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Limits for Learning with Language Models

Nicholas Asher, Swarnadeep Bhar, Akshay Chaturvedi, Julie Hunter, Soumya Paul

TL;DR

This paper establishes a theoretical limit on what language models can learn about linguistic meaning by integrating continuation semantics with formal semantics and the Borel hierarchy. It shows that universal quantification, entailment, and related semantic concepts fall outside the effective learnability of LLMs under standard inductive learning assumptions, constraining them to learn only certain basic (\Delta^0_1) sets. The authors formalize LLMs as distributions over continuations and connect learnability to statistical learning theory, ultimately arguing that higher-order semantic notions cannot be guaranteed by current architectures alone. They bolster the theory with empirical studies demonstrating quantification and order-related reasoning challenges in prevalent models like BERT, RoBERTa, GPT-3.5, and ChatGPT. The work implies that robust linguistic understanding requires integrating explicit linguistic structure into model design and training, rather than relying solely on scale, and it highlights important ethical considerations around model reliability in reasoning tasks.

Abstract

With the advent of large language models (LLMs), the trend in NLP has been to train LLMs on vast amounts of data to solve diverse language understanding and generation tasks. The list of LLM successes is long and varied. Nevertheless, several recent papers provide empirical evidence that LLMs fail to capture important aspects of linguistic meaning. Focusing on universal quantification, we provide a theoretical foundation for these empirical findings by proving that LLMs cannot learn certain fundamental semantic properties including semantic entailment and consistency as they are defined in formal semantics. More generally, we show that LLMs are unable to learn concepts beyond the first level of the Borel Hierarchy, which imposes severe limits on the ability of LMs, both large and small, to capture many aspects of linguistic meaning. This means that LLMs will continue to operate without formal guarantees on tasks that require entailments and deep linguistic understanding.

Limits for Learning with Language Models

TL;DR

This paper establishes a theoretical limit on what language models can learn about linguistic meaning by integrating continuation semantics with formal semantics and the Borel hierarchy. It shows that universal quantification, entailment, and related semantic concepts fall outside the effective learnability of LLMs under standard inductive learning assumptions, constraining them to learn only certain basic (\Delta^0_1) sets. The authors formalize LLMs as distributions over continuations and connect learnability to statistical learning theory, ultimately arguing that higher-order semantic notions cannot be guaranteed by current architectures alone. They bolster the theory with empirical studies demonstrating quantification and order-related reasoning challenges in prevalent models like BERT, RoBERTa, GPT-3.5, and ChatGPT. The work implies that robust linguistic understanding requires integrating explicit linguistic structure into model design and training, rather than relying solely on scale, and it highlights important ethical considerations around model reliability in reasoning tasks.

Abstract

With the advent of large language models (LLMs), the trend in NLP has been to train LLMs on vast amounts of data to solve diverse language understanding and generation tasks. The list of LLM successes is long and varied. Nevertheless, several recent papers provide empirical evidence that LLMs fail to capture important aspects of linguistic meaning. Focusing on universal quantification, we provide a theoretical foundation for these empirical findings by proving that LLMs cannot learn certain fundamental semantic properties including semantic entailment and consistency as they are defined in formal semantics. More generally, we show that LLMs are unable to learn concepts beyond the first level of the Borel Hierarchy, which imposes severe limits on the ability of LMs, both large and small, to capture many aspects of linguistic meaning. This means that LLMs will continue to operate without formal guarantees on tasks that require entailments and deep linguistic understanding.
Paper Structure (15 sections, 14 theorems, 2 equations, 1 table)

This paper contains 15 sections, 14 theorems, 2 equations, 1 table.

Table of Contents

  1. Introduction
  2. Context
  3. Language models and formal semantics with continuations
  4. LLMs and strings
  5. Linguistic meaning
  6. Learning limits for semantic concepts
  7. Learning the full meaning of every
  8. Generalizing our answer to Q2
  9. Statistical learning
  10. The Borel Hierarchy
  11. The importance of order
  12. Empirical investigations of LLMs with every
  13. Conclusions
  14. GPT 3.5 and ChatGPT on every
  15. ChatGPT and GPT3.5 on word order and argument order

Key Result

Proposition 1

Models that calculate distributions over strings using Equation calculation have non-degenerate distributions.

Theorems & Definitions (20)

  • Definition 1
  • Definition 2
  • Proposition 1
  • Definition 3
  • Proposition 2
  • Proposition 3
  • Proposition 4
  • Corollary 1
  • Definition 4
  • Definition 5
  • ...and 10 more