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Function name inference in stripped binaries is an important yet challenging task for many security applications, such as malware analysis and vulnerability discovery, due to the need to grasp binary code semantics amidst diverse instruction sets, architectures, compiler optimizations, and obfuscations. While machine learning has made significant progress in this field, existing methods often struggle with unseen data, constrained by their reliance on a limited vocabulary-based classification approach. In this paper, we present SymGen, a novel framework employing an autoregressive generation paradigm powered by domain-adapted generative large language models (LLMs) for enhanced binary code interpretation. We have evaluated SymGen on a dataset comprising 2,237,915 binary functions across four architectures (x86-64, x86-32, ARM, MIPS) with four levels of optimizations (O0-O3) where it surpasses the state-of-the-art with up to 409.3%, 553.5%, and 489.4% advancement in precision, recall, and F1 score, respectively, showing superior effectiveness and generalizability. Our ablation and case studies also demonstrate the significant performance boosts achieved by our design, e.g., the domain adaptation approach, alongside showcasing SymGen’s practicality in analyzing real-world binaries, e.g., obfuscated binaries and malware executables.