Related papers: An Adaptive KKT-Based Indicator for Convergence As…

We present a novel procedure for optimization based on the combination of efficient quantized tensor train representation and a generalized maximum matrix volume principle. We demonstrate the applicability of the new Tensor Train Optimizer…

The Kazantzis-Kravaris-Luenberger (KKL) observer provides a general framework for nonlinear state estimation by immersing the system dynamics into a stable linear or nonlinear latent dynamics. However, the performance of KKL observers…

Kalman filters are widely used for object tracking, where process and measurement noise are usually considered accurately known and constant. However, the exact known and constant assumptions do not always hold in practice. For example,…

The K-means algorithm is one of the most widely studied clustering algorithms in machine learning. While extensive research has focused on its ability to achieve a globally optimal solution, there still lacks a rigorous analysis of its…

Estimating entropy and mutual information consistently is important for many machine learning applications. The Kozachenko-Leonenko (KL) estimator (Kozachenko & Leonenko, 1987) is a widely used nonparametric estimator for the entropy of…

Inferring unknown constraints is a challenging and crucial problem in many robotics applications. When only expert demonstrations are available, it becomes essential to infer the unknown domain constraints to deploy additional agents…

Intelligent Tutoring Systems have become critically important in future learning environments. Knowledge Tracing (KT) is a crucial part of that system. It is about inferring the skill mastery of students and predicting their performance to…

In the present paper, we focus on the vector optimization problems with inequality constraints, where objective functions and constrained functions are Fr\'echet differentiable, and whose gradient mapping is locally Lipschitz on an open…

Inverted Generational Distance (IGD) has been widely considered as a reliable performance indicator to concurrently quantify the convergence and diversity of multi- and many-objective evolutionary algorithms. In this paper, an IGD…

Selecting an appropriate divergence measure is a critical aspect of machine learning, as it directly impacts model performance. Among the most widely used, we find the Kullback-Leibler (KL) divergence, originally introduced in kinetic…

We study a cardinality-constrained optimization problem with nonnegative variables in this paper. This problem is often encountered in practice. Firstly we study some properties on the optimal solutions of this optimization problem under…

A trajectory-following primal--dual interior-point method solves nonlinear optimization problems with inequality and equality constraints by approximately finding points satisfying perturbed Karush--Kuhn--Tucker optimality conditions for a…

The Transformer architecture has been successful across many domains, including natural language processing, computer vision and speech recognition. In keyword spotting, self-attention has primarily been used on top of convolutional or…

Knowledge Tracing (KT) monitors students' knowledge states and simulates their responses to question sequences. Existing KT models typically follow a single-step training paradigm, which leads to discrepancies with the multi-step inference…

We propose an algorithm to estimate the path-gradient of both the reverse and forward Kullback-Leibler divergence for an arbitrary manifestly invertible normalizing flow. The resulting path-gradient estimators are straightforward to…

In this work we are interested in stochastic particle methods for multi-objective optimization. The problem is formulated using parametrized, single-objective sub-problems which are solved simultaneously. To this end a consensus based…

We study the double kicked top (DKT), which is an extension of the standard quantum kicked top (QKT) model. The model allows us to study the transition from time-reversal symmetric to broken time-reversal symmetric dynamics. Our…

We consider a smooth pessimistic bilevel optimization problem, where the lower-level problem is convex and satisfies the Slater constraint qualification. These assumptions ensure that the Karush-Kuhn-Tucker (KKT) reformulation of our…

This paper studies bilevel polynomial optimization problems. To solve them, we give a method based on polynomial optimization relaxations. Each relaxation is obtained from the Kurash-Kuhn-Tucker (KKT) conditions for the lower level…

Rank-based metrics are some of the most widely used criteria for performance evaluation of computer vision models. Despite years of effort, direct optimization for these metrics remains a challenge due to their non-differentiable and…