Related papers: Constrained Differential Renormalization
Based only on simple principles of renormalization in coordinate space, we derive closed renormalized amplitudes and renormalization group constants at 1- and 2-loop orders for scalar field theories in general backgrounds. This is achieved…
Deep learning requires regularization mechanisms to reduce overfitting and improve generalization. We address this problem by a new regularization method based on distributional robust optimization. The key idea is to modify the…
The general method of the reduction in the number of coupling parameters is discussed. Using renormalization group invariance, theories with several independent couplings are related to a set of theories with a single coupling parameter.…
The method of differential renormalization is extended to the calculation of the one-loop graviton and gravitino corrections to $(g-2)_l$ in unbroken supergravity. Rewriting the singular contributions of all the diagrams in terms of only…
It is shown that the renormalization group method does not necessarily eliminate all secular terms in perturbation series to partial differential equations and a functional subspace of renormalizable secular solutions corresponds to a…
We propose and investigate efficient numerical methods for inverse problems related to Magnetic Resonance Imaging (MRI). Our goal is to extend the recent convergence results for the Landweber-Kaczmarz method obtained in [Haltmeier, Leitao,…
Semi-supervised learning is an important and active topic of research in pattern recognition. For classification using linear discriminant analysis specifically, several semi-supervised variants have been proposed. Using any one of these…
This paper pursues a twofold goal. First, we introduce and study in detail a new notion of variational analysis called generalized metric subregularity, which is a far-going extension of the conventional metric subregularity conditions. Our…
We present a technique for approximating generic normalization constants subject to constraints. The method is then applied to derive the exact asymptotics for the conditional normalization constant of constrained exponential random graphs.
This paper presents new variants of the averaged alternating modified reflections (AAMR) method for the best approximation problem. Under a mild constraint qualification, we first show its weak convergence and then establish a convergence…
Renormalization of massless Feynman amplitudes in $x$-space is reexamined here, using almost exclusively real-variable methods. We compute a wealth of concrete examples by means of recursive extension of distributions. This allows us to…
We consider the problem of recovering a set of correlated signals (e.g., images from different viewpoints) from a few linear measurements per signal. We assume that each sensor in a network acquires a compressed signal in the form of linear…
These lectures illustrate the key ideas of modern renormalization theory and effective field theories in the context of simple nonrelativistic quantum mechanics and the Schr\"odinger equation. They also discuss problems in QED, QCD and…
A reduction procedure for stochastic differential equations based on stochastic symmetries including Girsanov random transformations is proposed. In this setting, a new notion of reconstruction is given, involving the expectation values of…
We discuss the dependence of running couplings on the choice of regularization method in a general softly-broken N=1 supersymmetric theory. Regularization by dimensional reduction respects supersymmetry, but standard dimensional…
In this paper, we propose a constrained linear data-feature mapping model as an interpretable mathematical model for image classification using convolutional neural network (CNN) such as the ResNet. From this viewpoint, we establish the…
We review the renormalization of the electroweak sector of the standard model. The derivation also applies to the minimal supersymmetric standard model. We discuss regularization and the relation between the threshold corrections and the…
This article is an overview of supervised machine learning problems for regression and classification. Topics include: kernel methods, training by stochastic gradient descent, deep learning architecture, losses for classification,…
We investigate an operator renormalization group method to extract and describe the relevant degrees of freedom in the evolution of partial differential equations. The proposed renormalization group approach is formulated as an analytical…
We develop a formalism for performing real space renormalization group transformations of the "decimation type" using perturbation theory. The type of transformations beyond $d=1$ is nontrivial even for free theories. We check the formalism…