A Measure-Theoretic Characterization of Tight Language Models

• URL: http://arxiv.org/abs/2212.10502v2
• Date: Mon, 21 Aug 2023 18:01:57 GMT
• Title: A Measure-Theoretic Characterization of Tight Language Models
• Authors: Li Du, Lucas Torroba Hennigen, Tiago Pimentel, Clara Meister, Jason Eisner, Ryan Cotterell
• Abstract summary: In some pathological cases, probability mass can leak'' onto the set of infinite sequences. This paper offers a measure-theoretic treatment of language modeling. We prove that many popular language model families are in fact tight, meaning that they will not leak in this sense.
• Score: 105.16477132329416
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Language modeling, a central task in natural language processing, involves estimating a probability distribution over strings. In most cases, the estimated distribution sums to 1 over all finite strings. However, in some pathological cases, probability mass can ``leak'' onto the set of infinite sequences. In order to characterize the notion of leakage more precisely, this paper offers a measure-theoretic treatment of language modeling. We prove that many popular language model families are in fact tight, meaning that they will not leak in this sense. We also generalize characterizations of tightness proposed in previous works.

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