Related papers: On the explainability of quantum neural networks b…
The power and expressivity of deep classical neural networks can be attributed to non-linear input-output relations. Such non-linearities are at the heart of many computational tasks, such as data classification and pattern recognition.…
Recurrent neural networks are the foundation of many sequence-to-sequence models in machine learning, such as machine translation and speech synthesis. In contrast, applied quantum computing is in its infancy. Nevertheless there already…
Quantum machine learning has the potential for broad industrial applications, and the development of quantum algorithms for improving the performance of neural networks is of particular interest given the central role they play in machine…
We establish a formal bridge between qubit-based and photonic quantum computing. We do this by defining a functor from the ZX calculus to linear optical circuits. In the process we provide a compositional theory of quantum linear optics…
Conceptual and mathematical models of neurons have lagged behind empirical understanding for decades. Here we extend previous work in modeling biological systems with fully scale-independent quantum information-theoretic tools to develop a…
The term quantum neural computing indicates a unity in the functioning of the brain. It assumes that the neural structures perform classical processing and that the virtual particles associated with the dynamical states of the structures…
We report on a gate-based variational quantum classifier implemented with single photons and probabilistic gates, to emulate the standard quantum circuit model framework. We evaluate the expressive power of two deployable quantum neural…
Complex-valued neural networks (CVNNs) have been shown to be powerful nonlinear approximators when the input data can be properly modeled in the complex domain. One of the major challenges in scaling up CVNNs in practice is the design of…
We develop a variational framework to understand the properties of the functions learned by neural networks fit to data. We propose and study a family of continuous-domain linear inverse problems with total variation-like regularization in…
A "numerical set-expression" is a term specifying a cascade of arithmetic and logical operations to be performed on sets of non-negative integers. If these operations are confined to the usual Boolean operations together with the result of…
Linear Regression and neural networks are widely used to model data. Neural networks distinguish themselves from linear regression with their use of activation functions that enable modeling nonlinear functions. The standard argument for…
We are concerned with an approximation problem for a symmetric positive semidefinite matrix due to motivation from a class of nonlinear machine learning methods. We discuss an approximation approach that we call {matrix ridge…
Quantum operations on pure states can be fully represented by unitary matrices. Variational quantum circuits, also known as quantum neural networks, embed data and trainable parameters into gate-based operations and optimize the parameters…
Recent advances in machine learning have led to a surge in adoption of neural networks for various tasks, but lack of interpretability remains an issue for many others in which an understanding of the features influencing the prediction is…
In recent years, neural networks (NNs) have driven significant advances in machine learning. However, as tasks grow more complex, NNs often require large numbers of trainable parameters, which increases computational and energy demands.…
Representations of multivariate functions with low-dimensional functions that depend on subsets of original coordinates (corresponding of different orders of coupling) are useful in quantum dynamics and other applications, especially where…
Neuroscientists face challenges in analyzing high-dimensional neural recording data of dense functional networks. Without ground-truth reference data, finding the best algorithm for recovering neurologically relevant networks remains an…
The noisy intermediate-scale quantum (NISQ) devices enable the implementation of the variational quantum circuit (VQC) for quantum neural networks (QNN). Although the VQC-based QNN has succeeded in many machine learning tasks, the…
For the past 30 years or so, machine learning has stimulated a great deal of research in the study of approximation capabilities (expressive power) of a multitude of processes, such as approximation by shallow or deep neural networks,…
Characterizing the function spaces corresponding to neural networks can provide a way to understand their properties. In this paper we discuss how the theory of reproducing kernel Banach spaces can be used to tackle this challenge. In…