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Phase Transitions in Large Language Models and the $O(N)$ Model by Sun, Youran; Haghighat, Babak is a scholarly article available to read on EtoBox.

What is Phase Transitions in Large Language Models and the $O(N)$ Model about?

Large language models (LLMs) exhibit unprecedentedly rich scaling behaviors. In physics, scaling behavior is closely related to phase transitions, critical phenomena, and field theory. To investigate the phase transition phenomena in LLMs, we reformulated the Transformer architecture as an $O(N)$ model. Our study reveals two distinct phase transitions corresponding to the temperature used in text generation and the model's parameter size, respectively. The first phase transition enables us to estimate the internal dimension of the model, while the second phase transition is of \textit{higher-depth} and signals the emergence of new capabilities. As an application, the energy of the $O(N)$ model can be used to evaluate whether an LLM's parameters are sufficient to learn the training data.

Author

Sun, Youran; Haghighat, Babak

Published

2025

Language

EN