Related papers: From Data to Combinatorial Multivector field Throu…
We provide an up-to-date review of the recent constructive program for field theories of the vector, matrix and tensor type, focusing not on the models themselves but on the mathematical tools used.
An important and yet difficult problem in fitting multivariate mixture models is determining the mixture complexity. We develop theory and a unified framework for finding the nonparametric maximum likelihood estimator of a multivariate…
Multivector fields and differential forms at the continuum level have respectively two commutative associative products, a third composition product between them and various operators like $\partial$, $d$ and $*$ which are used to describe…
We present a general classification of Hamiltonian multivector fields and of Poisson forms on the extended multiphase space appearing in the geometric formulation of first order classical field theories. This is a prerequisite for computing…
Volume-based reconstruction is usually expensive both in terms of memory consumption and runtime. Especially for sparse geometric structures, volumetric representations produce a huge computational overhead. We present an efficient way to…
Estimation of Markov Random Field and covariance models from high-dimensional data represents a canonical problem that has received a lot of attention in the literature. A key assumption, widely employed, is that of {\em sparsity} of the…
The ability to form complex plans based on raw visual input is a litmus test for current capabilities of artificial intelligence, as it requires a seamless combination of visual processing and abstract algorithmic execution, two…
Graphs are a natural representation for systems based on relations between connected entities. Combinatorial optimization problems, which arise when considering an objective function related to a process of interest on discrete structures,…
Multimodal learning has mainly focused on learning large models on, and fusing feature representations from, different modalities for better performances on downstream tasks. In this work, we take a detour from this trend and study the…
This work aims to introduce the framework of polynomial optimization theory to solve fractional polynomial problems (FPPs). Unlike other widely used optimization frameworks, the proposed one applies to a larger class of FPPs, not…
Neural Combinatorial Optimization attempts to learn good heuristics for solving a set of problems using Neural Network models and Reinforcement Learning. Recently, its good performance has encouraged many practitioners to develop neural…
We describe a framework for reformulating and solving optimization problems that generalizes the well-known framework originally introduced by Benders. We discuss details of the application of the procedures to several classes of…
In this paper, we present a machine learning-based data generator framework tailored to aid researchers who utilize simulations to examine various physical systems or processes. High computational costs and the resulting limited data often…
We consider the problem of designing agents able to compute optimal decisions by composing data from multiple sources to tackle tasks involving: (i) tracking a desired behavior while minimizing an agent-specific cost; (ii) satisfying safety…
In recent years, there has been a growing interest in using learning-based approaches for solving combinatorial problems, either in an end-to-end manner or in conjunction with traditional optimization algorithms. In both scenarios, the…
Combinatorial optimization algorithms for graph problems are usually designed afresh for each new problem with careful attention by an expert to the problem structure. In this work, we develop a new framework to solve any combinatorial…
Given a matrix with partitions of its rows and columns and entries from a field, we give the necessary and sufficient conditions that it has a non--singular submatrix with certain number of rows from each row partition and certain number of…
Multi-material structural topology and shape optimization problems are formulated within a phase field approach. First-order conditions are stated and the relation of the necessary conditions to classical shape derivatives are discussed. An…
Synthetic images rendered by graphics engines are a promising source for training deep networks. However, it is challenging to ensure that they can help train a network to perform well on real images, because a graphics-based generation…
The paper briefly describes a basic set of special combinatorial engineering frameworks for solving complex problems in the field of hierarchical modular systems. The frameworks consist of combinatorial problems (and corresponding models),…