Related papers: Relative Resolution: An Analysis with the Kullback…
We consider the theoretical model of Bergmann and Lebowitz for open systems out of equilibrium and translate its principles in the adaptive resolution molecular dynamics technique (AdResS). We simulate Lennard-Jones fluids with open…
We discuss a class of coupled systems of nonlocal nonlinear balance laws modeling multilane traffic, with the nonlocality present in both convective and source terms. The uniqueness and existence of the entropy solution are proven via…
Referring Expression Comprehension (REC) is a popular multimodal task that aims to accurately detect target objects within a single image based on a given textual expression. However, due to the limitations of earlier models, traditional…
Maximizing the Kullback-Leibler divergence (KLD) is a fundamental problem in waveform design for active sensing and hypothesis testing, as it directly relates to the error exponent of detection probability. However, the associated…
Model or variable selection is usually achieved through ranking models according to the increasing order of preference. One of methods is applying Kullback-Leibler distance or relative entropy as a selection criterion. Yet that will raise…
We study the relative R\'enyi entropy (RRE) under local quenches in two-dimensional conformal field theories (CFTs), focusing on rational CFTs (RCFTs) and holographic CFTs. In RCFTs, the RRE evolves as a monotonic function over time,…
This paper establishes the minimum entropy principle (MEP) for the relativistic Euler equations with a broad class of equations of state (EOSs) and addresses the challenge of preserving the local version of the discovered MEP in high-order…
We study the problem of closeness testing for continuous distributions and its implications for causal discovery. Specifically, we analyze the sample complexity of distinguishing whether two multidimensional continuous distributions are…
In this paper, we investigate the matrix estimation problem in the multi-response regression model with measurement errors. A nonconvex error-corrected estimator based on a combination of the amended loss function and the nuclear norm…
The capability of a novel Kullback-Leibler divergence method is examined herein within the Kalman filter framework to select the input-parameter-state estimation execution with the most plausible results. This identification suffers from…
We present a general framework for the approximation of systems of hyperbolic balance laws. The novelty of the analysis lies in the construction of suitable relaxation systems and the derivation of a delicate estimate on the relative…
Supervised deep learning approaches can artificially increase the resolution of microscopy images by learning a mapping between two image resolutions or modalities. However, such methods often require a large set of hard-to-get…
Shannon entropy is not the only entropy that is relevant to machine-learning datasets, nor possibly even the most important one. Traditional entropies such as Shannon entropy capture information represented by elements' frequencies but not…
Reinforcement learning (RL) is a key paradigm for post-training large language models (LLMs), but the widely used Group Relative Policy Optimization (GRPO) often suffers from entropy collapse: exploration quickly disappears, policies…
Selecting an appropriate divergence measure is a critical aspect of machine learning, as it directly impacts model performance. Among the most widely used, we find the Kullback-Leibler (KL) divergence, originally introduced in kinetic…
The problem of filtering information from large correlation matrices is of great importance in many applications. We have recently proposed the use of the Kullback-Leibler distance to measure the performance of filtering algorithms in…
Standard single-image super-resolution (SR) upsamples and restores entire images. Yet several real-world applications require higher resolutions only in specific regions, such as license plates or faces, making the super-resolution of the…
The asymptotic correspondence between the probability mass function of the $q$-deformed multinomial distribution and the $q$-generalised Kullback-Leibler divergence, also known as Tsallis relative entropy, is established. The probability…
Tunable Diode Laser Absorption Spectroscopy (TDLAS) tomography has been widely used for in situ combustion diagnostics, yielding images of both species concentration and temperature. The temperature image is generally obtained from the…
Over the last decade, kernel methods for nonlinear processing have successfully been used in the machine learning community. The primary mathematical tool employed in these methods is the notion of the Reproducing Kernel Hilbert Space.…