Large Language Models (LLMs) are often quantized to lower precision to reduce the memory cost and latency in inference. However, quantization often degrades model performance, thus fine-tuning is required for various downstream tasks. Traditional fine-tuning methods such as stochastic gradient descent and Adam optimization require backpropagation, which is error-prone in the low-precision settings. To overcome these limitations, we propose the Quantized Zeroth-Order (QuZO) framework, specifically designed for fine-tuning LLMs through low-precision (e.g., 4- or 8-bit) forward passes. Our method avoids the low-precision straight-through estimator, which requires backward computation, and instead utilizes optimized stochastic rounding to mitigate increased bias. QuZO simplifies the training process, while achieving results comparable to first-order methods in FP8 and superior accuracy in INT8 and INT4 training. Experiments demonstrate that QuZO achieves competitive performance on classification, multi-choice, and generation tasks under low-bit training, including zero-shot reasoning tasks. Notably, QuZO incurs minimal overhead and reduces memory consumption by 2.94 ×–5.47 × compared to quantized first-order methods during LLaMA-7B fine-tuning.

Fine-tuning large language models (LLMs) has achieved remarkable performance across various natural language processing tasks, yet it demands more and more memory as model sizes keep growing. To address this issue, the recently proposed Memory-efficient Zeroth-order (MeZO) methods attempt to fine-tune LLMs using only forward passes, thereby avoiding the need for a backpropagation graph. However, significant performance drops and a high risk of divergence have limited their widespread adoption. In this paper, we propose the Adaptive Zeroth-order Tensor-Train Adaption (AdaZeta) framework, specifically designed to improve the performance and convergence of the ZO methods. To enhance dimension-dependent ZO estimation accuracy, we introduce a fast-forward, low-parameter tensorized adapter. To tackle the frequently observed divergence issue in large-scale ZO fine-tuning tasks, we propose an adaptive query number schedule that guarantees convergence. Detailed theoretical analysis and extensive experimental results on Roberta-Large and Llama-2-7B models substantiate the efficacy of our AdaZeta framework in terms of accuracy, memory efficiency, and convergence speed.