HELENE: Hessian Layer-wise Clipping and Gradient Annealing for Accelerating Fine-tuning LLM with Zeroth-order Optimization

TL;DR

HELENE is a novel optimizer that accelerates fine-tuning of large language models by combining second-order information with gradient annealing, leading to faster convergence and improved accuracy.

Contribution

It introduces HELENE, a scalable optimizer that integrates Hessian-based layer-wise clipping and gradient annealing, significantly enhancing convergence speed for large models.

Findings

Achieves up to 20x speedup over MeZO.

Improves average accuracy by 1.5%.

Compatible with full and parameter-efficient fine-tuning.

Abstract

Fine-tuning large language models (LLMs) poses significant memory challenges, as the back-propagation process demands extensive resources, especially with growing model sizes. Recent work, MeZO, addresses this issue using a zeroth-order (ZO) optimization method, which reduces memory consumption by matching the usage to the inference phase. However, MeZO experiences slow convergence due to varying curvatures across model parameters. To overcome this limitation, we introduce HELENE, a novel scalable and memory-efficient optimizer that integrates annealed A-GNB gradients with a diagonal Hessian estimation and layer-wise clipping, serving as a second-order pre-conditioner. This combination allows for faster and more stable convergence. Our theoretical analysis demonstrates that HELENE improves convergence rates, particularly for models with heterogeneous layer dimensions, by reducing the dependency on the total parameter space dimension. Instead, the method scales with the largest layer dimension, making it highly suitable for modern LLM architectures. Experimental results on RoBERTa-large and OPT-1.3B across multiple tasks show that HELENE achieves up to a 20x speedup compared to MeZO, with average accuracy improvements of 1.5%. Furthermore, HELENE remains compatible with both full parameter tuning and parameter-efficient fine-tuning (PEFT), outperforming several state-of-the-art optimizers. The codes will be released after reviewing.