Related papers: SaddleScape V1.0: A Python Package for Constructin…
Point tracking aims to follow visual points through complex motion, occlusion, and viewpoint changes, and has advanced rapidly with modern foundation models. Yet progress toward general point tracking remains constrained by limited…
The study of complex many-body systems via analysis of the trajectories of the units that dynamically move and interact within them is a non-trivial task. The workflow for extracting meaningful information from the raw trajectory data is…
High-index saddle dynamics (HiSD) serves as a competitive instrument in searching the any-index saddle points and constructing the solution landscape of complex systems. The Lagrangian multiplier terms in HiSD ensure the Stiefel manifold…
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…
Recent progress in semantic scene understanding has primarily been enabled by the availability of semantically annotated bi-modal (camera and LiDAR) datasets in urban environments. However, such annotated datasets are also needed for…
Recent focus on robustness to adversarial attacks for deep neural networks produced a large variety of algorithms for training robust models. Most of the effective algorithms involve solving the min-max optimization problem for training…
Steady states are invaluable in the study of dynamical systems. High-dimensional dynamical systems, due to a separation of time-scales, often evolve towards a lower dimensional manifold $M$. We introduce an approach to locate saddle points…
We introduce a generalized framework for Scene Change Detection (SCD) that addresses the core ambiguity of distinguishing "relevant" from "nuisance" changes, enabling effective joint training of a single model across diverse domains and…
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,…
We present the first public release (v0.1) of the open-source GADGET Dataframe Library: gadfly. The aim of this package is to leverage the capabilities of the broader python scientific computing ecosystem by providing tools for analyzing…
Semidefinite programming (SDP) provides a principled framework for convex relaxations of nonconvex geometric constraints in motion planning, yet existing solvers are too computationally expensive for real-time control, particularly on…
We analyze stochastic gradient descent for optimizing non-convex functions. In many cases for non-convex functions the goal is to find a reasonable local minimum, and the main concern is that gradient updates are trapped in saddle points.…
Seismology has witnessed significant advancements in recent years with the application of deep learning methods to address a broad range of problems. These techniques have demonstrated their remarkable ability to effectively extract…
Automating the design of heuristic search methods is an active research field within computer science, artificial intelligence and operational research. In order to make these methods more generally applicable, it is important to eliminate…
Finding constrained saddle points on Riemannian manifolds is significant for analyzing energy landscapes arising in physics and chemistry. Existing works have been limited to special manifolds that admit global regular level-set…
Saddle point problems, ubiquitous in optimization, extend beyond game theory to diverse domains like power networks and reinforcement learning. This paper presents novel approaches to tackle saddle point problem, with a focus on…
Autonomous Vehicles (AVs) need an accurate and up-to-date representation of the environment for safe navigation. Traditional methods, which often rely on detailed environmental representations constructed offline, struggle in dynamically…
Discovering governing equations from observational data remains a fundamental challenge in scientific modeling, particularly when the underlying mathematical structure is unknown. Traditional sparse identification methods like SINDy excel…
The saddle point (SP) calculation is a grand challenge for computationally intensive energy function in computational chemistry area, where the saddle point may represent the transition state (TS). The traditional methods need to evaluate…
The development of generalizable Novel View Synthesis (NVS) models is critically limited by the scarcity of large-scale training data featuring diverse and precise camera trajectories. While real-world captures are photorealistic, they are…