Critical Phase Transition Phenomena in Large Language Models: How Temperature Parameters Affect Text Generation Quality

This article discusses the critical phase transition phenomenon in large language models (LLMs). The study found that when adjusting the temperature parameter, the model undergoes a phase transition between low-temperature (ordered repetition) and high-temperature (disordered chaos) states, exhibiting critical behavior characteristics similar to those of natural language. This research provides a new framework for understanding the internal mechanisms of LLMs from a physics perspective, and has important implications for temperature parameter selection, model evaluation, and interpretability research.

Traditional LLM evaluation relies on single metrics such as perplexity and BLEU scores, which are difficult to capture qualitative changes in behavior. It was observed that when adjusting the temperature parameter, the model output transitions from ordered (low temperature) to disordered (high temperature), similar to phase transition phenomena in physics. Therefore, the research team explored whether LLMs exhibit critical phase transitions and their related characteristics.

The Pythia series models (160 million to 12 billion parameters) were selected to analyze the statistical properties of generated text at different temperatures. Temperature controls sampling randomness: low temperature selects high-probability tokens (deterministic output), while high temperature increases randomness (creative but possibly chaotic). Analysis metrics include correlation functions (long-distance token correlations), convergence speed (steady-state time), entropy, and complexity (randomness and structure).

Experiments revealed abrupt changes in the model's statistical properties when the temperature crosses the critical value: 1. Statistical quantities such as correlation length diverge near the critical point (a sign of phase transition); 2. Token correlations follow power-law decay (long-range correlations, a typical feature of critical systems); 3. The convergence process slows down (critical slowing down phenomenon); 4. The low-temperature phase shows structured repetition, the high-temperature phase is random and incoherent, and the transition zone is the stage for critical phenomena.

The behavior of the model near the critical point is highly similar to natural language—natural language is also in a critical state (neither too ordered nor too disordered). This suggests that LLMs learn the statistical structure of natural language through training, which corresponds exactly to the physical critical state, explaining the model's balance between creativity and coherence (walking the boundary between order and chaos).

1. Temperature parameter selection: Provides a theoretical basis for empirical selection; the model's performance near the critical point is rich but unstable; 2. Model evaluation: Need to consider statistical properties and avoid relying solely on accuracy metrics; 3. Interpretability: The phase transition framework provides a new tool for understanding LLMs; future research can explore the critical behavior of models with different architectures/scales.

Limitations: The experiments are based on Pythia models; whether other architectures (such as Transformer variants, mixture-of-experts models) exhibit similar behavior remains to be verified; the position/property of the critical point depends on training data and tasks. Future directions: Verify other architectures, explore dynamically adjusting temperature to guide generation patterns, study the impact of critical slowing down on real-time applications, etc.