# Mixing Times of Glauber Dynamics on Masked Language Models

arXiv: https://arxiv.org/abs/2605.16378 · HTML: https://mlsanity.com/paper/2605.16378/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 22 references that are in the map.
- First posted on arXiv 11 May 2026.

## Builds on (most cited first, 19 of 19)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [RealToxicityPrompts: Evaluating Neural Toxic Degeneration in Language Models](https://mlsanity.com/paper/2009.11462/) (2020)
- [Cross-lingual Language Model Pretraining](https://mlsanity.com/paper/1901.07291/) (2019)
- [Diffusion-LM Improves Controllable Text Generation](https://mlsanity.com/paper/2205.14217/) (2022)
- [StereoSet: Measuring stereotypical bias in pretrained language models](https://mlsanity.com/paper/2004.09456/) (2020)
- [Probing Classifiers: Promises, Shortcomings, and Advances](https://mlsanity.com/paper/2102.12452/) (2021)
- [Simple and Effective Masked Diffusion Language Models](https://mlsanity.com/paper/2406.07524/) (2024)
- [Discrete Diffusion Modeling by Estimating the Ratios of the Data Distribution](https://mlsanity.com/paper/2310.16834/) (2023)
- [CrowS-Pairs: A Challenge Dataset for Measuring Social Biases in Masked Language Models](https://mlsanity.com/paper/2010.00133/) (2020)
- [Smarter, Better, Faster, Longer: A Modern Bidirectional Encoder for Fast, Memory Efficient, and Long Context Finetuning and Inference](https://mlsanity.com/paper/2412.13663/) (2024)
- [The Woman Worked as a Babysitter: On Biases in Language Generation](https://mlsanity.com/paper/1909.01326/) (2019)
- [DiffuSeq: Sequence to Sequence Text Generation with Diffusion Models](https://mlsanity.com/paper/2210.08933/) (2022)
- [What do you learn from context? Probing for sentence structure in contextualized word representations](https://mlsanity.com/paper/1905.06316/) (2019)
- [How to Fine-Tune BERT for Text Classification?](https://mlsanity.com/paper/1905.05583/) (2019)
- [DiffusionBERT: Improving Generative Masked Language Models with Diffusion Models](https://mlsanity.com/paper/2211.15029/) (2022)
- [Visualizing and Understanding Neural Models in NLP](https://mlsanity.com/paper/1506.01066/) (2015)
- [BERT has a Mouth, and It Must Speak: BERT as a Markov Random Field Language Model](https://mlsanity.com/paper/1902.04094/) (2019)

## Built on by (most cited first, 2 of 2)

- [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)
- [An Identifiability Theory of Masked Prediction: Mode Blindness and Mask Schedules](https://mlsanity.com/paper/2608.01383/) (2026)

## Abstract (arXiv)

Masked language models (MLMs) define local conditional distributions over tokens but do not, in general, correspond to any consistent joint distribution over sequences. This raises a fundamental question: what global distributional behavior is induced when such conditionals are used iteratively for generation? We address this question by modeling iterative masked-token resampling as a Glauber dynamics Markov chain on the discrete space of token sequences. We first show that MLM conditionals are intrinsically incompatible: we introduce a rectangle test that certifies this incompatibility and empirically verify its prevalence across modern MLMs. We then provide a theoretical analysis of the induced Markov chain. Under bounded cross-token influence, we establish a high-temperature contraction result implying O(nlog n) mixing time where n is the sequence length. In contrast, we prove that under a uniform local margin condition, the chain exhibits metastability, with exponentially slow escape from semantic basins at low temperatures. Empirically, we demonstrate a phase transition in mixing behavior as a function of temperature and sequence length, consistent with the theoretical predictions. We further characterize the induced stationary behavior through semantic trajectories, identifying persistent structures such as long-lived traps and recurrent semantic basins, with political content serving as a measurable case study.