Related papers: Resummed Distribution Functions: Making Perturbati…
This paper presents an enhanced adaptive random Fourier features (ARFF) training algorithm for shallow neural networks, building upon the work introduced in "Adaptive Random Fourier Features with Metropolis Sampling", Kammonen et al.,…
We present an iterative framework to improve the amortized approximations of posterior distributions in the context of Bayesian inverse problems, which is inspired by loop-unrolled gradient descent methods and is theoretically grounded in…
We introduce a method for the estimation of uncertainties in density-functional-theory (DFT) calculations for atomistic systems. The method is based on the construction of an uncertainty-aware functional distribution (UAFD) in a space…
In this short paper, we are considering the connection between the \emph{Residual Distribution Schemes} (RD) and the \emph{Flux Reconstruction} (FR) approach. We demonstrate that flux reconstruction can be recast into the RD framework and…
In this paper the relation between nonanticipative rate distortion function (RDF) and Bayesian filtering theory is further investigated on general Polish spaces. The relation is established via an optimization on the space of conditional…
Using a recent calculation of the perturbative hard part for dilepton production that sums large threshold corrections to all orders in perturbative QCD, we compute the corresponding cross sections. The hard part has been evaluated using…
Nuclear density functional theory (DFT) is one of the main theoretical tools used to study the properties of heavy and superheavy elements, or to describe the structure of nuclei far from stability. While on-going efforts seek to better…
The joint nonanticipative rate distortion function (NRDF) for a tuple of random processes with individual fidelity criteria is considered. Structural properties of optimal test channel distributions are derived. Further, for the application…
We show that the functional renormalization group (FRG) allows for the calculation of the probability distribution function of the sum of strongly correlated random variables. On the example of the three-dimensional Ising model at…
In this work, we are devoted to the reconstruction of an unknown initial value from the terminal data. The asymptotic and root-distribution properties of Mittag-Leffler functions are used to establish stability of the backward problem.…
Reinforcement Learning from Human Feedback (RLHF) has become a cornerstone technique for post-training large language models. While most existing approaches rely on the reverse KL-regularization, recent empirical studies have begun…
Recovery of signals with elements defined on the nodes of a graph, from compressive measurements is an important problem, which can arise in various domains such as sensor networks, image reconstruction and group testing. In some scenarios,…
We develop a renormalization group (RG)-based perturbation scheme for a class of ordinary differential equations, including first-order systems with semisimple or nilpotent linear parts, as well as scalar higher-order equations. The key…
We consider a remote source coding problem subject to a {distortion function}. Contrary to the use of the classical separable distortion criterion, herein we consider the more general, $f$-separable distortion measure and study its…
Various perturbation series are factorially divergent. The behavior of their high-order terms can be found by Lipatov's method, according to which they are determined by the saddle-point configurations (instantons) of appropriate functional…
Operator learning is a data-driven approximation of mappings between infinite-dimensional function spaces, such as the solution operators of partial differential equations. Kernel-based operator learning can offer accurate, theoretically…
We discuss the resummation approach in QCD Analytic Perturbation Theory (APT). We start with a simple example of asymptotic power series for a zero-dimensional analog of the scalar $g\,\phi^4$ model. Then we give a short historic preamble…
Perturbative renormalization group theory is developed as a unified tool for global asymptotic analysis. With numerous examples, we illustrate its application to ordinary differential equation problems involving multiple scales, boundary…
Anomaly detection in time series data is crucial across various domains. The scarcity of labeled data for such tasks has increased the attention towards unsupervised learning methods. These approaches, often relying solely on reconstruction…
Rabi oscillations have long been thought to be out of reach in simulations using time-dependent density functional theory (TDDFT), a prominent symptom of the failure of the adiabatic approximation for non-perturbative dynamics. We present a…