# Phase Transitions in the Output Distribution of Large Language Models

arXiv: https://arxiv.org/abs/2405.17088 · HTML: https://mlsanity.com/paper/2405.17088/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 59 of its 118 references that are in the map.
- First posted on arXiv 27 May 2024.

## Builds on (most cited first, 30 of 59)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [Beyond the Imitation Game: Quantifying and extrapolating the capabilities of language models](https://mlsanity.com/paper/2206.04615/) (2022)
- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [Scaling Language Models: Methods, Analysis & Insights from Training Gopher](https://mlsanity.com/paper/2112.11446/) (2021)
- [Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 small](https://mlsanity.com/paper/2211.00593/) (2022)
- [Scaling Vision Transformers](https://mlsanity.com/paper/2106.04560/) (2021)
- [Reconciling modern machine learning practice and the bias-variance trade-off](https://mlsanity.com/paper/1812.11118/) (2018)
- [Progress measures for grokking via mechanistic interpretability](https://mlsanity.com/paper/2301.05217/) (2023)
- [Towards Automated Circuit Discovery for Mechanistic Interpretability](https://mlsanity.com/paper/2304.14997/) (2023)
- [Deep Double Descent: Where Bigger Models and More Data Hurt](https://mlsanity.com/paper/1912.02292/) (2019)
- [Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasets](https://mlsanity.com/paper/2201.02177/) (2022)
- [Deep Learning Scaling is Predictable, Empirically](https://mlsanity.com/paper/1712.00409/) (2017)
- [Are Emergent Abilities of Large Language Models a Mirage?](https://mlsanity.com/paper/2304.15004/) (2023)
- [Scaling Laws for Autoregressive Generative Modeling](https://mlsanity.com/paper/2010.14701/) (2020)
- [Opening the Black Box of Deep Neural Networks via Information](https://mlsanity.com/paper/1703.00810/) (2017)
- [The Effects of Reward Misspecification: Mapping and Mitigating Misaligned Models](https://mlsanity.com/paper/2201.03544/) (2022)
- [Language Models Represent Space and Time](https://mlsanity.com/paper/2310.02207/) (2023)
- [NIPS 2016 Tutorial: Generative Adversarial Networks](https://mlsanity.com/paper/1701.00160/) (2016)
- [Exponential expressivity in deep neural networks through transient chaos](https://mlsanity.com/paper/1606.05340/) (2016)
- [Towards Understanding Grokking: An Effective Theory of Representation Learning](https://mlsanity.com/paper/2205.10343/) (2022)
- [Gradient Descent Happens in a Tiny Subspace](https://mlsanity.com/paper/1812.04754/) (2018)
- [A Constructive Prediction of the Generalization Error Across Scales](https://mlsanity.com/paper/1909.12673/) (2019)
- [Predictability and Surprise in Large Generative Models](https://mlsanity.com/paper/2202.07785/) (2022)

## Built on by (most cited first, 7 of 7)

- [Model Organisms for Emergent Misalignment](https://mlsanity.com/paper/2506.11613/) (2025)
- [Phase transition in large language models and the criticality of natural languages](https://mlsanity.com/paper/2406.05335/) (2024)
- [Decomposing Behavioral Phase Transitions in LLMs: Order Parameters for Emergent Misalignment](https://mlsanity.com/paper/2508.20015/) (2025)
- [From Density Matrices to Phase Transitions in Deep Learning: Spectral Early Warnings and Interpretability](https://mlsanity.com/paper/2603.29805/) (2026)
- [Another Turn, Better Output? A Turn-Wise Analysis of Iterative LLM Prompting](https://mlsanity.com/paper/2509.06770/) (2025)
- [What Iterated Self-Feeding Probes of Language Models Measure, and a test that separates the construction from the model](https://mlsanity.com/paper/2608.10986/) (2026)
- [Temperature-driven inversion and nonlinear dynamics in ChatGPT-like AIs](https://mlsanity.com/paper/2608.00939/) (2026)

## Abstract (arXiv)

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.