  Prior studies on the emergence in large models have primarily focused on how
the functional capabilities of large language models (LLMs) scale with model
size. Our research, however, transcends this traditional paradigm, aiming to
deepen our understanding of the emergence within LLMs by placing a special
emphasis not just on the model size but more significantly on the complex
behavior of neuron interactions during the training process. By introducing the
concepts of "self-organization" and "multifractal analysis," we explore how
neuron interactions dynamically evolve during training, leading to "emergence,"
mirroring the phenomenon in natural systems where simple micro-level
interactions give rise to complex macro-level behaviors. To quantitatively
analyze the continuously evolving interactions among neurons in large models
during training, we propose the Neuron-based Multifractal Analysis (NeuroMFA).
Utilizing NeuroMFA, we conduct a comprehensive examination of the emergent
behavior in LLMs through the lens of both model size and training process,
paving new avenues for research into the emergence in large models.
