Related papers: A Reexamination of the COnfLUX 2.5D LU Factorizati…
In this paper, we revisit implicit regularization from the ground up using notions from dynamical systems and invariant subspaces of Morse functions. The key contributions are a new criterion for implicit regularization---a leading…
This paper presents a new lower bound for the discrete strategy improvement algorithm for solving parity games due to Voege and Jurdziski. First, we informally show which structures are difficult to solve for the algorithm. Second, we…
Coreference resolution systems are typically trained with heuristic loss functions that require careful tuning. In this paper we instead apply reinforcement learning to directly optimize a neural mention-ranking model for coreference…
Our contribution in this paper is two folded. We consider first the case of linear programming with real coefficients and give a method which allows the computation of a new upper bound on the distance from the origin to a feasible point.…
Multi-attributed graph matching is a problem of finding correspondences between two sets of data while considering their complex properties described in multiple attributes. However, the information of multiple attributes is likely to be…
In this paper, we develop a novel distributed algorithm for addressing convex optimization with both nonlinear inequality and linear equality constraints, where the objective function can be a general nonsmooth convex function and all the…
The low-rank approximation properties of Randomly Pivoted LU (RPLU), a variant of Gaussian elimination where pivots are sampled proportional to the squared entries of the Schur complement, are analyzed. It is shown that the RPLU iterates…
Recovering matrices from compressive and grossly corrupted observations is a fundamental problem in robust statistics, with rich applications in computer vision and machine learning. In theory, under certain conditions, this problem can be…
We derive approximation algorithms for the nonnegative matrix factorization problem, i.e. the problem of factorizing a matrix as the product of two matrices with nonnegative coefficients. We form convex approximations of this problem which…
This article provides an original understanding of the behavior of a class of graph-oriented semi-supervised learning algorithms in the limit of large and numerous data. It is demonstrated that the intuition at the root of these methods…
Branes and defects in topological Landau-Ginzburg models are described by matrix factorisations. We revisit the problem of deforming them and discuss various deformation methods as well as their relations. We have implemented these…
This paper focuses on the convergence certificates of the majorized proximal alternating minimization (PAM) method with subspace correction, proposed in \cite{TaoQianPan22} for the column $\ell_{2,0}$-norm regularized factorization model…
Low-rank factorization is a popular model compression technique that minimizes the error $\delta$ between approximated and original weight matrices. Despite achieving performances close to the original models when $\delta$ is optimized, a…
We conduct a study and comparison of superiorization and optimization approaches for the reconstruction problem of superiorized/regularized least-squares solutions of underdetermined linear equations with nonnegativity variable bounds.…
This paper concerns a class of DC composite optimization problems which, as an extension of convex composite optimization problems and DC programs with nonsmooth components, often arises in robust factorization models of low-rank matrix…
The elementary theory of bivariate linear Diophantine equations over polynomial rings is used to construct causal lifting factorizations (elementary matrix decompositions) for causal two-channel FIR perfect reconstruction transfer matrices…
Nonconvex optimization problems are widespread in modern machine learning and data science. We introduce an extrapolation strategy into a class of preconditioned second-order convex splitting algorithms for nonconvex optimization problems.…
Gradient descent for matrix factorization exhibits an implicit bias toward approximately low-rank solutions. While existing theories often assume the boundedness of iterates, empirically the bias persists even with unbounded sequences. This…
When solving decision-making problems with mathematical optimization, some constraints or objectives may lack analytic expressions but can be approximated from data. When an approximation is made by neural networks, the underlying problem…
The randomized extended Kaczmarz and Gauss-Seidel algorithms have attracted much attention because of their ability to treat all types of linear systems (consistent or inconsistent, full rank or rank-deficient). In this paper, we interpret…