Related papers: Decimation flows in constraint satisfaction proble…
Message passing algorithms have proved surprisingly successful in solving hard constraint satisfaction problems on sparse random graphs. In such applications, variables are fixed sequentially to satisfy the constraints. Message passing is…
We study the susceptibility propagation, a message-passing algorithm to compute correlation functions. It is applied to constraint satisfaction problems and its accuracy is examined. As a heuristic method to find a satisfying assignment, we…
Matrix factorization is an inference problem that has acquired importance due to its vast range of applications that go from dictionary learning to recommendation systems and machine learning with deep networks. The study of its fundamental…
Many decision-making problems in engineering applications such as transportation, power system and operations research require repeatedly solving large-scale linear programming problems with a large number of different inputs. For example,…
In the context of solving large distributed constraint optimization problems (DCOP), belief-propagation and approximate inference algorithms are candidates of choice. However, in general, when the factor graph is very loopy (i.e. cyclic),…
Unsplittable flow problems cover a wide range of telecommunication and transportation problems and their efficient resolution is key to a number of applications. In this work, we study algorithms that can scale up to large graphs and…
Normalizing flow is a generative modeling approach with efficient sampling. However, Flow-based models suffer two issues: 1) If the target distribution is manifold, due to the unmatch between the dimensions of the latent target distribution…
Density deconvolution is the task of estimating a probability density function given only noise-corrupted samples. We can fit a Gaussian mixture model to the underlying density by maximum likelihood if the noise is normally distributed, but…
Let F be a uniformly distributed random k-SAT formula with n variables and m clauses. Non-rigorous statistical mechanics ideas have inspired a message passing algorithm called Belief Propagation Guided Decimation for finding satisfying…
We introduce and study the random "locked" constraint satisfaction problems. When increasing the density of constraints, they display a broad "clustered" phase in which the space of solutions is divided into many isolated points. While the…
We study an optimization problem related to the approximation of given data by a linear combination of transformed modes. In the simplest case, the optimization problem reduces to a minimization problem well-studied in the context of proper…
Flow matching has emerged as a powerful generative modeling approach with flexible choices of source distribution. While Gaussian distributions are commonly used, the potential for better alternatives in high-dimensional data generation…
In many power system optimization problems, we observe that only a small fraction of the line flow constraints ever become active at the optimal solution, despite variations in the load profile and generation costs. This observation has…
We introduce a version of the cavity method for diluted mean-field spin models that allows the computation of thermodynamic quantities similar to the Franz-Parisi quenched potential in sparse random graph models. This method is developed in…
We consider the problem of efficiently solving large-scale linear least squares problems that have one or more linear constraints that must be satisfied exactly. Whilst some classical approaches are theoretically well founded, they can face…
We consider a routing problem which plays an important role in several applications, primarily in communication network planning and VLSI layout design. The original underlying graph algorithmic task is called Disjoint Paths problem. In…
Decentralized optimization methods enable on-device training of machine learning models without a central coordinator. In many scenarios communication between devices is energy demanding and time consuming and forms the bottleneck of the…
In this work, we present a new approach to analyze the gradient flow for a positive semi-definite matrix denoising problem in an extensive-rank and high-dimensional regime. We use recent linear pencil techniques of random matrix theory to…
We study optimization algorithms for the finite sum problems frequently arising in machine learning applications. First, we propose novel variants of stochastic gradient descent with a variance reduction property that enables linear…
Flow delegation is a flexible technique to mitigate flow table capacity bottlenecks in Software-defined Networks (SDN). Such bottlenecks occur when SDN switches provide insufficient flow table capacity which leads to performance degradation…