相关论文: PrecoG: an efficient unitary split preconditioner …

We present an online preconditioning technique for the primal-dual hybrid gradient (PDHG) algorithm for linear programming (LP). The method adaptively updates primal and dual preconditioners using an online optimization framework. To…

Solving the normal equations corresponding to large sparse linear least-squares problems is an important and challenging problem. For very large problems, an iterative solver is needed and, in general, a preconditioner is required to…

In this paper, we further investigate and refine the subspace-constrained preconditioning technique to enhance the theoretical and numerical convergence properties of randomized iterative methods for solving linear systems. In particular,…

Tensor decomposition has emerged as a prominent technique to learn low-dimensional representation under the supervision of reconstruction error, primarily benefiting data inference tasks like completion and imputation, but not…

We propose an augmented Lagrangian-based preconditioner to accelerate the convergence of Krylov subspace methods applied to linear systems of equations with a block three-by-three structure such as those arising from mixed finite element…

This work develops neural-network--based preconditioners to accelerate solution of the Wilson-Dirac normal equation in lattice quantum field theories. The approach is implemented for the two-flavor lattice Schwinger model near the critical…

Structured convex optimization on weighted graphs finds numerous applications in machine learning and computer vision. In this work, we propose a novel adaptive preconditioning strategy for proximal algorithms on this problem class. Our…

Fully connected Graph Transformers (GT) have rapidly become prominent in the static graph community as an alternative to Message-Passing models, which suffer from a lack of expressivity, oversquashing, and under-reaching. However, in a…

High-quality data plays a critical role in the pretraining and fine-tuning of large language models (LLMs), even determining their performance ceiling to some degree. Consequently, numerous data selection methods have been proposed to…

Recent efforts to accelerate LLM pretraining have focused on computationally-efficient approximations that exploit second-order structure. This raises a key question for large-scale training: how much performance is forfeited by these…

This paper introduces a new preconditioning technique that is suitable for matrices arising from the discretization of a system of PDEs on unstructured grids. The preconditioner satisfies a so-called filtering property, which ensures that…

Though linguistic knowledge emerges during large-scale language model pretraining, recent work attempt to explicitly incorporate human-defined linguistic priors into task-specific fine-tuning. Infusing language models with syntactic or…

Gaussian process hyperparameter optimization requires linear solves with, and log-determinants of, large kernel matrices. Iterative numerical techniques are becoming popular to scale to larger datasets, relying on the conjugate gradient…

The Muon optimizer, a matrix-structured algorithm that leverages spectral orthogonalization of gradients, is a milestone in the pretraining of large language models. However, the underlying mechanisms of Muon -- particularly the role of…

We present a preconditioning of a generalized forward-backward splitting algorithm for finding a zero of a sum of maximally monotone operators $\sum_{i=1}^{n} A_i + B$ with $B$ cocoercive, involving only the computation of $B$ and of the…

Graph pre-training has achieved remarkable success in recent years, delivering transferable representations for downstream adaptation. However, most existing methods are designed for either homogeneous or heterogeneous graphs, thereby…

To keep massive MIMO systems cost-efficient, power amplifiers with rather small output dynamic ranges are employed. They may distort the transmit signal and degrade the performance. This paper proposes a distortion aware precoding scheme…

Trained on the large corpus, pre-trained language models (PLMs) can capture different levels of concepts in context and hence generate universal language representations. They can benefit multiple downstream natural language processing…

We derive nonlinear acceleration methods based on the limited memory BFGS (L-BFGS) update formula for accelerating iterative optimization methods of alternating least squares (ALS) type applied to canonical polyadic (CP) and Tucker tensor…

A linearly implicit conservative difference scheme is applied to discretize the attractive coupled nonlinear Schr\"odinger equations with fractional Laplacian. Complex symmetric linear systems can be obtained, and the system matrices are…