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Parameter-efficient fine-tuning (PEFT) methods, which fine-tune only a subset of model parameters, offer a promising solution by reducing the computational costs of tuning large language models (LLMs) while maintaining their performance.…

In this paper, we study the problem of learning multi-dimensional Gaussian Mixture Models (GMMs), with a specific focus on model order selection and efficient mixing distribution estimation. We first establish an information-theoretic lower…

Various parameter-efficient fine-tuning (PEFT) techniques have been proposed to enable computationally efficient fine-tuning while maintaining model performance. However, existing PEFT methods are still limited by the growing number of…

We analyze optimal complexity of adaptive finite element methods (AFEMs) for general second-order linear elliptic partial differential equations (PDEs) in the Lax-Milgram setting. To this end, we formulate an adaptive algorithm which steers…

Parameter-efficient fine-tuning (PEFT) has attracted significant attention due to the growth of pre-trained model sizes and the need to fine-tune (FT) them for superior downstream performance. Despite a surge in new PEFT methods, a…

Parameter-efficient fine-tuning (PEFT) has emerged as a crucial approach for adapting large vision transformers to downstream tasks without the prohibitive computational costs of full fine-tuning. While existing visual prompt tuning (VPT)…

Fine-tuning Large Language Models (LLMs) typically involves either full fine-tuning, which updates all model parameters, or Parameter-Efficient Fine-Tuning (PEFT), which adjusts a small subset of parameters. However, both approaches have…

This paper delves into the pressing need in Parameter-Efficient Fine-Tuning (PEFT) for Large Language Models (LLMs). While LLMs possess remarkable capabilities, their extensive parameter requirements and associated computational demands…

Parameter Efficient Fine-Tuning (PEFT) techniques have drawn significant attention due to their ability to yield competitive results while updating only a small portion of the adjustable parameters. However, existing PEFT methods pose…

Parameter-efficient fine-tuning (PEFT) methods have emerged as a practical solution for adapting large foundation models to downstream tasks, reducing computational and memory costs by updating only a small subset of parameters. Among them,…

We present a novel Parameter-Efficient Fine-Tuning (PEFT) method, dubbed as Adaptive Freezing of Low Rank Adaptation (AFLoRA). Specifically, for each pre-trained frozen weight tensor, we add a parallel path of trainable low-rank matrices,…

We use the ideas of goal-oriented error estimation and adaptivity to design and implement an efficient adaptive algorithm for approximating linear quantities of interest derived from solutions to elliptic partial differential equations…

Gaussian processes (GPs) are generally regarded as the gold standard surrogate model for emulating computationally expensive computer-based simulators. However, the problem of training GPs as accurately as possible with a minimum number of…

In this paper, we consider an approximation method, and a novel general analysis, for second-order elliptic differential equations with heterogeneous multiscale coefficients. We obtain convergence of the Generalized Multi-scale Finite…

This paper presents an extensive examination of Parameter-Efficient Fine-Tuning (PEFT) for embedding domain specific facts into Large Language Models (LLMs), focusing on improving the fine-tuning process by categorizing question-answer (QA)…

This paper is concerned with the numerical approximation of quantities of interest associated with solutions to parametric elliptic partial differential equations (PDEs). The key novelty of this work is in its focus on the quantities of…

In this paper, we provide a novel method for the estimation of unknown parameters of the Gaussian Mixture Model (GMM) in Positron Emission Tomography (PET). A vast majority of PET imaging methods are based on reconstruction model that is…

This paper studies the partial estimation of Gaussian graphical models from high-dimensional empirical observations. We derive a convex formulation for this problem using $\ell_1$-regularized maximum-likelihood estimation, which can be…

Large-scale foundation models have demonstrated remarkable versatility across a wide range of downstream tasks. However, fully fine-tuning these models incurs prohibitive computational costs, motivating the development of…

We study the gradient Expectation-Maximization (EM) algorithm for Gaussian Mixture Models (GMM) in the over-parameterized setting, where a general GMM with $n>1$ components learns from data that are generated by a single ground truth…