Related papers: Deep Quantum Neural Networks are Gaussian Process

Building a quantum analog of classical deep neural networks represents a fundamental challenge in quantum computing. A key issue is how to address the inherent non-linearity of classical deep learning, a problem in the quantum domain due to…

Recent years have witnessed an increasing interest in the correspondence between infinitely wide networks and Gaussian processes. Despite the effectiveness and elegance of the current neural network Gaussian process theory, to the best of…

Quantum machine learning has established as an interdisciplinary field to overcome limitations of classical machine learning and neural networks. This is a field of research which can prove that quantum computers are able to solve problems…

Quantum Neural Networks (QNNs) with random structures have poor trainability due to the exponentially vanishing gradient as the circuit depth and the qubit number increase. This result leads to a general belief that a deep QNN will not be…

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…

Machine learning and quantum computing are two technologies that are causing a paradigm shift in the performance and behavior of certain algorithms, achieving previously unattainable results. Machine learning (kernel classification) has…

Quantum machine learning, focusing on quantum neural networks (QNNs), remains a vastly uncharted field of study. Current QNN models primarily employ variational circuits on an ansatz or a quantum feature map, often requiring multiple…

Quantum neural networks (QNNs) play a pivotal role in addressing complex tasks within quantum machine learning, analogous to classical neural networks in deep learning. Ensuring consistent performance across diverse datasets is crucial for…

We present a Gaussian kernel loss function and training algorithm for convolutional neural networks that can be directly applied to both distance metric learning and image classification problems. Our method treats all training features…

Kernel methods are a cornerstone of classical machine learning. The idea of using quantum computers to compute kernels has recently attracted attention. Quantum embedding kernels (QEKs) constructed by embedding data into the Hilbert space…

Hybrid Quantum Neural Networks (HQNNs) combine classical learning with parameterized quantum circuits, but their practical performance is often limited by (i) the noise of Noisy Intermediate-Scale Quantum (NISQ) devices and (ii) the large,…

While deep neural networks (DNNs) and Gaussian Processes (GPs) are both popularly utilized to solve problems in reinforcement learning, both approaches feature undesirable drawbacks for challenging problems. DNNs learn complex nonlinear…

The behavior of the gradient descent (GD) algorithm is analyzed for a deep neural network model with skip-connections. It is proved that in the over-parametrized regime, for a suitable initialization, with high probability GD can find a…

Whilst deep neural networks have shown great empirical success, there is still much work to be done to understand their theoretical properties. In this paper, we study the relationship between random, wide, fully connected, feedforward…

Knowing whether a Quantum Machine Learning model would perform well on a given dataset before training it can help to save critical resources. However, gathering a priori information about model performance (e.g., training speed, critical…

In current noisy intermediate-scale quantum devices, hybrid quantum-classical neural networks (HQNNs) represent a promising solution that combines the strengths of classical machine learning with quantum computing capabilities. Compared to…

Quantum kernel methods are a promising method in quantum machine learning thanks to the guarantees connected to them. Their accessibility for analytic considerations also opens up the possibility of prescreening datasets based on their…

Quantum computing has been revolutionizing the development of algorithms. However, only noisy intermediate-scale quantum devices are available currently, which imposes several restrictions on the circuit implementation of quantum…

At initialization, artificial neural networks (ANNs) are equivalent to Gaussian processes in the infinite-width limit, thus connecting them to kernel methods. We prove that the evolution of an ANN during training can also be described by a…

A neural architecture with randomly initialized weights, in the infinite width limit, is equivalent to a Gaussian Random Field whose covariance function is the so-called Neural Network Gaussian Process kernel (NNGP). We prove that a…