Related papers: Duality of Fix-Points for Distributive Lattices

While Deep Neural Networks (DNNs) push the state-of-the-art in many machine learning applications, they often require millions of expensive floating-point operations for each input classification. This computation overhead limits the…

This paper investigates the fixed-time consensus problem under directed topologies. By using a motion-planning approach, a class of distributed fixed-time algorithms are developed for a multi-agent system with double-integrator dynamics. In…

Distributed resource allocation is a central task in network systems such as smart grids, water distribution networks, and urban transportation systems. When solving such problems in practice it is often important to have nonasymptotic…

This paper is concerned with the problem of exact MAP inference in general higher-order graphical models by means of a traditional linear programming relaxation approach. In fact, the proof that we have developed in this paper is a rather…

Given a Hilbert space and a finite family of operators defined on the space, the common fixed point problem (CFPP) is to find a point in the intersection of the fixed point sets of these operators. Instances of the problem have numerous…

Neural networks are widely used as a model for classification in a large variety of tasks. Typically, a learnable transformation (i.e. the classifier) is placed at the end of such models returning a value for each class used for…

The fully dynamic transitive closure problem asks to maintain reachability information in a directed graph between arbitrary pairs of vertices, while the graph undergoes a sequence of edge insertions and deletions. The problem has been…

We present a version of the domino shuffling algorithm (due to Elkies, Kuperberg, Larsen and Propp) which works on a different lattice: the hexagonal lattice superimposed on its dual graph. We use our algorithm to count perfect matchings on…

This paper aims to address distributed optimization problems over directed and time-varying networks, where the global objective function consists of a sum of locally accessible convex objective functions subject to a feasible set…

We design and analyze an algorithm for computing rational points of hypersurfaces defined over a finite field based on searches on "vertical strips", namely searches on parallel lines in a given direction. Our results show that, on average,…

Recently, accelerated algorithms using the anchoring mechanism for minimax optimization and fixed-point problems have been proposed, and matching complexity lower bounds establish their optimality. In this work, we present the surprising…

We consider the lattice of all the weak factorization systems on a given finite lattice. We prove that it is semidistributive, trim and congruence uniform. We deduce a graph theoretical approach to the problem of enumerating transfer…

This paper proposes graph analysis methods to fully automate the fault location identification task in power distribution systems. The proposed methods take basic unordered data from power distribution systems as input, including branch…

We investigate the convergence of the primal-dual algorithm for composite optimization problems when the objective functions are weakly convex. We introduce a modified duality gap function, which is a lower bound of the standard duality gap…

This paper extends algorithms that remove the fixed point bias of decentralized gradient descent to solve the more general problem of distributed optimization over subspace constraints. Leveraging the integral quadratic constraint…

In this paper, we propose a new splitting algorithm for dynamical low-rank approximation motivated by the fibre bundle structure of the set of fixed rank matrices. We first introduce a geometric description of the set of fixed rank matrices…

When proving the correctness of a method for slicing probabilistic programs, it was previously discovered by the authors that for a fixed point iteration to work one needs a non-standard starting point for the iteration. This paper presents…

This paper presents a novel neural network architecture featuring automatic fixation point selection, designed to efficiently address complex tasks with reduced network size and computational overhead. The proposed model consists of: a…

Birkhoff's representation theorem (Birkhoff, 1937) defines a bijection between elements of a distributive lattice and the family of upper sets of an associated poset. Although not used explicitly, this result is at the backbone of the…

This paper presents a twice continuously differentiable penalty function for nonlinear semidefinite programming problems. In some optimization methods, such as penalty methods and augmented Lagrangian methods, their convergence property can…