相关论文: Global Minimum Depth In Edwards-Anderson Model

We study abelian anyons at the mean-field/almost-bosonic level, whose dynamics are governed by the Chern-Simons-Schr\"odinger system. We consider the dimensional reduction of this 2D model by introducing an anisotropic trapping potential,…

Anomaly detection using dimensionality reduction has been an essential technique for monitoring multidimensional data. Although deep learning-based methods have been well studied for their remarkable detection performance, their…

Stochastic gradient descent (SGD) has been found to be surprisingly effective in training a variety of deep neural networks. However, there is still a lack of understanding on how and why SGD can train these complex networks towards a…

In a recent work, Esmer et al. describe a simple method - Approximate Monotone Local Search - to obtain exponential approximation algorithms from existing parameterized exact algorithms, polynomial-time approximation algorithms and, more…

We estimate the global minimum variance (GMV) portfolio in the high-dimensional case using results from random matrix theory. This approach leads to a shrinkage-type estimator which is distribution-free and it is optimal in the sense of…

The main aim of this paper is to provide an analysis of gradient descent (GD) algorithms with gradient errors that do not necessarily vanish, asymptotically. In particular, sufficient conditions are presented for both stability (almost sure…

It has been observed in a variety of contexts that gradient descent methods have great success in solving low-rank matrix factorization problems, despite the relevant problem formulation being non-convex. We tackle a particular instance of…

Full 3D inversion of time-domain Airborne ElectroMagnetic (AEM) data requires specialists' expertise and a tremendous amount of computational resources, not readily available to everyone. Consequently, quasi-2D/3D inversion methods are…

We develop a general framework for data-driven approximation of input-output maps between infinite-dimensional spaces. The proposed approach is motivated by the recent successes of neural networks and deep learning, in combination with…

Exact ground states of two-dimensional Ising spin glasses with Gaussian and bimodal (+- J) distributions of the disorder are calculated using a ``matching'' algorithm, which allows large system sizes of up to N=480^2 spins to be…

It is well-known that due to the lack of a technique to obtain the a-priori $L^{\infty}$ estimate of the artificial viscosity solutions of the Cauchy problem for the one-dimensional Euler-Poisson (or hydrodynamic) model for semiconductors,…

We study adaptive data-dependent dimensionality reduction in the context of supervised learning in general metric spaces. Our main statistical contribution is a generalization bound for Lipschitz functions in metric spaces that are…

Recent experiments have shown that, often, when training a neural network with gradient descent (GD) with a step size $\eta$, the operator norm of the Hessian of the loss grows until it approximately reaches $2/\eta$, after which it…

The rapid evolution of satellite-borne Earth Observation (EO) systems has revolutionized terrestrial monitoring, yielding petabyte-scale archives. However, the immense computational and storage requirements for global-scale analysis often…

Within the framework of string field theory the intrinsic Hausdorff dimension d_H of the ensemble of surfaces in two-dimensional quantum gravity has recently been claimed to be 2m for the class of unitary minimal models (p = m+1,q = m).…

We have simulated Edwards-Anderson (EA) as well as Sherrington-Kirkpatrick systems of L^3 spins. After averaging over large sets of EA system samples of 3 =< L =< 10, we obtain accurate numbers for distributions p(q) of the overlap…

Two aspects of neural networks that have been extensively studied in the recent literature are their function approximation properties and their training by gradient descent methods. The approximation problem seeks accurate approximations…

Monocular Depth and Surface Normals Estimation (MDSNE) is crucial for tasks such as 3D reconstruction, autonomous navigation, and underwater exploration. Current methods rely either on discriminative models, which struggle with transparent…

Models (i.e., governing equations) are fundamental to science and engineering. Advances in data acquisition now make it possible to extract interpretable, low dimensional descriptions from high dimensional observations. However, existing…

We develop a geometric convergence theory for neural-network optimization within the minimizing movement scheme (MMS) framework. Reformulating each neural MMS step as a minimization over the set of increments in a Hilbert space, we show…