Phase Transitions in the Output Distribution of Large Language Models

In a physical system, changing parameters such as temperature can induce a phase transition: an abrupt change from one state of matter to another. Analogous phenomena have recently been observed in large language models. Typically, the task of identifying phase transitions requires human analysis and some prior understanding of the system to narrow down which low-dimensional properties to monitor and analyze. Statistical methods for the automated detection of phase transitions from data have recently been proposed within the physics community. These methods are largely system agnostic and, as shown here, can be adapted to study the behavior of large language models. In particular, we quantify distributional changes in the generated output via statistical distances, which can be efficiently estimated with access to the probability distribution over next-tokens. This versatile approach is capable of discovering new phases of behavior and unexplored transitions -- an ability that is particularly exciting in light of the rapid development of language models and their emergent capabilities.

Machine learning phase transitions: Connections to the Fisher information

Despite the widespread use and success of machine-learning techniques for detecting phase transitions from data, their working principle and fundamental limits remain elusive. Here, we explain the inner workings and identify potential failure modes of these techniques by rooting popular machine-learning indicators of phase transitions in information-theoretic concepts. Using tools from information geometry, we prove that several machine-learning indicators of phase transitions approximate the square root of the system's (quantum) Fisher information from below -- a quantity that is known to indicate phase transitions but is often difficult to compute from data. We numerically demonstrate the quality of these bounds for phase transitions in classical and quantum systems.