Fine-tuning large language models (LLMs) using standard first-order (FO) optimization oftendrives training toward sharp, poorly generalizing minima. Conversely, zeroth-order (ZO) methods offer stronger exploratory behaviorwithout 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 Hi-ZFO (Hierarchical Zeroth- and First-Order 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.

Fine-tuning all parameters of large language models (LLMs) requires significant computational resources and is time-consuming. Recent parameter-efficient tuning methods such as Adapter tuning, Prefix tuning, and LoRA allow for updating a small subset of parameters in large language models. However, they can only save approximately 30% of the training memory requirements, due to the problem that gradient computation and backpropagation are still necessary for these methods. This paper proposes a novel parameter-efficient tuning method for LLMs without calculating their gradients. Leveraging the discernible similarities between the parameter-efficient modules of the same task learned by both large and small language models, we put forward a strategy for transferring the parameter-efficient modules, originally derived from small language models to much larger ones. To ensure a smooth and effective adaptation process, we further introduce a Bridge model to guarantee dimensional consistency while also stimulating a dynamic interaction between the models. We demonstrate the effectiveness of our method using the T5 and GPT-2 series of language models on the SuperGLUE benchmark. Our method achieves comparable performance to both fine-tuning and parameter-efficient tuning on large language models without needing gradient-based optimization. Additionally, our method achieves up to 5.7x memory reduction compared to parameter-efficient tuning.