Related papers: Improved high-index saddle dynamics for finding sa…

In this paper, we propose a variant of Riemannian stochastic recursive gradient method that can achieve second-order convergence guarantee and escape saddle points using simple perturbation. The idea is to perturb the iterates when gradient…

The broad success of theoretical and experimental quantum optimal control is intimately connected to the topology of the underlying control landscape. For several common quantum control goals, including the maximization of an observable…

Finding index-1 saddle points is crucial for understanding phase transitions. In this work, we propose a simple yet efficient approach, the spring pair method (SPM), to accurately locate saddle points. Without requiring Hessian information,…

This paper considers continuously differentiable functions of two vector variables that have (possibly a continuum of) min-max saddle points. We study the asymptotic convergence properties of the associated saddle-point dynamics…

This paper deals with a second-order primal-dual dynamical system with Hessian-driven damping and Tikhonov regularization terms in connection with a convex-concave bilinear saddle point problem. We first obtain a fast convergence rate of…

We consider the evolution equations for the bulk viscous pressure, diffusion current and shear tensor derived within second-order relativistic dissipative hydrodynamics from kinetic theory. By matching the higher order moments directly to…

We consider distributed smooth nonconvex unconstrained optimization over networks, modeled as a connected graph. We examine the behavior of distributed gradient-based algorithms near strict saddle points. Specifically, we establish that (i)…

In this paper we fully describe the trajectory of gradient flow over diagonal linear networks in the limit of vanishing initialisation. We show that the limiting flow successively jumps from a saddle of the training loss to another until…

We describe all possible topological structures of Morse-Smale flows without closed trajectories on a three-dimensional sphere, which have two sources, two sinks, one saddle of Morse index 1, one saddle of Morse index 2, and no more than 10…

In this article, we study the convergence of Mirror Descent (MD) and Optimistic Mirror Descent (OMD) for saddle point problems satisfying the notion of coherence as proposed in Mertikopoulos et al. We prove convergence of OMD with exact…

In this paper, we explore a broad class of constrained saddle point problems with a bilevel structure, wherein the upper-level objective function is nonconvex-concave and smooth over compact and convex constraint sets, subject to a strongly…

In Hamiltonian systems subjected to periodic perturbations the stable and unstable manifolds of the unstable periodic orbits provide the dynamical "skeleton" that drives the mixing process and bounds the chaotic regions of the phase space.…

Dynamical systems that describe the escape from the basins of attraction of stable invariant sets are presented and analyzed. It is shown that the stable fixed points of such dynamical systems are the index-1 saddle points. Generalizations…

The first part of this paper studies the evolution of gradient flow for homogeneous neural networks near a class of saddle points exhibiting a sparsity structure. The choice of these saddle points is motivated from previous works on…

We propose a derivative-free saddle-search algorithm designed to locate transition states using only function evaluations. The algorithm employs a nested architecture consisting of an inner eigenvector search and an outer saddle-point…

Loss functions with a large number of saddle points are one of the major obstacles for training modern machine learning models efficiently. First-order methods such as gradient descent are usually the methods of choice for training machine…

Stochastically controlled stochastic gradient (SCSG) methods have been proved to converge efficiently to first-order stationary points which, however, can be saddle points in nonconvex optimization. It has been observed that a stochastic…

In this paper, we propose a class of general second-order primal-dual dynamical systems with Tikhonov regularization and Hessian-driven damping for solving convex-concave bilinear saddle point problems. The proposed dynamical system…

We present a method called Manifold Interpolating Optimal-Transport Flow (MIOFlow) that learns stochastic, continuous population dynamics from static snapshot samples taken at sporadic timepoints. MIOFlow combines dynamic models, manifold…

The value of a highly oscillatory integral is typically determined asymptotically by the behaviour of the integrand near a small number of critical points. These include the endpoints of the integration domain and the so-called stationary…