Related papers: SaddleScape V1.0: A Python Package for Constructin…
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…
We propose a novel end-to-end pipeline for online long-range vectorized high-definition (HD) map construction using on-board camera sensors. The vectorized representation of HD maps, employing polylines and polygons to represent map…
Gaussian Processes (GPs) are flexible, nonparametric Bayesian models widely used for regression and classification because of their ability to capture complex data patterns and quantify predictive uncertainty. However, the O(n^3)…
This article introduces a software package release for geometrically reasoning about the \textit{safety} desiderata of (complex) dynamical systems via level set methods. In emphasis, safety is analyzed with Hamilton-Jacobi equations. In…
Gradient-related first-order methods have become the workhorse of large-scale numerical optimization problems. Many of these problems involve nonconvex objective functions with multiple saddle points, which necessitates an understanding of…
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…
The article is devoted to the development of algorithmic methods ensuring efficient complexity bounds for strongly convex-concave saddle point problems in the case when one of the groups of variables is high-dimensional, and the other is…
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…
We consider convex-concave saddle point problems, and more generally convex optimization problems we refer to as $\textit{saddle problems}$, which include the partial supremum or infimum of convex-concave saddle functions. Saddle problems…
Finding saddle points of dynamical systems is an important problem in practical applications such as the study of rare events of molecular systems. Gentlest ascent dynamics (GAD) is one of a number of algorithms in existence that attempt to…
`scores` is a Python package containing mathematical functions for the verification, evaluation and optimisation of forecasts, predictions or models. It supports labelled n-dimensional (multidimensional) data, which is used in many…
We consider a generic convex-concave saddle point problem with separable structure, a form that covers a wide-ranged machine learning applications. Under this problem structure, we follow the framework of primal-dual updates for saddle…
Methods with adaptive scaling of different features play a key role in solving saddle point problems, primarily due to Adam's popularity for solving adversarial machine learning problems, including GANS training. This paper carries out a…
The emergence of large-scale AI models, like GPT-4, has significantly impacted academia and industry, driving the demand for high-performance computing (HPC) to accelerate workloads. To address this, we present HPCClusterScape, a…
Data frames in scripting languages are essential abstractions for processing structured data. However, existing data frame solutions are either not distributed (e.g., Pandas in Python) and therefore have limited scalability, or they are not…
Data visualizations can reveal trends and patterns that are not otherwise obvious from the raw data or summary statistics. While visualizing low-dimensional data is relatively straightforward (for example, plotting the change in a variable…
The gentlest ascent dynamics (GAD) (Nonlinearity, vol. 24, no. 6, p1831, 2011) is a continuous time dynamics coupling both the position and the direction variables to efficiently locate the saddle point with a given index. These saddle…
We consider strongly-convex-strongly-concave saddle point problems assuming we have access to unbiased stochastic estimates of the gradients. We propose a stochastic accelerated primal-dual (SAPD) algorithm and show that SAPD sequence,…
Stellar abundance analysis relies on flexible, high-performance spectral synthesis. To meet these needs, we present PySME v1.0, an updated Python implementation of Spectroscopy Made Easy (SME) designed for precise and survey-scale modelling…
Instance Space Analysis is a methodology to evaluate algorithm performance across diverse problem fields. Through visualisation and exploratory data analysis techniques, Instance Space Analysis offers objective, data-driven insights into…