Related papers: Renormalization in the neural network-quantum fiel…
We investigate to what extent renormalization can be understood as an algebraic manipulation on concatenated one-loop integrals. We find that the resulting algebra indicates a useful connection to knot theory as well as number theory and…
The renormalisation of NN scattering in theories with zero-range interactions is examined using a cut-off regularisation and taking the cut-off to infinity. Inclusion of contact interactions that depend on energy as well as momentum allows…
Quantum neural networks (QNNs) use parameterized quantum circuits with data-dependent inputs and generate outputs through the evaluation of expectation values. Calculating these expectation values necessitates repeated circuit evaluations,…
Quantum network is an emerging type of network structure that leverages the principles of quantum mechanics to transmit and process information. Compared with classical data reconstruction algorithms, quantum networks make image…
The aim of this paper is to describe how to use regularization and renormalization to construct a perturbative quantum field theory from a Lagrangian. We first define renormalizations and Feynman measures, and show that although there need…
Disordered systems are interesting for many physical reasons. In this article, we study the renormalization group property of quenched disorder systems in the presence of a boundary. We construct examples of scalar field theories in various…
A systematic study of recursive renormalization of Feynman amplitudes is carried out both in Euclidean and in Minkowski configuration space. For a massless quantum field theory (QFT) we use the technique of extending associate homogeneous…
In all nontrivial cases renormalization, as it is usually formulated, is not a change of integration variables in the functional integral, plus parameter redefinitions, but a set of replacements, of actions and/or field variables and…
Understanding entanglement remains one of the most intriguing problems in physics. While particle and site entanglement have been studied extensively, the investigation of length or energy scale entanglement, quantifying the information…
Existing neural networks are memory-consuming and computationally intensive, making deploying them challenging in resource-constrained environments. However, there are various methods to improve their efficiency. Two such methods are…
We study two--loop renormalization in $(2+\epsilon)$--dimensional quantum gravity. As a first step towards the full calculation, we concentrate on the divergences which are proportional to the number of matter fields. We calculate the…
The Neural Tangent Kernel (NTK) has recently attracted intense study, as it describes the evolution of an over-parameterized Neural Network (NN) trained by gradient descent. However, it is now well-known that gradient descent is not always…
Recent research has tried to extend the concept of renormalization, which is naturally defined for geometric objects, to more general networks with arbitrary topology. The current attempts do not naturally apply to directed networks, for…
The asymptotic high momentum behaviour of quantum field theories with cubic interactions is investigated using renormalization group techniques in the asymmetric limit x << 1. Particular emphasis is paid to theories with interactions…
Quantum neural networks (QNNs) play an important role as an emerging technology in the rapidly growing field of quantum machine learning. While their empirical success is evident, the theoretical explorations of QNNs, particularly their…
It is shown how to construct renormalization group flows of quantum field theories in real space, as opposed to the usual Wilsonian approach in momentum space. This is achieved by generalizing the multiscale entanglement renormalization…
The process of renormalization to eliminate divergences arising in quantum field theory is not uniquely defined; one can always perform a finite renormalization, rendering finite perturbative results ambiguous. The consequences of making…
Generalization is an important feature of neural network, and there have been many studies on it. Recently, with the development of quantum compu-ting, it brings new opportunities. In this paper, we studied a class of quantum neural network…
A key open question in quantum computation is what advantages quantum neural networks (QNNs) may have over classical neural networks (NNs), and in what situations these advantages may transpire. Here we address this question by studying the…
Generalization beyond a training dataset is a main goal of machine learning, but theoretical understanding of generalization remains an open problem for many models. The need for a new theory is exacerbated by recent observations in deep…