The long-range dependencies among the tokens, which originate from hierarchical structures, are a defining hallmark of human language. However, whether similar dependencies exist within the sequential vocalization of non-human animals remains a topic of investigation. Transformer architectures, known for their ability to model long-range dependencies among tokens, provide a powerful tool for investigating this phenomenon. In this study, we employed the Transformer architecture to analyze the songs of Bengalese finch (Lonchura striata domestica), which are characterized by their highly variable and complex syllable sequences. To this end, we developed FinchGPT, a Transformer-based model trained on a textualized corpus of birdsongs, which outperformed other architecture models in this domain. Attention weight analysis revealed that FinchGPT effectively captures long-range dependencies within syllables sequences. Furthermore, reverse engineering approaches demonstrated the impact of computational and biological manipulations on its performance: restricting FinchGPT's attention span and disrupting birdsong syntax through the ablation of specific brain nuclei markedly influenced the model's outputs. Our study highlights the transformative potential of large language models (LLMs) in deciphering the complexities of animal vocalizations, offering a novel framework for exploring the structural properties of non-human communication systems while shedding light on the computational distinctions between biological brains and artificial neural networks.