and physical consistency in dynamics modeling. Methods such as CNNs or equivariant neural networks use…

Equivariant neural networks provide a principled framework for incorporating symmetry into learning architectures and have been extensively analyzed through the lens of their separation power, that is, the ability to distinguish inputs…

Deep learning has been shown to be able to recognize data patterns better than humans in specific circumstances or contexts. In parallel, quantum computing has demonstrated to be able to output complex wave functions with a few number of…

We introduce Group equivariant Convolutional Neural Networks (G-CNNs), a natural generalization of convolutional neural networks that reduces sample complexity by exploiting symmetries. G-CNNs use G-convolutions, a new type of layer that…

We survey the mathematical foundations of geometric deep learning, focusing on group equivariant and gauge equivariant neural networks. We develop gauge equivariant convolutional neural networks on arbitrary manifolds $\mathcal{M}$ using…

Convolutional Neural Network (CNN) is a popular model in computer vision and has the advantage of making good use of the correlation information of data. However, CNN is challenging to learn efficiently if the given dimension of data or…

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.…

In recent years, deep learning techniques have shown great success in various tasks related to inverse problems, where a target quantity of interest can only be observed through indirect measurements by a forward operator. Common approaches…

We study the problem of learning equivariant neural networks via gradient descent. The incorporation of known symmetries ("equivariance") into neural nets has empirically improved the performance of learning pipelines, in domains ranging…

Quantum neural networks (QNNs) represent a pioneering intersection of quantum computing and deep learning. In this study, we unveil a fundamental convolution property inherent to QNNs, stemming from the natural parallelism of quantum gate…

Data arrives at our senses as a continuous stream, smoothly transforming from one instant to the next. These smooth transformations can be viewed as continuous symmetries of the environment that we inhabit, defining equivalence relations…

Quantum convolutional neural networks (QCNNs) represent a promising approach in quantum machine learning, paving new directions for both quantum and classical data analysis. This approach is particularly attractive due to the absence of the…

The last few decades have seen significant breakthroughs in the fields of deep learning and quantum computing. Research at the junction of the two fields has garnered an increasing amount of interest, which has led to the development of…

We introduce Quantum Graph Neural Networks (QGNN), a new class of quantum neural network ansatze which are tailored to represent quantum processes which have a graph structure, and are particularly suitable to be executed on distributed…

Quantum machine learning has established as an interdisciplinary field to overcome limitations of classical machine learning and neural networks. This is a field of research which can prove that quantum computers are able to solve problems…