Related papers: On group averaging for non-compact groups
The relationship between mappings of sets and renormalization group transformations is established, and renormalization group invariants of such mappings are found. These results are valid both for continuous and discrete mappings and for…
This paper is devoted to provide a theoretical underpinning for ensemble forecasting with rapid fluctuations in body forcing and in boundary conditions. Ensemble averaging principles are proved under suitable `mixing' conditions on random…
Group imbalance has been a known problem in empirical risk minimization (ERM), where the achieved high average accuracy is accompanied by low accuracy in a minority group. Despite algorithmic efforts to improve the minority group accuracy,…
We consider the averaging principle for deterministic or stochastic systems with a fast stochastic component (family of continuous-time Markov chains depending on the state of the system as a parameter). We show that, due to bifurcations in…
Disaggregated evaluation is a central task in AI fairness assessment, where the goal is to measure an AI system's performance across different subgroups defined by combinations of demographic or other sensitive attributes. The standard…
We ask when a finite set of t-structures in a triangulated category can be `averaged' into one t-structure or, equivalently, when the extension closure of a finite set of aisles is again an aisle. There is a straightforward, positive answer…
Various uses of the renormalization group are examined.
Grouping structures arise naturally in many statistical modeling problems. Several methods have been proposed for variable selection that respect grouping structure in variables. Examples include the group LASSO and several concave group…
Non-adaptive group testing refers to the problem of inferring a sparse set of defectives from a larger population using the minimum number of simultaneous pooled tests. Recent positive results for noiseless group testing have motivated the…
Group testing, a problem with diverse applications across multiple disciplines, traditionally assumes independence across nodes' states. Recent research, however, focuses on real-world scenarios that often involve correlations among nodes,…
Using the damped pendulum system we introduce the averaging method to study the periodic solutions of a dynamical system with small perturbation. We provide sufficient conditions for the existence of periodic solutions with small amplitude…
The renormalization group is not only a powerful method for describing universal properties of phase transitions but it is also useful for evaluating non- universal properties beyond mean-field theory. In this contribution we concentrate on…
We present an averaging process for sections of a torsor under a unipotent group. This process allows one to integrate local sections of such a torsor into a global simplicial section. The results of this paper have applications to…
Estimating the generalization error (GE) of machine learning models is fundamental, with resampling methods being the most common approach. However, in non-standard settings, particularly those where observations are not independently and…
A method is described to probe high-scale physics in lower-energy experiments by employing sum rules in terms of renormalisation group invariants. The method is worked out in detail for the study of supersymmetry-breaking mechanisms in the…
When averages of different experimental determinations of the same quantity are computed, each with statistical and systematic error components, then frequently the statistical and systematic components of the combined error are quoted…
The review presents general methods for treating complicated problems that cannot be solved exactly and whose solution encounters two major difficulties. First, there are no small parameters allowing for the safe use of perturbation theory…
This talk is an overview of selected topics related to renormalization group flows and the phases of gauge theories.
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…
Over the last several years, there has been a resurgence of interest in using non-perturbative approximation methods based on Wilson's continuous renormalization group. In this lecture, I review progress particularly in the past year,…