LORENZA: Enhancing Generalization in Low-Rank Gradient LLM Training via Efficient Zeroth-Order Adaptive SAM

2025-02-26

AI Summary

To address the poor generalization and weak robustness of parameter-efficient fine-tuning (PEFT) methods under resource constraints, this paper proposes AdaZo-SAM—the first zeroth-order adaptive Sharpness-Aware Minimization framework requiring only a single gradient estimate—and LORENZA, a low-rank gradient optimization method that unifies full-parameter updates with memory compression via randomized SVD. Integrating zeroth-order stochastic estimation, SAM principles, Adam-style momentum, and low-rank subspace projection, the approach ensures theoretical convergence while significantly enhancing multi-task generalization. Experiments on large language model (LLM) fine-tuning demonstrate state-of-the-art trade-offs between accuracy and GPU memory efficiency: memory consumption is reduced by up to 67%, and cross-task average accuracy improves by 2.8%.

Technology Category

• Machine Learning: Large Multimodal Models (LMMs)
• Search and Optimization: Sampling/Simulation-based Search
• Natural Language Processing: (Large) Language Models

Application Category

• Search and Retrieval-Augmented AI: Large language models for search
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation

Abstract

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 (LLMs). Existing PEFT methods often lack robustness and fail to generalize effectively across diverse tasks, leading to suboptimal performance in real-world scenarios. To address this, we present a new highly computationally efficient framework called AdaZo-SAM, combining Adam and Sharpness-Aware Minimization (SAM) while requiring only a single-gradient computation in every iteration. This is achieved using a stochastic zeroth-order estimation to find SAM's ascent perturbation. We provide a convergence guarantee for AdaZo-SAM and show that it improves the generalization ability of state-of-the-art PEFT methods. Additionally, we design a low-rank gradient optimization method named LORENZA, which is a memory-efficient version of AdaZo-SAM. LORENZA utilizes a randomized SVD scheme to efficiently compute the subspace projection matrix and apply optimization steps onto the selected subspace. This technique enables full-parameter fine-tuning with adaptive low-rank gradient updates, achieving the same reduced memory consumption as gradient-low-rank-projection methods. We provide a convergence analysis of LORENZA and demonstrate its merits for pre-training and fine-tuning LLMs.

Problem

• Improves generalization in low-rank gradient LLM training
• Enhances computational efficiency with zeroth-order adaptive SAM
• Reduces memory usage via randomized SVD optimization

Innovation

• AdaZo-SAM combines Adam and SAM
• LORENZA uses low-rank gradient optimization
• Stochastic zeroth-order estimation applied