相关论文: Pairing renormalization and regularization within …

Despite huge successes on a wide range of tasks, neural networks are known to sometimes struggle to generalise to unseen data. Many approaches have been proposed over the years to promote the generalisation ability of neural networks,…

We formulate the renormalization procedure using the domain wall regularization that is based on the heat-kernel method. The quantum effects of both fermions and bosons (gauge fields) are taken into account. The background field method is…

Deep Neural Networks have achieved remarkable success relying on the developing high computation capability of GPUs and large-scale datasets with increasing network depth and width in image recognition, object detection and many other…

Recently \cite{Horowitz:2022rpp,Horowitz:2022uak}, denominator regularisation (Den. Reg.) scheme has been proposed to handle divergences in quantum field theory. It is shown to yield results as simple as in dimensional regularisation scheme…

A divergence-free approach to relativistic quantum electrodynamics based on regularisation of equations of quantum mechanics is discussed. This approach is shown to be exactly equivalent to the conventional Feynman-Dyson renormalisation…

We illustrate the dimensional regularization technique using a simple problem from elementary electrostatics. We contrast this approach with the cutoff regularization approach, and demonstrate that dimensional regularization preserves the…

We discuss an alternative method to mass renormalize a quantum field Hamiltonian based on a requirement that the vacuum and single-particle sectors are not self-scattering. We illustrate the feasibility of this method for the concrete…

We discuss structural aspects of the functional renormalisation group. Flows for a general class of correlation functions are derived, and it is shown how symmetry relations of the underlying theory are lifted to the regularised theory. A…

The graph matching problem is a significant special case of the Quadratic Assignment Problem, with extensive applications in pattern recognition, computer vision, protein alignments and related fields. As the problem is NP-hard, relaxation…

Scalar field theory at finite temperature is investigated via an improved renormalization group prescription which provides an effective resummation over all possible non-overlapping higher loop graphs. Explicit analyses for the lambda…

We give an introduction to renormalisation, focusing first on a pedagogical description of fundamental concepts of the procedure and its features, then we introduce the renormalisation group and its equations. We discuss then the case of…

The study of nonlinear phenomena in systems with many degrees of freedom often relies on complex numerical simulations. In trying to model realistic situations, these systems may be coupled to an external environment which drives their…

We study the application of the exact renormalisation group to a many-fermion system with a short-range attractive force. We introduce a boson field to describe pairing effects, and take a simple ansatz for the effective action. We derive a…

The strong correlation between neurons or filters can significantly weaken the generalization ability of neural networks. Inspired by the well-known Tammes problem, we propose a novel diversity regularization method to address this issue,…

A Shell-model-Like APproach (SLAP) suggested to treat the pairing correlations in relativistic mean field theory is introduced, in which the occupancies thus obtained having been iterated back into the densities. The formalism and numerical…

We consider the inverse problem of reconstructing inhomogeneities by performing a finite number of scattering measurements of acoustic type in the time-harmonic setting. We set up the reconstruction as a fully discrete variational problem…

The point-splitting renormalization method offers a prescription to calculate finite expectation values of quadratic operators constructed from quantum fields in a general curved spacetime. It has been recently shown by Levi and Ori that…

In recent years, mixup regularization has gained popularity as an effective way to improve the generalization performance of deep learning models by training on convex combinations of training data. While many mixup variants have been…

We consider regularization methods based on the coupling of Tikhonov regularization and projection strategies. From the resulting constraint regularization method we obtain level set methods in a straight forward way. Moreover, we show that…

We describe the use of the Density Matrix Renormalization Group method as a means of approximately solving large-scale nuclear shell-model problems. We focus on an angular-momentum-conserving variant of the method and report test results…