Related papers: A corrected Maslov index for complex saddle trajec…

The Maslov correction to the wave function is to the jump of $-\pi/2$ in the phase when the system passes through a caustic point. This phenomenon is related to the second variation and to the geometry of paths, as conveniently explained in…

For various reasons, it seems necessary to include complex saddle points in the "Euclidean" path integral of General Relativity. But some sort of restriction on the allowed complex saddle points is needed to avoid various unphysical…

Quantitative inversion algorithms allow for the reconstruction of electrical properties (such as permittivity, and conductivity) for every point in a scene. However, they are challenging to use on measured datasets due to the need to know…

Recent advances in symbolic dynamic programming (SDP) combined with the extended algebraic decision diagram (XADD) data structure have provided exact solutions for mixed discrete and continuous (hybrid) MDPs with piecewise linear dynamics…

For a real valued function, a point is critical if its derivatives are zero, and a critical point is a saddle point if it is not a local extrema. In this paper, we study algorithms to find saddle points of general Morse index. Our approach…

This paper presents an alternative approach for the computation of trajectory segments on slow manifolds of saddle type. This approach is based on iterative methods rather than collocation-type methods. Compared to collocation methods, that…

Directional tests to compare incomplete undirected graphs are developed in the general context of covariance selection for Gaussian graphical models. The exactness of the underlying saddlepoint approximation is proved for chordal graphs and…

We prove error estimates for the semi-implicit numerical scheme of sphere-constrained high-index saddle dynamics, which serves as a powerful instrument in finding saddle points and constructing the solution landscapes of constrained systems…

Data assimilation algorithms combine information from observations and prior model information to obtain the most likely state of a dynamical system. The linearised weak-constraint four-dimensional variational assimilation problem can be…

We describe a new phenomenon in the study of the real-time path integral, where complex classical paths hit singularities of the potential and need to be analytically continued beyond the space for which they solve the boundary value…

In this paper we investigate the convergence of a recently popular class of first-order primal-dual algorithms for saddle point problems under the presence of errors occurring in the proximal maps and gradients. We study several types of…

We propose and analyze several inexact regularized Newton-type methods for finding a global saddle point of convex-concave unconstrained min-max optimization problems. Compared to first-order methods, our understanding of second-order…

Saddle-point problems have recently gained increased attention from the machine learning community, mainly due to applications in training Generative Adversarial Networks using stochastic gradients. At the same time, in some applications…

The problem of computing saddle points is important in certain problems in numerical partial differential equations and computational chemistry, and is often solved numerically by a minimization problem over a set of mountain passes. We…

In this paper, we propose a primal-dual algorithm with a novel momentum term using the partial gradients of the coupling function that can be viewed as a generalization of the method proposed by Chambolle and Pock in 2016 to solve saddle…

Nonconvex optimization underlies many modern machine learning and control tasks, where saddle points pose the dominant obstacle to reliable convergence in high-dimensional settings. Escaping these saddle points deterministically using…

A saddlepoint approximation of the Student's t-statistic was derived by Daniels and Young [Biometrika 78 (1991) 169-179] under the very stringent exponential moment condition that requires that the underlying density function go down at…

We show that the semi-classical analysis of generic Euclidean path integrals necessarily requires complexification of the action and measure, and consideration of complex saddle solutions. We demonstrate that complex saddle points have a…

This note is concerned with accurate and computationally efficient approximations of moments of Gaussian random variables passed through sigmoid or softmax mappings. These approximations are semi-analytical (i.e. they involve the numerical…

Saddle points constitute a crucial challenge for first-order gradient descent algorithms. In notions of classical machine learning, they are avoided for example by means of stochastic gradient descent methods. In this work, we provide…