相关论文: Robust Implicit Adaptive Low Rank Time-Stepping Me…

Implicit solvers present strong limitations when used on supercomputing facilities and in particular for adaptive mesh-refinement codes. We present a new method for implicit adaptive time-stepping on adaptive mesh refinement-grids. We…

We consider a framework for the construction of iterative schemes for operator equations that combine low-rank approximation in tensor formats and adaptive approximation in a basis. Under fairly general assumptions, we obtain a rigorous…

We consider one-step methods for integrating stochastic differential equations and prove pathwise convergence using ideas from rough path theory. In contrast to alternative theories of pathwise convergence, no knowledge is required of…

Fine-tuning Large Language Models (LLMs) remains structurally uncertain despite parameter-efficient methods such as Low-Rank Adaptation (LoRA), as the layer-specific roles of internal representations are poorly understood, leading to…

Layer factorization has emerged as a widely used technique for training memory-efficient neural networks. However, layer factorization methods face several challenges, particularly a lack of robustness during the training process. To…

We propose a method for rank $k$ approximation to a given input matrix $X \in \mathbb{R}^{d \times n}$ which runs in time \[ \tilde{O} \left(d ~\cdot~ \min\left\{n + \tilde{sr}(X) \,G^{-2}_{k,p+1}\ ,\ n^{3/4}\, \tilde{sr}(X)^{1/4}…

This paper proposes a scalable binary CUR low-rank approximation algorithm that leverages parallel selection of representative rows and columns within a deterministic framework. By employing a blockwise adaptive cross approximation…

This article is an extended version of previous work of the authors [40, 41] on low-rank matrix estimation in the presence of constraints on the factors into which the matrix is factorized. Low-rank matrix factorization is one of the basic…

Parameter-efficient fine-tuning methods like Low-Rank Adaptation (LoRA) have become essential for deploying large language models, yet their static parameter allocation remains suboptimal for inputs of varying complexity. We present…

Understanding the implicit regularization imposed by neural network architectures and gradient based optimization methods is a key challenge in deep learning and AI. In this work we provide sharp results for the implicit regularization…

Low-rank structure is a common implicit assumption in many modern reinforcement learning (RL) algorithms. For instance, reward-free and goal-conditioned RL methods often presume that the successor measure admits a low-rank representation.…

Domain adaptation methods reduce domain shift typically by learning domain-invariant features. Most existing methods are built on distribution matching, e.g., adversarial domain adaptation, which tends to corrupt feature discriminability.…

Over the past years Robust PCA has been established as a standard tool for reliable low-rank approximation of matrices in the presence of outliers. Recently, the Robust PCA approach via nuclear norm minimization has been extended to…

A space-time adaptive scheme is presented for solving advection equations in two space dimensions. The gradient-augmented level set method using a semi-Lagrangian formulation with backward time integration is coupled with a point value…

Efficient and accurate low-rank approximation (LRA) methods are of great significance for large-scale data analysis. Randomized tensor decompositions have emerged as powerful tools to meet this need, but most existing methods perform poorly…

Low-Rank Adaptation (LoRA) fine-tunes large models by learning low-rank updates on top of frozen weights, dramatically reducing trainable parameters and memory. In this work, we address the gap between training with full steps with low-rank…

The advent of parameter-efficient fine-tuning methods has significantly reduced the computational burden of adapting large-scale pretrained models to diverse downstream tasks. However, existing approaches often struggle to achieve robust…

Numerous applications in data mining and machine learning require recovering a matrix of minimal rank. Robust principal component analysis (RPCA) is a general framework for handling this kind of problems. Nuclear norm based convex surrogate…

Neural operators have emerged as data-driven surrogates for solving partial differential equations (PDEs), and their success hinges on efficiently modeling the long-range, global coupling among spatial points induced by the underlying…

The influence-matrix formalism provides an alternative route to the classical simulation of quantum dynamics. Because influence matrices retain information only about the effective bath seen by local observables, they are expected to be…