Related papers: Theory for Equivariant Quantum Neural Networks
Recent works show that group equivariance as an inductive bias improves neural network performance for both classification and generation. However, designing group-equivariant neural networks is challenging when the group of interest is…
This paper introduces a new model to learn graph neural networks equivariant to rotations, translations, reflections and permutations called E(n)-Equivariant Graph Neural Networks (EGNNs). In contrast with existing methods, our work does…
Quantum Machine Learning (QML) has recently emerged as a highly promising research frontier. Within this domain, Quantum Neural Networks (QNNs),characterized by Variational Quantum Circuits (VQCs) at their core and featuring layers of…
Group equivariance (e.g. SE(3) equivariance) is a critical physical symmetry in science, from classical and quantum physics to computational biology. It enables robust and accurate prediction under arbitrary reference transformations. In…
This work is about understanding the impact of invariance and equivariance on generalisation in supervised learning. We use the perspective afforded by an averaging operator to show that for any predictor that is not equivariant, there is…
In recent years, with rapid progress in the development of quantum technologies, quantum machine learning has attracted a lot of interest. In particular, a family of hybrid quantum-classical neural networks, consisting of classical and…
Group convolutions and cross-correlations, which are equivariant to the actions of group elements, are commonly used in mathematics to analyze or take advantage of symmetries inherent in a given problem setting. Here, we provide efficient…
One hypothesis for the success of deep neural networks (DNNs) is that they are highly expressive, which enables them to be applied to many problems, and they have a strong inductive bias towards solutions that are simple, known as…
In this paper, we address the challenge of multivariate time-series forecasting using quantum machine learning techniques. We introduce adaptation strategies that extend variational quantum circuit models, traditionally limited to…
Hybrid quantum-classical neural networks represent a promising frontier in the search for improved machine learning models. This thesis explores the integration of quantum layers within classical convolutional neural network architectures,…
Neural networks are a promising tool for characterizing intermediate-scale quantum devices from limited amounts of measurement data. A challenging problem in this area is to learn the action of an unknown quantum process on an ensemble of…
Quantum neural networks (QNNs) have emerged as a leading strategy to establish applications in machine learning, chemistry, and optimization. While the applications of QNN have been widely investigated, its theoretical foundation remains…
Quantum deep learning is a research field for the use of quantum computing techniques for training deep neural networks. The research topics and directions of deep learning and quantum computing have been separated for long time, however by…
We consider the prediction of the Hamiltonian matrix, which finds use in quantum chemistry and condensed matter physics. Efficiency and equivariance are two important, but conflicting factors. In this work, we propose a SE(3)-equivariant…
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…
Group Convolutional Neural Networks (G-CNNs) constrain learned features to respect the symmetries in the selected group, and lead to better generalization when these symmetries appear in the data. If this is not the case, however,…
Many recent machine learning tasks resort to quantum computing to improve classification accuracy and training efficiency by taking advantage of quantum mechanics, known as quantum machine learning (QML). The variational quantum circuit…
Equivariance is a nice property to have as it produces much more parameter efficient neural architectures and preserves the structure of the input through the feature mapping. Even though some combinations of transformations might never…
This paper presents a comprehensive evaluation of the potential of Quantum Convolutional Neural Networks (QCNNs) in comparison to classical Convolutional Neural Networks (CNNs) and Artificial / Classical Neural Network (ANN) models. With…
Incorporating permutation equivariance into neural networks has proven to be useful in ensuring that models respect symmetries that exist in data. Symmetric tensors, which naturally appear in statistics, machine learning, and graph theory,…