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

• URL: http://arxiv.org/abs/2405.13798v1
• Date: Wed, 22 May 2024 16:23:40 GMT
• Title: Slaves to the Law of Large Numbers: An Asymptotic Equipartition Property for Perplexity in Generative Language Models
• Authors: Raghu Mudumbai, Tyler Bell,
• Abstract summary: We show that the perplexity of any large text produced by a language model must converge to the average entropy of its token distributions. This work has possible practical applications for understanding and improving AI detection" tools.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose a new asymptotic equipartition property for the perplexity of a large piece of text generated by a language model and present theoretical arguments for this property. Perplexity, defined as a inverse likelihood function, is widely used as a performance metric for training language models. Our main result states that the logarithmic perplexity of any large text produced by a language model must asymptotically converge to the average entropy of its token distributions. This means that language models are constrained to only produce outputs from a ``typical set", which we show, is a vanishingly small subset of all possible grammatically correct outputs. We present preliminary experimental results from an open-source language model to support our theoretical claims. This work has possible practical applications for understanding and improving ``AI detection" tools and theoretical implications for the uniqueness, predictability and creative potential of generative models.

Related papers

• The Distributional Hypothesis Does Not Fully Explain the Benefits of Masked Language Model Pretraining [27.144616560712493]
  We investigate whether better sample efficiency and the better generalization capability of models pretrained with masked language modeling can be attributed to the semantic similarity encoded in the pretraining data's distributional property. Our results illustrate our limited understanding of model pretraining and provide future research directions.
  arXiv  Detail & Related papers  (2023-10-25T00:31:29Z)
• TRIGO: Benchmarking Formal Mathematical Proof Reduction for Generative Language Models [68.65075559137608]
  We propose TRIGO, an ATP benchmark that not only requires a model to reduce a trigonometric expression with step-by-step proofs but also evaluates a generative LM's reasoning ability on formulas. We gather trigonometric expressions and their reduced forms from the web, annotate the simplification process manually, and translate it into the Lean formal language system. We develop an automatic generator based on Lean-Gym to create dataset splits of varying difficulties and distributions in order to thoroughly analyze the model's generalization ability.
  arXiv  Detail & Related papers  (2023-10-16T08:42:39Z)
• Token-wise Decomposition of Autoregressive Language Model Hidden States for Analyzing Model Predictions [9.909170013118775]
  This work presents a linear decomposition of final hidden states from autoregressive language models based on each initial input token. Using the change in next-word probability as a measure of importance, this work first examines which context words make the biggest contribution to language model predictions.
  arXiv  Detail & Related papers  (2023-05-17T23:55:32Z)
• On Robustness of Prompt-based Semantic Parsing with Large Pre-trained Language Model: An Empirical Study on Codex [48.588772371355816]
  This paper presents the first empirical study on the adversarial robustness of a large prompt-based language model of code, codex. Our results demonstrate that the state-of-the-art (SOTA) code-language models are vulnerable to carefully crafted adversarial examples.
  arXiv  Detail & Related papers  (2023-01-30T13:21:00Z)
• Evaluating Distributional Distortion in Neural Language Modeling [81.83408583979745]
  A heavy-tail of rare events accounts for a significant amount of the total probability mass of distributions in language. Standard language modeling metrics such as perplexity quantify the performance of language models (LM) in aggregate. We develop a controlled evaluation scheme which uses generative models trained on natural data as artificial languages.
  arXiv  Detail & Related papers  (2022-03-24T01:09:46Z)
• An Application of Pseudo-Log-Likelihoods to Natural Language Scoring [5.382454613390483]
  A language model with relatively few parameters and training steps can outperform it on a recent large data set. We produce some absolute state-of-the-art results for common sense reasoning in binary choice tasks. We argue that robustness of the smaller model ought to be understood in terms of compositionality.
  arXiv  Detail & Related papers  (2022-01-23T22:00:54Z)
• Automatically Identifying Semantic Bias in Crowdsourced Natural Language Inference Datasets [78.6856732729301]
  We introduce a model-driven, unsupervised technique to find "bias clusters" in a learned embedding space of hypotheses in NLI datasets. interventions and additional rounds of labeling can be performed to ameliorate the semantic bias of the hypothesis distribution of a dataset.
  arXiv  Detail & Related papers  (2021-12-16T22:49:01Z)
• Exploring Lexical Irregularities in Hypothesis-Only Models of Natural Language Inference [5.283529004179579]
  Natural Language Inference (NLI) or Recognizing Textual Entailment (RTE) is the task of predicting the entailment relation between a pair of sentences. Models that understand entailment should encode both, the premise and the hypothesis. Experiments by Poliak et al. revealed a strong preference of these models towards patterns observed only in the hypothesis.
  arXiv  Detail & Related papers  (2021-01-19T01:08:06Z)
• Goal-directed Generation of Discrete Structures with Conditional Generative Models [85.51463588099556]
  We introduce a novel approach to directly optimize a reinforcement learning objective, maximizing an expected reward. We test our methodology on two tasks: generating molecules with user-defined properties and identifying short python expressions which evaluate to a given target value.
  arXiv  Detail & Related papers  (2020-10-05T20:03:13Z)
• Limits of Detecting Text Generated by Large-Scale Language Models [65.46403462928319]
  Some consider large-scale language models that can generate long and coherent pieces of text as dangerous, since they may be used in misinformation campaigns. Here we formulate large-scale language model output detection as a hypothesis testing problem to classify text as genuine or generated.
  arXiv  Detail & Related papers  (2020-02-09T19:53:23Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.