Related papers: Accelerating the alternating projection algorithm …
Optimization algorithms such as projected Newton's method, FISTA, mirror descent, and its variants enjoy near-optimal regret bounds and convergence rates, but suffer from a computational bottleneck of computing ``projections'' in…
In this paper we explore acceleration techniques for large scale nonconvex optimization problems with special focuses on deep neural networks. The extrapolation scheme is a classical approach for accelerating stochastic gradient descent for…
We introduce a relaxed-projection splitting algorithm for solving variational inequalities in Hilbert spaces for the sum of nonsmooth maximal monotone operators, where the feasible set is defined by a nonlinear and nonsmooth continuous…
Tenfold improvements in computation speed can be brought to the alternating direction method of multipliers (ADMM) for Semidefinite Programming with virtually no decrease in robustness and provable convergence simply by projecting…
This paper proposes a new method for estimating sparse precision matrices in the high dimensional setting. It has been popular to study fast computation and adaptive procedures for this problem. We propose a novel approach, called Sparse…
We present a novel two-level sketching extension of the Alternating Anderson-Picard (AAP) method for accelerating fixed-point iterations in challenging single- and multi-physics simulations governed by discretized partial differential…
We propose a new subgradient method for the minimization of nonsmooth convex functions over a convex set. To speed up computations we use adaptive approximate projections only requiring to move within a certain distance of the exact…
The (unweighted) point-separation problem asks, given a pair of points $s$ and $t$ in the plane, and a set of candidate geometric objects, for the minimum-size subset of objects whose union blocks all paths from $s$ to $t$. Recent work has…
Fitting an unknown number of hyperplanes to data is a fundamental yet challenging problem in machine learning, characterized by its non-convexity, non-differentiability, and unknown model order. Existing approaches often struggle with local…
For a real affine hyperplane arrangement, we define an integer intersection matrix with a natural $q$-deformation related to the intersections of bounded chambers of the arrangement. By connecting the integer matrix to a bilinear form of…
The affine Grassmannian is a noncompact smooth manifold that parameterizes all affine subspaces of a fixed dimension. It is a natural generalization of Euclidean space, points being zero-dimensional affine subspaces. We will realize the…
A partial affine plane of order $n$ is a point-line incidence structure with $n^2$ points and $n$ points on each line, such that every two lines meet in at most one point. In this paper, we show that a partial affine plane of order $n$, $n$…
Multi-vector dense retrieval methods like ColBERT systematically use a single-layer linear projection to reduce the dimensionality of individual vectors. In this study, we explore the implications of the MaxSim operator on the gradient…
In this paper, we propose a general framework to accelerate significantly the algorithms for nonnegative matrix factorization (NMF). This framework is inspired from the extrapolation scheme used to accelerate gradient methods in convex…
Many computer graphics problems require computing geometric shapes subject to certain constraints. This often results in non-linear and non-convex optimization problems with globally coupled variables, which pose great challenge for…
A topological hyperplane is a subspace of R^n (or a homeomorph of it) that is topologically equivalent to an ordinary straight hyperplane. An arrangement of topological hyperplanes in R^n is a finite set H such that k topological…
Inference of latent feature models in the Bayesian nonparametric setting is generally difficult, especially in high dimensional settings, because it usually requires proposing features from some prior distribution. In special cases, where…
We introduce a class of maps from an affine flat into a Riemannian manifold that solve an elliptic system defined by the natural second order elliptic operator of the affine structure and the nonlinear Riemann geometry of the target. These…
We describe an algorithm that, given any full-rank matrix A having fewer rows than columns, can rapidly compute the orthogonal projection of any vector onto the null space of A, as well as the orthogonal projection onto the row space of A,…
The convergence of Boltzmann Fokker Planck solution can become arbitrarily slow with iterative procedures like source iteration. This paper derives and investigates a nonlinear diffusion acceleration scheme for the solution of the Boltzmann…