  Large Language Models (LLMs), such as the Generative Pretrained Transformer
(GPT), have achieved tremendous success in various language tasks, but their
emergent abilities have also raised many questions, concerns, and challenges
that need to be addressed. To gain a better understanding of the models' inner
mechanisms, we analyze the hidden state and channel wave dynamics in a small
GPT, focusing on the coherence of wave patterns in terms of cross-channel
correlation and individual auto-correlation. Our findings suggest that wave
dynamics offer consistent and repeatable intrinsic oscillation modes, along
with context-aware plasticity and expressiveness in language generation. By
analyzing wave patterns, coherence, and clustering, we provide a systematic way
to identify and interpret the functionality of the hidden state channels,
paving the way to understand and control higher-level language pattern
formation. In addition, we investigate the Poisson statistics of spelling
errors in text sequence generation across various levels of model training and
observe a phase-transition-like process. As coherence builds up, there is a
competition between the generation of correct and misspelled words. However,
once the model is adequately trained and significant coherence has emerged, the
coherent process becomes strong enough to effectively suppress spelling errors,
preventing the cascade amplification of defects. The distribution of correct
spellings transitions from Poissonian to Sub-Poissonian, while the distribution
of misspellings shows the opposite trend. By leveraging concepts and techniques
from quantum physics, we gain novel insights into the dynamics of the small
GPT. This approach can be extended to larger language models that exhibit more
complex coherent language patterns, opening up opportunities to interpret their
emergent capabilities and develop more specialized models.
