Related papers: Trained quantum neural networks are Gaussian proce…

We study the supervised learning problem under either of the following two models: (1) Feature vectors ${\boldsymbol x}_i$ are $d$-dimensional Gaussians and responses are $y_i = f_*({\boldsymbol x}_i)$ for $f_*$ an unknown quadratic…

In this paper we provide explicit upper bounds on some distances between the (law of the) output of a random Gaussian NN and (the law of) a random Gaussian vector. Our results concern both shallow random Gaussian neural networks with…

Probabilistic machine learning models are distinguished by their ability to integrate prior knowledge of noise statistics, smoothness parameters, and training data uncertainty. A common approach involves modeling data with Gaussian…

Gaussian processes (GPs) are an attractive class of machine learning models because of their simplicity and flexibility as building blocks of more complex Bayesian models. Meanwhile, graph neural networks (GNNs) emerged recently as a…

Although tensor networks are powerful tools for simulating low-dimensional quantum physics, tensor network algorithms are very computationally costly in higher spatial dimensions. We introduce quantum gauge networks: a different kind of…

Bayesian inference promises a framework for principled uncertainty quantification of neural network predictions. Barriers to adoption include the difficulty of fully characterizing posterior distributions on network parameters and the…

Quantum neural networks (QNNs), an interdisciplinary field of quantum computing and machine learning, have attracted tremendous research interests due to the specific quantum advantages. Despite lots of efforts developed in computer vision…

Generative Flow Networks (GFlowNets) are a new family of probabilistic samplers where an agent learns a stochastic policy for generating complex combinatorial structure through a series of decision-making steps. Despite being inspired from…

The training of a parameterized model largely depends on the landscape of the underlying loss function. In particular, vanishing gradients are a central bottleneck in the scalability of variational quantum algorithms (VQAs), and are known…

Wide neural networks with random weights and biases are Gaussian processes, as originally observed by Neal (1995) and more recently by Lee et al. (2018) and Matthews et al. (2018) for deep fully-connected networks, as well as by Novak et…

We provide in this paper a concrete method for training a quantum neural network to maximize the relevant information about a property that is transmitted through the network. This is significant because it gives an operationally well…

Quantum neural networks (QNNs) encounter significant challenges in realizing nonlinear behavior and effectively optimizing parameters. This study addresses these issues by modeling nonlinearity through a Taylor series expansion, where the…

In a recently published paper [1], it is shown that deep neural networks (DNNs) with random Gaussian weights preserve the metric structure of the data, with the property that the distance shrinks more when the angle between the two data…

Recurrent neural networks play an important role in both research and industry. With the advent of quantum machine learning, the quantisation of recurrent neural networks has become recently relevant. We propose fully quantum recurrent…

Quantum neural networks (QNNs) is a parameterized quantum circuit model, which can be trained by gradient-based optimizer, can be used for supervised learning, regression tasks, combinatorial optimization, etc. Although many works have…

We introduce a general method for building neural networks on quantum computers. The quantum neural network is a variational quantum circuit built in the continuous-variable (CV) architecture, which encodes quantum information in continuous…

Gradient descent methods have long been the de facto standard for training deep neural networks. Millions of training samples are fed into models with billions of parameters, which are slowly updated over hundreds of epochs. Recently, it's…

Quantum computing enables quantum neural networks (QNNs) to have great potentials to surpass artificial neural networks (ANNs). The powerful generalization of neural networks is attributed to nonlinear activation functions. Although various…

Graph convolutional neural networks~(GCNs) have recently demonstrated promising results on graph-based semi-supervised classification, but little work has been done to explore their theoretical properties. Recently, several deep neural…

Quantum state tomography (QST) aiming at reconstructing the density matrix of a quantum state plays an important role in various emerging quantum technologies. Recognizing the challenges posed by imperfect measurement data, we develop a…