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The functional renormalization group method is used to take into account the vacuum polarization around localized bound states generated by external potential. The application to Atomic Physics leads to improved Hartree-Fock and Kohn-Sham…
Humans tend to mine objects by learning from a group of images or several frames of video since we live in a dynamic world. In the computer vision area, many researches focus on co-segmentation (CoS), co-saliency detection (CoSD) and video…
Pose Graph Optimization (PGO) is an important non-convex optimization problem and is the state-of-the-art formulation for SLAM in robotics. It also has applications like camera motion estimation, structure from motion and 3D reconstruction…
Optimization problem, which is aimed at finding the global minimal value of a given cost function, is one of the central problem in science and engineering. Various numerical methods have been proposed to solve this problem, among which the…
The large-scale focusing inversion of gravity and magnetic potential field data using $L_1$-norm regularization is considered. The use of the randomized singular value decomposition methodology facilitates tackling the computational…
Neural operators have become an effective framework for learning mappings between function spaces, yet most existing architectures realize operators within a single representational domain, such as physical, spectral, or latent space. In…
Bayesian optimization (BO) methods are useful for optimizing functions that are expensive to evaluate, lack an analytical expression and whose evaluations can be contaminated by noise. These methods rely on a probabilistic model of the…
We present an efficient implementation of the Density Matrix Renormalization Group (DMRG) algorithm that includes an optimal ordering of the proton and neutron orbitals and an efficient expansion of the active space utilizing various…
Although many techniques have been applied to matrix factorization (MF), they may not fully exploit the feature structure. In this paper, we incorporate the grouping effect into MF and propose a novel method called Robust Matrix…
The decomposition of complex structures into simpler substructures is a powerful technique with a wide range of applications. We study the computation of decompositions in the context of programmable matter. The amoebot model is a…
Information geometric optimization (IGO) is a general framework for stochastic optimization problems aiming at limiting the influence of arbitrary parametrization choices. The initial problem is transformed into the optimization of a smooth…
We present a general framework for understanding and analyzing critical behaviour in gravitational collapse. We adopt the method of renormalization group, which has the following advantages. (1) It provides a natural explanation for various…
Cooperative co-evolution (CC) algorithms, based on the divide-and-conquer strategy, have emerged as the predominant approach to solving large-scale global optimization (LSGO) problems. The efficiency and accuracy of the grouping stage…
This chapter describes modal decompositions in the framework of matrix factorizations. We highlight the differences between classic space-time decompositions and 2D discrete transforms and discuss the general architecture underpinning…
We develop a method for optimization in shape spaces, i.e., sets of surfaces modulo re-parametrization. Unlike previously proposed gradient flows, we achieve superlinear convergence rates through a subtle approximation of the shape Hessian,…
This paper generalizes the optimized gradient method (OGM) that achieves the optimal worst-case cost function bound of first-order methods for smooth convex minimization. Specifically, this paper studies a generalized formulation of OGM and…
Initialization is essential to monocular Simultaneous Localization and Mapping (SLAM) problems. This paper focuses on a novel initialization method for monocular SLAM based on planar features. The algorithm starts by homography estimation…
Inspired by the remarkable success of large neural networks, there has been significant interest in understanding the generalization performance of over-parameterized models. Substantial efforts have been invested in characterizing how…
The Cartesian reverse derivative is a categorical generalization of reverse-mode automatic differentiation. We use this operator to generalize several optimization algorithms, including a straightforward generalization of gradient descent…
The renormalization group method is applied to the study of discrete dynamical systems. As a particular example, the Henon map is considered as applied to describe the transverse betatron oscillations in a cyclic accelerator or storage ring…