Hi-ZFO: Hierarchical Zeroth- and First-Order LLM Fine-Tuning via Importance-Guided Tensor Selection

TL;DR

Hi-ZFO introduces a hierarchical hybrid optimization method combining zeroth- and first-order techniques, adaptively applying them to different model layers to improve fine-tuning efficiency and generalization of large language models.

Contribution

This paper proposes Hi-ZFO, a novel hybrid framework that adaptively combines zeroth- and first-order optimization for LLM fine-tuning, enhancing performance and reducing training time.

Findings

Achieves superior performance across diverse tasks.

Reduces training time significantly.

Effectively escapes local minima during training.

Abstract

Fine-tuning large language models (LLMs) using standard first-order (FO) optimization often drives training toward sharp, poorly generalizing minima. Conversely, zeroth-order (ZO) methods offer stronger exploratory behavior without relying on explicit gradients, yet suffer from slow convergence. More critically, our analysis reveals that in generative tasks, the vast output and search space significantly amplify estimation variance, rendering ZO methods both noisy and inefficient. To address these challenges, we propose \textbf{Hi-ZFO} (\textbf{Hi}erarchical \textbf{Z}eroth- and \textbf{F}irst-\textbf{O}rder optimization), a hybrid framework designed to synergize the precision of FO gradients with the exploratory capability of ZO estimation. Hi-ZFO adaptively partitions the model through layer-wise importance profiling, applying precise FO updates to critical layers while leveraging ZO optimization for less sensitive ones. Notably, ZO in Hi-ZFO is not merely a memory-saving surrogate; it is intentionally introduced as a source of "beneficial stochasticity" to help the model escape the local minima where pure FO optimization tends to stagnate. Validated across diverse generative, mathematical, and code reasoning tasks, Hi-ZFO consistently achieves superior performance while significantly reducing the training time. These results demonstrate the effectiveness of hierarchical hybrid optimization for LLM fine-tuning.