Related papers: Gauge optimization and duality
Graphical models represent multivariate and generally not normalized probability distributions. Computing the normalization factor, called the partition function, is the main inference challenge relevant to multiple statistical and…
We consider solving large scale nonconvex optimisation problems with nonnegativity constraints. Such problems arise frequently in machine learning, such as nonnegative least-squares, nonnegative matrix factorisation, as well as problems…
An universal primal-dual approach of description equilibriums in large class of hierarchical congestion population games is proposed. At the very core of the approach is hierarchy of enclosed to each other transport networks. In different…
It is shown that the idea of ``minimal'' coupling to gauge fields can be conveniently implemented in the proper time formalism by identifying the equivalent of a ``covariant derivative''. This captures some of the geometric notion of the…
In recent work arXiv:2109.07820 we have shown the equivalence of the widely used nonconvex (generalized) branched transport problem with a shape optimization problem of a street or railroad network, known as (generalized) urban planning…
Gauge symmetry enhancing, at specific points of the compactification space, is a distinguished feature of string theory. In this work we discuss the breaking of such symmetries with tools provided by Double Field Theory (DFT). As a main…
In this note we explore duality in reverse convex optimization with reverse convex inequality constraints. While we are examining the special case of a finite index set of the inequality constraints, we are primarily interested in the…
We present a new probabilistic modelling framework based on the recent notion of normal factor graph (NFG). We show that the proposed NFG models and their transformations unify some existing models such as factor graphs, convolutional…
We propose a new class of convex penalty functions, called \emph{variational Gram functions} (VGFs), that can promote pairwise relations, such as orthogonality, among a set of vectors in a vector space. These functions can serve as…
A framework is presented whereby a general convex conic optimization problem is transformed into an equivalent convex optimization problem whose only constraints are linear equations and whose objective function is Lipschitz continuous.…
Gauging and duality transformations, two of the most useful tools in many-body physics, are shown to be equivalent up to constant depth quantum circuits in the case of one-dimensional quantum lattice models. This is demonstrated by making…
Dimensional reduction in two dimensions of gravity in higher dimension, or more generally of d=3 gravity coupled to a sigma-model on a symmetric space, is known to possess an infinite number of symmetries. We show that such a bidimensional…
Bayesian optimization is a popular formalism for global optimization, but its computational costs limit it to expensive-to-evaluate functions. A competing, computationally more efficient, global optimization framework is optimistic…
We reformulate the problem of modularity maximization over the set of partitions of a network as a conic optimization problem over the completely positive cone, converting it from a combinatorial optimization problem to a convex continuous…
The present article is an exposition of a theory of discrete convex functions on certain graph structures, developed by the author in recent years. This theory is a spin-off of discrete convex analysis by Murota, and is motivated by…
In typical applications of Bayesian optimization, minimal assumptions are made about the objective function being optimized. This is true even when researchers have prior information about the shape of the function with respect to one or…
We study a class of convex-concave min-max problems in which the coupled component of the objective is linear in at least one of the two decision vectors. We identify such problem structure as interpolating between the bilinearly and…
We introduce an extended framework for the simultaneous gauging of modulated symmetries in $(d+1)$ dimensions, employing {\it multiple} gauge symmetry operators whose corresponding gauging procedures must be carried out simultaneously.…
In a completely systematic and geometric way, we derive maximal and half-maximal supersymmetric gauged double field theories in lower than ten dimensions. To this end, we apply a simple twisting ansatz to the $D=10$ ungauged maximal and…
A simple algorithm is proposed for constructing generators of gauge symmetry as well as reducibility relations for arbitrary systems of field equations in two dimensions.