相关论文: Connecting Tikhonov regularization to the maximum …

Computational color constancy is a preprocessing step used in many camera systems. The main aim is to discount the effect of the illumination on the colors in the scene and restore the original colors of the objects. Recently, several deep…

The computation of transport coefficients, even in linear response, is a major challenge for theoretical methods that rely on analytic continuation of correlations functions obtained numerically in Matsubara space. While maximum entropy…

Novel Monte Carlo estimators are proposed to solve both the Tikhonov regularization (TR) and the interpolation problems on graphs. These estimators are based on random spanning forests (RSF), the theoretical properties of which enable to…

Entanglement entropy has been a powerful tool for analyzing phases and criticality in pure ground states via quantum Monte Carlo (QMC). However, mixed-state entanglement, relevant to systems with dissipation, finite temperature, and…

We introduce an adaptive viscosity regularization approach for the numerical solution of systems of nonlinear conservation laws with shock waves. The approach seeks to solve a sequence of regularized problems consisting of the system of…

We consider the problem of reconstructing 2D images from randomly under-sampled confocal microscopy samples. The well known and widely celebrated total variation regularization, which is the L1 norm of derivatives, turns out to be…

Dimensional regularization of Euclidean momentum space integrals is a highly successful technique in renormalization of quantum field theories. While it yields a straightforward algorithmic method, with which to evaluate diagrams beyond…

With the regular decomposition technique, we decompose the space $\mathbf{H}_0^s(\mathbf{curl}; \Omega)$ into the sum of a vector potential space and the gradient of a scalar space, both possessing higher regularity. Based on this new high…

In an idealistic setting, quantum metrology protocols allow to sense physical parameters with mean squared error that scales as $1/N^2$ with the number of particles involved---substantially surpassing the $1/N$-scaling characteristic to…

The max-relative entropy together with its smoothed version is a basic tool in quantum information theory. In this paper, we derive the exact exponent for the asymptotic decay of the small modification of the quantum state in smoothing the…

A reliable method for characterizing quantum operations that is suitable for improving and validating their accuracies is indispensable for realizing a practical quantum computer. Known methods are still not sufficient because they lack…

Recent years have seen the rise of convolutional neural network techniques in exemplar-based image synthesis. These methods often rely on the minimization of some variational formulation on the image space for which the minimizers are…

We perform a comprehensive analysis of the quantum-enhanced Monte Carlo method [Nature, 619, 282-287 (2023)], aimed at identifying the optimal working point of the algorithm. We observe an optimal mixing Hamiltonian strength and analyze the…

We revisit the problem of determining the real-frequency density response in quantum fluids via analytical continuation of imaginary-time quantum Monte Carlo data. We demonstrate that the average spectrum method (ASM) is capable of…

Impressive progress has been made in the past decade in the study of technological applications of varied types of quantum systems. With industry giants like IBM laying down their roadmap for scalable quantum devices with more than…

We show several results on convergence of the Monte Carlo method applied to consistent approximations of the isentropic Euler system of gas dynamics with uncertain initial data. Our method is based on combination of several new concepts. We…

We consider choice of the regularization parameter in Tikhonov method if the noise level of the data is unknown. One of the best rules for the heuristic parameter choice is the quasi-optimality criterion where the parameter is chosen as the…

We propose a general framework for entropy-regularized average-reward reinforcement learning in Markov decision processes (MDPs). Our approach is based on extending the linear-programming formulation of policy optimization in MDPs to…

Random feature approximation is arguably one of the most popular techniques to speed up kernel methods in large scale algorithms and provides a theoretical approach to the analysis of deep neural networks. We analyze generalization…

Chinese text recognition is more challenging than Latin text due to the large amount of fine-grained Chinese characters and the great imbalance over classes, which causes a serious overfitting problem. We propose to apply Maximum Entropy…