Related papers: Locating saddle points using gradient extremals on…

The properties of higher-index saddle points have been invoked in recent theories of the dynamics of supercooled liquids. Here we examine in detail a mapping of configurations to saddle points using minimization of $|\nabla E|^2$, which has…

We propose a stochastic optimization method for minimizing loss functions, expressed as an expected value, that adaptively controls the batch size used in the computation of gradient approximations and the step size used to move along such…

When analyzing parametric statistical models, a useful approach consists in modeling geometrically the parameter space. However, even for very simple and commonly used hierarchical models like statistical mixtures or stochastic deep neural…

Point clouds provide a compact and efficient representation of 3D shapes. While deep neural networks have achieved impressive results on point cloud learning tasks, they require massive amounts of manually labeled data, which can be costly…

Anomaly detection based on 3D point cloud data is an important research problem and receives more and more attention recently. Untrained anomaly detection based on only one sample is an emerging research problem motivated by real…

In this paper, we consider the problem of minimizing a smooth function on a Riemannian manifold and present a Riemannian gradient method with momentum. The proposed algorithm represents a substantial and nontrivial extension of a recently…

We present SKD, a novel keypoint detector that uses saliency to determine the best candidates from a point cloud for tasks such as registration and reconstruction. The approach can be applied to any differentiable deep learning descriptor…

Deep reinforcement learning (DRL) demonstrates great potential in mapless navigation domain. However, such a navigation model is normally restricted to a fixed configuration of the range sensor because its input format is fixed. In this…

A novel similarity-covariant feature detector that extracts points whose neighbourhoods, when treated as a 3D intensity surface, have a saddle-like intensity profile. The saddle condition is verified efficiently by intensity comparisons on…

Matching 3D rigid point clouds in complex environments robustly and accurately is still a core technique used in many applications. This paper proposes a new architecture combining error estimation from sample covariances and dual global…

Saddle-point configurations, such as the Euclidean bounce and sphalerons, are known to be difficult to find numerically. In this Letter we study a new method, Quartic Gradient Flow, to search for such configurations. The central idea is to…

Traditional object detection methods face performance degradation challenges in complex scenarios such as low-light conditions and heavy occlusions due to a lack of high-level semantic understanding. To address this, this paper proposes an…

Motivated by the super-diffusivity of self-repelling random walk, which has roots in statistical physics, this paper develops a new perturbation mechanism for optimization algorithms. In this mechanism, perturbations are adapted to the…

We study a class of misspecified saddle point (SP) problems, where the optimization objective depends on an unknown parameter that must be learned concurrently from data. Unlike existing studies that assume parameters are fully known or…

In this paper, we introduce a multilevel algorithm for approximating variational formulations of symmetric saddle point systems. The algorithm is based on availability of families of stable finite element pairs and on the availability of…

We propose a stochastic extension of the primal-dual hybrid gradient algorithm studied by Chambolle and Pock in 2011 to solve saddle point problems that are separable in the dual variable. The analysis is carried out for general…

Although adversarial examples and model robustness have been extensively studied in the context of linear models and neural networks, research on this issue in tree-based models and how to make tree-based models robust against adversarial…

In this paper, we analyze gradient-free methods with one-point feedback for stochastic saddle point problems $\min_{x}\max_{y} \varphi(x, y)$. For non-smooth and smooth cases, we present analysis in a general geometric setup with arbitrary…

We study the problem of finding the global Riemannian center of mass of a set of data points on a Riemannian manifold. Specifically, we investigate the convergence of constant step-size gradient descent algorithms for solving this problem.…

Learning dynamical systems through operator-theoretic representations provides a powerful framework for analyzing complex dynamics, as spectral quantities such as eigenvalues and invariant structures encode characteristic time scales and…