mlsanityData to 7 Oct 2026

Slaves to the Law of Large Numbers: An Asymptotic Equipartition Property for Perplexity in Generative Language Models

arXiv 2405.13798 ↗First posted 22 May 2024cs.CL cs.AI cs.ITcited by 4

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Abstract (arXiv)

We prove a new asymptotic un-equipartition property for the perplexity of long texts generated by a language model and present supporting experimental evidence from open-source models. Specifically we show that the logarithmic perplexity of any large text generated by a language model must asymptotically converge to the average entropy of its token distributions. This defines a ``typical set'' that all long synthetic texts generated by a language model must belong to. We refine the concept of ''typical set'' to include only grammatically correct texts. We then show that this refined typical set is a vanishingly small subset of all possible grammatically correct texts for a very general definition of grammar. This means that language models are strongly constrained in the range of their possible behaviors and outputs. We make no simplifying assumptions (such as stationarity) about the statistics of language model outputs, and therefore our results are directly applicable to practical real-world models without any approximations. We discuss possible applications of the typical set concept to problems such as detecting synthetic texts and membership inference in training datasets.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 13 of its 54 references that are in the map. First posted on arXiv 22 May 2024.

Builds on

13 of 54 references.

References · 13

  1. 2017Attention Is All You Needcited by 59,932
  2. 2020Language Models are Few-Shot Learnerscited by 32,199
  3. 2019The Curious Case of Neural Text Degenerationcited by 2,881
  4. 2020Extracting Training Data from Large Language Modelscited by 2,144
  5. 2023DetectGPT: Zero-Shot Machine-Generated Text Detection using Probability Curvaturecited by 705
  6. 2019GLTR: Statistical Detection and Visualization of Generated Textcited by 490
  7. 2024Spotting LLMs With Binoculars: Zero-Shot Detection of Machine-Generated Textcited by 255
  8. 2020Artificial Fingerprinting for Generative Models: Rooting Deepfake Attribution in Training Datacited by 200
  9. 2023The Science of Detecting LLM-Generated Textscited by 126
  10. 2023A Survey on LLM-Generated Text Detection: Necessity, Methods, and Future Directionscited by 101
  11. 2021Language Model Evaluation Beyond Perplexitycited by 77
  12. 2024Position: Understanding LLMs Requires More Than Statistical Generalizationcited by 20
1 more
  1. 2020A Tale of Two Perplexities: Sensitivity of Neural Language Models to Lexical Retrieval Deficits in Dementia of the Alzheimer's Typecited by 9

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 2; 2026: 2.

4 papers.

  1. 2025LLM Probability Concentration: How Alignment Shrinks the Generative Horizoncited by 26
  2. 2025Inv-Entropy: A Fully Probabilistic Framework for Uncertainty Quantification in Language Modelscited by 6
  3. 2026Not All Denoising Steps Are Equal: Model Scheduling for Faster Masked Diffusion Language Modelscited by 1
  4. 2026Rethinking Probability-Based Reinforcement Learning From Posterior Concentrationcited by 0

Similar, not cited

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  1. 2026The Probabilistic Structure of Large Language Models
  2. 2026Is my model perplexed for the right reason? Contrasting LLMs' Benchmark Behavior with Token-Level Perplexity
  3. 2026Beyond Confidence: The Rhythms of Reasoning in Generative Models
  4. 2024Large Language Models are Easily Confused: A Quantitative Metric, Security Implications and Typological Analysis
  5. 2025Correlation Dimension of Auto-Regressive Large Language Models
  6. 2024A Probabilistic Perspective on Unlearning and Alignment for Large Language Models
  7. 2025Scaling Laws of Synthetic Data for Language Models
  8. 2025What is an "Abstract Reasoner"? Revisiting Experiments and Arguments about Large Language Models