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Proposing an effective and flexible matrix to represent a graph is a fundamental challenge that has been explored from multiple perspectives, e.g., filtering in Graph Fourier Transforms. In this work, we develop a novel and general…

Quantum neural networks (QNNs), represented by parameterized quantum circuits, can be trained in the paradigm of supervised learning to map input data to predictions. Much work has focused on theoretically analyzing the expressive power of…

In the recent years we have witnessed a rapid development of new algorithmic techniques for parameterized algorithms for graph separation problems. We present experimental evaluation of two cornerstone theoretical results in this area:…

Tensor diagonalization means transforming a given tensor to an exactly or nearly diagonal form through multiplying the tensor by non-orthogonal invertible matrices along selected dimensions of the tensor. It is generalization of approximate…

We establish a family of subspace-based learning method for multi-view learning using the least squares as the fundamental basis. Specifically, we investigate orthonormalized partial least squares (OPLS) and study its important properties…

In areas such as computer software and hardware, manufacturing systems, and transportation, engineers encounter networks with arbitrarily large numbers of isomorphic subprocesses. Parameterized systems provide a framework for modeling such…

Estimating properties of quantum states, such as fidelities, molecular energies, and correlation functions, is a fundamental task in quantum information science. Due to the limitation of practical quantum devices, including limited circuit…

Hyperspectral analysis has gained popularity over recent years as a way to infer what materials are displayed on a picture whose pixels consist of a mixture of spectral signatures. Computing both signatures and mixture coefficients is known…

Constrained least squares problems arise in many applications. Their memory and computation costs are expensive in practice involving high-dimensional input data. We employ the so-called "sketching" strategy to project the least squares…

Tensor networks (TNs) have become one of the most essential building blocks for various fields of theoretical physics such as condensed matter theory, statistical mechanics, quantum information, and quantum gravity. This review provides a…

Recurrent Neural Network (RNN) are a popular choice for modeling temporal and sequential tasks and achieve many state-of-the-art performance on various complex problems. However, most of the state-of-the-art RNNs have millions of parameters…

Tensor-network techniques have enjoyed outstanding success in physics, and have recently attracted attention in machine learning, both as a tool for the formulation of new learning algorithms and for enhancing the mathematical understanding…

Tensor networks provide compact and scalable representations of high-dimensional data, enabling efficient computation in fields such as quantum physics, numerical partial differential equations (PDEs), and machine learning. This paper…

In the context of kernel machines, polynomial and Fourier features are commonly used to provide a nonlinear extension to linear models by mapping the data to a higher-dimensional space. Unless one considers the dual formulation of the…

In this paper we formulate and solve a robust least squares problem for a system of linear equations subject to quantization error in the data matrix. Ordinary least squares fails to consider uncertainty in the operator, modeling all noise…

The expressivity of Graph Neural Networks (GNNs) has been studied broadly in recent years to reveal the design principles for more powerful GNNs. Graph canonization is known as a typical approach to distinguish non-isomorphic graphs, yet…

The proposed article aims at offering a comprehensive tutorial for the computational aspects of structured matrix and tensor factorization. Unlike existing tutorials that mainly focus on {\it algorithmic procedures} for a small set of…

Graph convolutional networks (GCNs) have been attracting widespread attentions due to their encouraging performance and powerful generalizations. However, few work provide a general view to interpret various GCNs and guide GCNs' designs. In…

Tensor decompositions, which represent an $N$-order tensor using approximately $N$ factors of much smaller dimensions, can significantly reduce the number of parameters. This is particularly beneficial for high-order tensors, as the number…

Neural network parameterizations exhibit inherent symmetries that yield multiple equivalent minima within the loss landscape. Scale Graph Metanetworks (ScaleGMNs) explicitly leverage these symmetries by proposing an architecture equivariant…