Related papers: Numerical Stability of the Nystr\"om Method

In this paper we address the issue of output instability of deep neural networks: small perturbations in the visual input can significantly distort the feature embeddings and output of a neural network. Such instability affects many deep…

Clustering under most popular objective functions is NP-hard, even to approximate well, and so unlikely to be efficiently solvable in the worst case. Recently, Bilu and Linial \cite{Bilu09} suggested an approach aimed at bypassing this…

Kernel methods offer the flexibility to learn complex relationships in modern, large data sets while enjoying strong theoretical guarantees on quality. Unfortunately, these methods typically require cubic running time in the data set size,…

Kernel based methods provide a way to reconstruct potentially high-dimensional functions from meshfree samples, i.e., sampling points and corresponding target values. A crucial ingredient for this to be successful is the distribution of the…

Encrypted dynamic controllers that operate for an unlimited time have been a challenging subject of research. The fundamental difficulty is the accumulation of errors and scaling factors in the internal state during operation.…

A lack of software reproducibility has become increasingly apparent in the last several years, calling into question the validity of scientific findings affected by published tools. Reproducibility issues may have numerous sources of error,…

We consider the implementation of the split-step method where the linear part of the nonlinear Schr\"odinger equation is solved using a finite-difference discretization of the spatial derivative. The von Neumann analysis predicts that this…

Updating machine learning models with new information usually improves their predictive performance, yet, in many applications, it is also desirable to avoid changing the model predictions too much. This property is called stability. In…

The parametric instability arising when ordinary differential equations (ODEs) are numerically integrated with Runge-Kutta-Nystr\"om (RKN) methods with varying step sizes is investigated. It is shown that when linear constant coefficient…

Motivated by the need for the rigorous analysis of the numerical stability of variational least-squares kernel-based methods for solving second-order elliptic partial differential equations, we provide previously lacking stability…

We provide sufficient conditions for instability of the subgradient method with constant step size around a local minimum of a locally Lipschitz semi-algebraic function. They are satisfied by several spurious local minima arising in robust…

This paper introduces a new proximal stochastic gradient method with variance reduction and stabilization for minimizing the sum of a convex stochastic function and a group sparsity-inducing regularization function. Since the method may be…

We consider the model introduced by Bilu and Linial (2010), who study problems for which the optimal clustering does not change when distances are perturbed. They show that even when a problem is NP-hard, it is sometimes possible to obtain…

In this paper we consider the training of single hidden layer neural networks by pseudoinversion, which, in spite of its popularity, is sometimes affected by numerical instability issues. Regularization is known to be effective in such…

Structural dynamics models with nonlinear stiffness appear, for example, when analyzing systems with nonlinear material behavior or undergoing large deformations. For complex systems, these models become too large for real-time applications…

A method is suggested for treating those complicated physical problems for which exact solutions are not known but a few approximation terms of a calculational algorithm can be derived. The method permits one to answer the following rather…

The essential difficulty of gradient-based bilevel optimization using implicit differentiation is to estimate the inverse Hessian vector product with respect to neural network parameters. This paper proposes to tackle this problem by the…

In this paper, we consider robust stability analysis of large-scale sparsely interconnected uncertain systems. By modeling the interconnections among the subsystems with integral quadratic constraints, we show that robust stability analysis…

A new improved transfer matrix method (TMM) is presented. It is shown that the method not only overcomes the numerical instability found in the original TMM, but also greatly improves the scalability of computation. The new improved TMM has…

Selecting regularization parameters in penalized high-dimensional graphical models in a principled, data-driven, and computationally efficient manner continues to be one of the key challenges in high-dimensional statistics. We present…