Related papers: Equivalence of Dimensional Reduction and Dimension…
Some form of nonperturbative regularization is necessary if effective field theory treatments of the NN interaction are to yield finite answers. We discuss various regularization schemes used in the literature. Two of these methods involve…
For theories with multiple couplings we construct simple expressions for the four-dimensional (or, in general, integer-dimensional) renormalization constants assuming that all divergences are logarithmical. These expressions allow relating…
The sum of all ladder and rainbow diagrams in $\phi^3$ theory near 6 dimensions leads to self-consistent higher order differential equations in coordinate space which are not particularly simple for arbitrary dimension D. We have now…
The minibatch stochastic gradient descent method (SGD) is widely applied in deep learning due to its efficiency and scalability that enable training deep networks with a large volume of data. Particularly in the distributed setting, SGD is…
Large strongly correlated systems provide a challenge to modern electronic structure methods, because standard density functionals usually fail and traditional quantum chemical approaches are too demanding. The density-matrix…
We extend the universal one-loop effective action (UOLEA) by operators which translate between dimensional reduction (DRED) and dimensional regularization (DREG). These regularization scheme translating operators allow for an application of…
Despite perfectly interpolating the training data, deep neural networks (DNNs) can often generalize fairly well, in part due to the "implicit regularization" induced by the learning algorithm. Nonetheless, various forms of regularization,…
Regularisation theory in Banach spaces, and non--norm-squared regularisation even in finite dimensions, generally relies upon Bregman divergences to replace norm convergence. This is comparable to the extension of first-order optimisation…
Two-loop $\beta$-function and anomalous dimension are calculated for N=1 supersymmetric quantum electrodynamics, regularized by higher derivatives in the minimal subtraction scheme. The result for two-loop contribution to the…
Smoothness is a key inductive bias in machine learning and is closely related to generalization. Existing smoothness-inducing methods typically rely either on explicit gradient regularization, which often incurs substantial computational…
Regularization by Denoising (RED), as recently proposed by Romano, Elad, and Milanfar, is powerful image-recovery framework that aims to minimize an explicit regularization objective constructed from a plug-in image-denoising function.…
Inverse problems are inherently ill-posed, suffering from non-uniqueness and instability. Classical regularization methods provide mathematically well-founded solutions, ensuring stability and convergence, but often at the cost of reduced…
There has been a lot of interest in sufficient dimension reduction (SDR) methodologies as well as nonlinear extensions in the statistics literature. In this note, we use classical results regarding metric spaces and positive definite…
The renormalization algorithm based on regularization methods with two regulators is analyzed by means of explicit computations. We show in particular that regularization by higher covariant derivative terms can be complemented with…
Perturbation theory is a crucial tool for many physical systems, when exact solutions are not available, or nonperturbative numerical solutions are intractable. Naive perturbation theory often fails on long timescales, leading to secularly…
The matching between Schrodinger Functional renormalization schemes and conventional perturbative schemes is usually done using an intermediate lattice scheme. We propose to do the matching directly. This requires the perturbative…
We give a simple and elegant proof of the Equivalence Theorem, stating that two field theories related by nonlinear field transformations have the same S matrix. We are thus able to identify a subclass of nonrenormalizable field theories…
We consider variants of dimensional regularization, including the four-dimensional helicity scheme (FDH) and dimensional reduction (DRED), and present the gluon and quark form factors in the FDH scheme at next-to-next-to-leading order. We…
Various formulations of the exact renormalization group can be compared in the perturbative domain, in which we have reliable expressions for regularization-independent (universal) quantities. We consider the renormalization of the…
This is the first in a series of papers addressing the phenomenon of dimensional transmutation in nonrelativistic quantum mechanics within the framework of dimensional regularization. Scale-invariant potentials are identified and their…