Related papers: Permutation-equivariant quantum convolutional neur…

Quantum neural networks combine quantum computing with advanced data-driven methods, offering promising applications in quantum machine learning. However, the optimal paradigm for balancing trainability and expressivity in QNNs remains an…

Quantum and classical machine learning have been naturally connected through kernel methods, which have also served as proof-of-concept for quantum advantage. Quantum embeddings encode classical data into quantum feature states, enabling…

Recent advances in deep learning and Transformers have driven major breakthroughs in robotics by employing techniques such as imitation learning, reinforcement learning, and LLM-based multimodal perception and decision-making. However,…

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…

We introduce a Sinkhorn-type algorithm for producing quantum permutation matrices encoding symmetries of graphs. Our algorithm generates square matrices whose entries are orthogonal projections onto one-dimensional subspaces satisfying a…

While Quantum Convolutional Neural Networks (QCNNs) offer a theoretical paradigm for quantum machine learning, their practical implementation is severely bottlenecked by barren plateaus -- the exponential vanishing of gradients -- and poor…

Equivariant neural networks (ENNs) have been shown to be extremely effective in applications involving underlying symmetries. By construction ENNs cannot produce lower symmetry outputs given a higher symmetry input. However, symmetry…

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…

The weight-sharing mechanism of convolutional kernels ensures translation-equivariance of convolution neural networks (CNNs). Recently, rotation-equivariance has been investigated. However, research on scale-equivariance or simultaneous…

The neural network and quantum computing are both significant and appealing fields, with their interactive disciplines promising for large-scale computing tasks that are untackled by conventional computers. However, both developments are…

How can prior knowledge on the transformation invariances of a domain be incorporated into the architecture of a neural network? We propose Equivariant Transformers (ETs), a family of differentiable image-to-image mappings that improve the…

$G$-equivariant convolutional neural networks (GCNNs) is a geometric deep learning model for data defined on a homogeneous $G$-space $\mathcal{M}$. GCNNs are designed to respect the global symmetry in $\mathcal{M}$, thereby facilitating…

Convolutional Neural Networks (CNNs) traditionally encode translation equivariance via the convolution operation. Generalization to other transformations has recently received attraction to encode the knowledge of the data geometry in group…

Quantum neural networks (QNN) have been proposed as a promising architecture for quantum machine learning. There exist a number of different quantum circuit designs being branded as QNNs, however no clear candidate has presented itself as…

Convolutional neural networks revolutionized computer vision and natrual language processing. Their efficiency, as compared to fully connected neural networks, has its origin in the architecture, where convolutions reflect the translation…

Variational quantum algorithms are gaining attention as an early application of Noisy Intermediate-Scale Quantum (NISQ) devices. One of the main problems of variational methods lies in the phenomenon of Barren Plateaus, present in the…

The rapid growth of computer vision and increasingly complex image recognition tasks has exposed fundamental computational limitations of classical machine learning models, motivating the exploration of quantum computing as an emerging new…

Representing and learning from graphs is essential for developing effective machine learning models tailored to non-Euclidean data. While Graph Neural Networks (GNNs) strive to address the challenges posed by complex, high-dimensional graph…

Equivariant machine learning is an approach for designing deep learning models that respect the symmetries of the problem, with the aim of reducing model complexity and improving generalization. In this paper, we focus on an extension of…

Graph neural networks excel at modeling pairwise interactions, but they cannot flexibly accommodate higher-order interactions and features. Topological deep learning (TDL) has emerged recently as a promising tool for addressing this issue.…