Phase transition on a context-sensitive random language model with short range interactions

Since the random language model was proposed by E. DeGiuli [Phys. Rev. Lett. 122, 128301], language models have been investigated intensively from the viewpoint of statistical mechanics. Recently, the existence of a Berezinskii--Kosterlitz--Thouless transition was numerically demonstrated in models with long-range interactions between symbols. In statistical mechanics, it has long been known that long-range interactions can induce phase transitions. Therefore, it has remained unclear whether phase transitions observed in language models originate from genuinely linguistic properties that are absent in conventional spin models. In this study, we construct a random language model with short-range interactions and numerically investigate its statistical properties. Our model belongs to the class of context-sensitive grammars in the Chomsky hierarchy and allows explicit reference to contexts. We find that a phase transition occurs even when the model refers only to contexts whose length remains constant with respect to the sentence length. This result indicates that finite-temperature phase transitions in language models are genuinely induced by the intrinsic nature of language, rather than by long-range interactions.

First numerical observation of the Berezinskii-Kosterlitz-Thouless transition in language models

Several power-law critical properties involving different statistics in natural languages -- reminiscent of scaling properties of physical systems at or near phase transitions -- have been documented for decades. The recent rise of large language models (LLMs) has added further evidence and excitement by providing intriguing similarities with notions in physics such as scaling laws and emergent abilities. However, specific instances of classes of generative language models that exhibit phase transitions, as understood by the statistical physics community, are lacking. In this work, inspired by the one-dimensional Potts model in statistical physics we construct a simple probabilistic language model that falls under the class of context sensitive grammars (CSG), and numerically demonstrate an unambiguous phase transition in the framework of a natural language model. We explicitly show that a precisely defined order parameter -- that captures symbol frequency biases in the sentences generated by the language model -- changes from strictly 0 to a strictly nonzero value (in the infinite-length limit of sentences), implying a mathematical singularity arising when tuning the parameter of the stochastic language model we consider. Furthermore, we identify the phase transition as a variant of the Berezinskii-Kosterlitz-Thouless (BKT) transition, which is known to exhibit critical properties not only at the transition point but also in the entire phase. This finding leads to the possibility that critical properties in natural languages may not require careful fine-tuning nor self-organized criticality, but is generically explained by the underlying connection between language structures and the BKT phases.