Trust the Direction, Search the Step: Zero-and-First-Order Methods for LLM Fine-Tuning

Step-size selection remains a central challenge in large-scale neural network optimization; conservative steps slow convergence, while aggressive steps can destabilize it. We combine \textbf{Z}ero-and-\textbf{F}irst-\textbf{O}rder optimization~(ZFO) and propose a lightweight framework that decouples