Related papers: Improved Generalization Bound and Learning of Spar…

Recently, Musco and Woodruff (FOCS, 2017) showed that given an $n \times n$ positive semidefinite (PSD) matrix $A$, it is possible to compute a $(1+\epsilon)$-approximate relative-error low-rank approximation to $A$ by querying…

Efficient fine-tuning plays a fundamental role in modern large models, with low-rank adaptation emerging as a particularly promising approach. However, the existing variants of LoRA are hampered by limited expressiveness, a tendency to…

Learning-to-Rank (LTR) is a supervised machine learning approach that constructs models specifically designed to order a set of items or documents based on their relevance or importance to a given query or context. Despite significant…

In this work, we propose norm-bounded low-rank adaptation (NB-LoRA) for parameter-efficient fine tuning. NB-LoRA is a novel parameterization of low-rank weight adaptations that admits explicit bounds on each singular value of the adaptation…

Algorithm-dependent generalization error bounds are central to statistical learning theory. A learning algorithm may use a large hypothesis space, but the limited number of iterations controls its model capacity and generalization error.…

Information-theoretic (IT) generalization bounds have been used to study the generalization of learning algorithms. These bounds are intrinsically data- and algorithm-dependent so that one can exploit the properties of data and algorithm to…

This survey highlights the recent advances in algorithms for numerical linear algebra that have come from the technique of linear sketching, whereby given a matrix, one first compresses it to a much smaller matrix by multiplying it by a…

Adapting large language models (LLMs) to downstream tasks via full fine-tuning is increasingly impractical due to its computational and memory demands. Parameter-efficient fine-tuning (PEFT) approaches such as Low-Rank Adaptation (LoRA)…

We propose an online learning algorithm for a class of machine learning models under a separable stochastic approximation framework. The essence of our idea lies in the observation that certain parameters in the models are easier to…

Laplace approximation (LA) and its linearized variant (LLA) enable effortless adaptation of pretrained deep neural networks to Bayesian neural networks. The generalized Gauss-Newton (GGN) approximation is typically introduced to improve…

We study classic streaming and sparse recovery problems using deterministic linear sketches, including l1/l1 and linf/l1 sparse recovery problems (the latter also being known as l1-heavy hitters), norm estimation, and approximate inner…

Large pre-trained models, such as large language models (LLMs), present significant resource challenges for fine-tuning due to their extensive parameter sizes, especially for applications in mobile systems. To address this, Low-Rank…

Low-Rank Adaptation (LoRA) enables parameter-efficient fine-tuning of large models by decomposing weight updates into low-rank matrices, significantly reducing storage and computational overhead. While effective, standard LoRA lacks…

Low-Rank Adaptation (LoRA) is a widely-used parameter-efficient finetuning method for large language models. LoRA saves memory by training only low rank perturbations to selected weight matrices. In this work, we compare the performance of…

Fine-tuning pre-trained large language models in a parameter-efficient manner is widely studied for its effectiveness and efficiency. The popular method of low-rank adaptation (LoRA) offers a notable approach, hypothesizing that the…

Kernel methods are learning algorithms that enjoy solid theoretical foundations while suffering from important computational limitations. Sketching, which consists in looking for solutions among a subspace of reduced dimension, is a well…

Recently, metric learning and similarity learning have attracted a large amount of interest. Many models and optimisation algorithms have been proposed. However, there is relatively little work on the generalization analysis of such…

We study the generalization properties of ridge regression with random features in the statistical learning framework. We show for the first time that $O(1/\sqrt{n})$ learning bounds can be achieved with only $O(\sqrt{n}\log n)$ random…

The Johnson--Lindenstrauss (JL) lemma is a powerful tool for dimensionality reduction in modern algorithm design. The lemma states that any set of high-dimensional points in a Euclidean space can be flattened to lower dimensions while…

Learning from label proportions (LLP) is a generalization of supervised learning in which the training data is available as sets or bags of feature-vectors (instances) along with the average instance-label of each bag. The goal is to train…