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Matrix scaling is a classical problem with a wide range of applications. It is known that the Sinkhorn algorithm for matrix scaling is interpreted as alternating e-projections from the viewpoint of classical information geometry. Recently,…
The $\alpha$-sandwiched R\'enyi divergence satisfies the data processing inequality, i.e. monotonicity under quantum operations, for $\alpha\geq 1/2$. In this article, we derive a necessary and sufficient algebraic condition for equality in…
In coherent diffractive imaging (CDI) the resolution of the reconstructed object is limited by the numerical aperture of the experimental setup. We present here a theoretical and numerical study for achieving super-resolution by…
Dataset distillation (DD) aims to construct compact synthetic datasets that allow models to achieve comparable performance to full-data training while substantially reducing storage and computation. Despite rapid empirical progress, its…
Understanding geometric properties of natural language processing models' latent spaces allows the manipulation of these properties for improved performance on downstream tasks. One such property is the amount of data spread in a model's…
Spatiotemporal data imputation plays a crucial role in various fields such as traffic flow monitoring, air quality assessment, and climate prediction. However, spatiotemporal data collected by sensors often suffer from temporal…
Graph pattern matching, which aims to discover structural patterns in graphs, is considered one of the most fundamental graph mining problems in many real applications. Despite previous efforts, existing systems face two main challenges.…
Parameters of differential equations are essential to characterize intrinsic behaviors of dynamic systems. Numerous methods for estimating parameters in dynamic systems are computationally and/or statistically inadequate, especially for…
Diffusion models represent the state-of-the-art in generative modeling. Due to their high training costs, many works leverage pre-trained diffusion models' powerful representations for downstream tasks, such as face super-resolution (FSR),…
The failure of roughness parameters to predict surface properties stems from their inherent scale-dependence; in other words, the measured value depends on the way it was measured. Here we take advantage of this scale-dependence to develop…
Signal scaling is a fundamental operation of practical importance in which a signal is enlarged or shrunk in the coordinate direction(s). Scaling or magnification is not trivial for signals of a discrete variable since the signal values may…
Computational image reconstruction algorithms generally produce a single image without any measure of uncertainty or confidence. Regularized Maximum Likelihood (RML) and feed-forward deep learning approaches for inverse problems typically…
We present a spectral analysis for matrix scaling and operator scaling. We prove that if the input matrix or operator has a spectral gap, then a natural gradient flow has linear convergence. This implies that a simple gradient descent…
A perturbative treatment of reduced density operators of quantum subsystems is implemented in the same spirit as Fermi Golden Rule for scattering. Analytic expressions for linear entropy (a measure of purity loss, and in some cases of…
The recent introduction of geometric partition entropy brought a new viewpoint to non-parametric entropy quantification that incorporated the impacts of informative outliers, but its original formulation was limited to the context of a…
Differential Privacy (DP) is a well-established framework to quantify privacy loss incurred by any algorithm. Traditional formulations impose a uniform privacy requirement for all users, which is often inconsistent with real-world scenarios…
We call an objective function or algorithm symmetric with respect to an input if after swapping two parts of the input in any algorithm, the solution of the algorithm and the output remain the same. More formally, for a permutation $\pi$ of…
Data visualization is the process by which data of any size or dimensionality is processed to produce an understandable set of data in a lower dimensionality, allowing it to be manipulated and understood more easily by people. The goal of…
To quantify degree of spatial inhomogeneity for multiphase materials we adapt the entropic descriptor (ED) of a pillar model developed to greyscale images. To uncover the contribution of each phase we introduce the suitable 'phase…
Measurements can be viewed as interactions between a measured system and a pointer system that imprint information about the system on the pointer. For so-called unbiased interactions, the measurement statistics--the information…