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

• URL: http://arxiv.org/abs/2405.13798v3
• Date: Thu, 30 Jan 2025 12:03:48 GMT
• Title: Slaves to the Law of Large Numbers: An Asymptotic Equipartition Property for Perplexity in Generative Language Models
• Authors: Avinash Mudireddy, Tyler Bell, Raghu Mudumbai,
• Abstract summary: We show that the logarithmic perplexity of any large text generated by a language model must 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. Results suggest possible applications to important practical problems such as (a) detecting synthetic AI-generated text, and (b) testing whether a text was used to train a language model.
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• Abstract: We prove a new asymptotic 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 show that this typical set is a vanishingly small subset of all possible grammatically correct outputs. These results suggest possible applications to important practical problems such as (a) detecting synthetic AI-generated text, and (b) testing whether a text was used to train a language model. 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.

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