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Entailment Semantics Can Be Extracted from an Ideal Language Model

William Merrill, Alex Warstadt, Tal Linzen

TL;DR

It is proved that entailment judgments between sentences can be extracted from an ideal language model that has perfectly learned its target distribution, assuming the training sentences are generated by Gricean agents, i.e., agents who follow fundamental principles of communication from the linguistic theory of pragmatics.

Abstract

Language models are often trained on text alone, without additional grounding. There is debate as to how much of natural language semantics can be inferred from such a procedure. We prove that entailment judgments between sentences can be extracted from an ideal language model that has perfectly learned its target distribution, assuming the training sentences are generated by Gricean agents, i.e., agents who follow fundamental principles of communication from the linguistic theory of pragmatics. We also show entailment judgments can be decoded from the predictions of a language model trained on such Gricean data. Our results reveal a pathway for understanding the semantic information encoded in unlabeled linguistic data and a potential framework for extracting semantics from language models.

Entailment Semantics Can Be Extracted from an Ideal Language Model

TL;DR

It is proved that entailment judgments between sentences can be extracted from an ideal language model that has perfectly learned its target distribution, assuming the training sentences are generated by Gricean agents, i.e., agents who follow fundamental principles of communication from the linguistic theory of pragmatics.

Abstract

Language models are often trained on text alone, without additional grounding. There is debate as to how much of natural language semantics can be inferred from such a procedure. We prove that entailment judgments between sentences can be extracted from an ideal language model that has perfectly learned its target distribution, assuming the training sentences are generated by Gricean agents, i.e., agents who follow fundamental principles of communication from the linguistic theory of pragmatics. We also show entailment judgments can be decoded from the predictions of a language model trained on such Gricean data. Our results reveal a pathway for understanding the semantic information encoded in unlabeled linguistic data and a potential framework for extracting semantics from language models.
Paper Structure (13 sections, 5 theorems, 46 equations)

This paper contains 13 sections, 5 theorems, 46 equations.

Table of Contents

  1. Uncountable World Spaces
  2. RSA
  3. Non-Dynamic RSA
  4. Base Case
  5. Inductive Case
  6. Dynamic RSA
  7. Base Case
  8. Inductive Case
  9. General Relations and Speakers
  10. Forward Direction
  11. Backward Direction
  12. Discussion
  13. Proofs for Learning Bounds

Key Result

lemma 1

Let $\mathbbm{1}_{\mathcal{S}}$ be the indicator function for set $\mathcal{S}$. Let $f : \mathcal{W} \to \mathbb{R}$ be some function such that $\inf_{w \in \mathcal{W}} f(w) > 0$. For any sets $\mathcal{A}, \mathcal{B}$ such that $\mathcal{A} \subseteq \mathcal{B} \subseteq \mathcal{W}$, then $p(\

Theorems & Definitions (18)

  • definition 1: Entailment
  • lemma 1
  • proof
  • lemma 2
  • proof
  • lemma 3
  • proof
  • theorem 1
  • proof
  • theorem 2
  • ...and 8 more