Related papers: Winner-Relaxing Self-Organizing Maps
We consider a new hierarchy of semidefinite relaxations for the general polynomial optimization problem $(P):\:f^{\ast}=\min \{\,f(x):x\in K\,\}$ on a compact basic semi-algebraic set $K\subset\R^n$. This hierarchy combines some advantages…
We prove a general result demonstrating the power of Lagrangian relaxation in solving constrained maximization problems with arbitrary objective functions. This yields a unified approach for solving a wide class of {\em subset selection}…
In this paper, we consider the model reduction problem of large-scale systems, such as systems obtained through the discretization of partial differential equations. We propose a computationally optimal randomized proper orthogonal…
Traditional optimization methods rely on the use of single-precision floating point arithmetic, which can be costly in terms of memory size and computing power. However, mixed precision optimization techniques leverage the use of both…
This paper presents a novel method for accelerating path-planning tasks in unknown scenes with obstacles by utilizing Wasserstein Generative Adversarial Networks (WGANs) with Gradient Penalty (GP) to approximate the distribution of…
This paper studies generalized semi-infinite programs (GSIPs) given by polynomials. We propose a hierarchy of polynomial optimization relaxations to solve them. They are based on Lagrange multiplier expressions and polynomial extensions.…
We propose a relaxation-based approximate inference algorithm that samples near-MAP configurations of a binary pairwise Markov random field. We experiment on MAP inference tasks in several restricted Boltzmann machines. We also use our…
Remote sensing image registration is valuable for image-based navigation system despite posing many challenges. As the search space of registration is usually non-convex, the optimization algorithm, which aims to search the best…
We consider a network topology design problem in which an initial undirected graph underlying the network is given and the objective is to select a set of edges to add to the graph to optimize the coherence of the resulting network. We show…
The paper introduces the first formulation of convex Q-learning for Markov decision processes with function approximation. The algorithms and theory rest on a relaxation of a dual of Manne's celebrated linear programming characterization of…
We describe an explainable AI saliency map method for use with deep convolutional neural networks (CNN) that is much more efficient than popular fine-resolution gradient methods. It is also quantitatively similar or better in accuracy. Our…
The advancement of artificial intelligence has cast a new light on the development of optimization algorithm. This paper proposes to learn a two-phase (including a minimization phase and an escaping phase) global optimization algorithm for…
Despite broad interest in self-organizing systems, there are few quantitative, experimentally-applicable criteria for self-organization. The existing criteria all give counter-intuitive results for important cases. In this Letter, we…
We propose a moment relaxation for two problems, the separation and covering problem with semi-algebraic sets generated by a polynomial of degree d. We show that (a) the optimal value of the relaxation finitely converges to the optimal…
Minimal problems in computer vision raise the demand of generating efficient automatic solvers for polynomial equation systems. Given a polynomial system repeated with different coefficient instances, the traditional Gr\"obner basis or…
We introduce a new virtual environment for simulating a card game known as "Big 2". This is a four-player game of imperfect information with a relatively complicated action space (being allowed to play 1,2,3,4 or 5 card combinations from an…
We study offline Reinforcement Learning in large infinite-horizon discounted Markov Decision Processes (MDPs) when the reward and transition models are linearly realizable under a known feature map. Starting from the classic linear-program…
A new technique of global optimization and its applications in particular to neural networks are presented. The algorithm is also compared to other global optimization algorithms such as Gradient descent (GD), Monte Carlo (MC), Genetic…
Self-Organizing Maps are commonly used for unsupervised learning purposes. This paper is dedicated to the certain modification of SOM called SOMN (Self-Organizing Mixture Networks) used as a mechanism for representing grayscale digital…
Image retargeting, which resizes images to one with a prescribed aspect ratio by determining an optimal warping map, has gained substantial interest in imaging science. Despite significant advances, existing methods often fail to ensure…