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While large language models (LLMs) have emerged as a significant advancement in artificial intelligence, the hardware and computational costs for training LLMs are also significantly burdensome. Among the state-of-the-art optimizers, AdamW…

Huge pretrained language models (LMs) have demonstrated surprisingly good zero-shot capabilities on a wide variety of tasks. This gives rise to the appealing vision of a single, versatile model with a wide range of functionalities across…

Safe derivative-free optimization under unknown constraints is a fundamental challenge in modern learning and control. Existing zeroth-order (ZO) methods typically still assume access to a first-order oracle of the constraint functions or…

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 vast majority of successful deep neural networks are trained using variants of stochastic gradient descent (SGD) algorithms. Recent attempts to improve SGD can be broadly categorized into two approaches: (1) adaptive learning rate…

Large Language Models (LLMs) perform well on many NLP tasks, but fine-tuning them on resource-constrained mobile devices is challenging due to high memory and computation costs, despite growing demands for privacy-preserving…

Spectral optimizers such as Muon have recently shown strong empirical performance in large-scale language model training, but the source and extent of their advantage remain poorly understood. We study this question through the linear…

Forward-mode automatic differentiation (FmAD) and zero-order (ZO) optimization have been proposed as memory-efficient alternatives to backpropagation (BP) for gradient computation, especially in low-resource settings. However, their…

Federated fine-tuning of large language models (LLMs) with low-rank adaptation (LoRA) offers a communication-efficient and privacy-preserving solution for task-specific adaptation. Naive aggregation of LoRA modules introduces noise due to…

Fine-tuning large language models (LLMs) with backpropagation\textemdash even for a subset of parameters such as LoRA\textemdash can be much more memory-consuming than inference and is often deemed impractical for resource-constrained…

Advances in large language models have driven strong performance across many tasks, but their memory and compute costs still hinder deployment. SVD-based compression reduces storage and can speed up inference via low-rank factors, yet…

This paper introduces an efficient strategy to transform Large Language Models (LLMs) into Multi-Modal Large Language Models (MLLMs). By conceptualizing this transformation as a domain adaptation process, i.e., transitioning from text…

$\ell_0$ constrained optimization is prevalent in machine learning, particularly for high-dimensional problems, because it is a fundamental approach to achieve sparse learning. Hard-thresholding gradient descent is a dominant technique to…

Automated optimization modeling via Large Language Models (LLMs) has emerged as a promising approach to assist complex human decision-making. While post-training has become a pivotal technique to enhance LLMs' capabilities in this domain,…

In many real-world problems, first-order (FO) derivative evaluations are too expensive or even inaccessible. For solving these problems, zeroth-order (ZO) methods that only need function evaluations are often more efficient than FO methods…

We study robust parameter-efficient fine-tuning (PEFT) techniques designed to improve accuracy and generalization while operating within strict computational and memory hardware constraints, specifically focusing on large-language models…

Training large language models (LLMs) encounters challenges in GPU memory consumption due to the high memory requirements of model states. The widely used Zero Redundancy Optimizer (ZeRO) addresses this issue through strategic sharding but…

Multimodal Large Language Models (MLLMs) have played an increasingly important role in multimodal intelligence. However, the existing fine-tuning methods often ignore cross-modal heterogeneity, limiting their full potential. In this work,…

We study the implicit bias of momentum-based optimizers on smooth homogeneous models. We show that \textit{momentum steepest descent} algorithms like Muon (spectral norm), MomentumGD ($\ell_2$ norm), and Signum ($\ell_\infty$ norm) are…

Full fine-tuning of Large Language Models (LLMs) is notoriously memory-intensive, primarily because conventional optimizers such as SGD or Adam assume access to exact gradients derived from cached activations. Existing solutions either…