Rule Extrapolation in Language Models: A Study of Compositional Generalization on OOD Prompts

TL;DR

This paper investigates how large language models generalize to out-of-distribution prompts involving rule violations, focusing on formal languages to understand the influence of architecture on compositional generalization.

Contribution

It introduces the concept of rule extrapolation for OOD compositional generalization and evaluates various architectures, laying groundwork for a normative theory inspired by algorithmic information theory.

Findings

Transformers and other architectures exhibit varying abilities in rule extrapolation.

Formal language evaluation reveals architecture-dependent generalization behaviors.

Initial theoretical insights connect rule extrapolation to algorithmic information theory.

Abstract

LLMs show remarkable emergent abilities, such as inferring concepts from presumably out-of-distribution prompts, known as in-context learning. Though this success is often attributed to the Transformer architecture, our systematic understanding is limited. In complex real-world data sets, even defining what is out-of-distribution is not obvious. To better understand the OOD behaviour of autoregressive LLMs, we focus on formal languages, which are defined by the intersection of rules. We define a new scenario of OOD compositional generalization, termed rule extrapolation. Rule extrapolation describes OOD scenarios, where the prompt violates at least one rule. We evaluate rule extrapolation in formal languages with varying complexity in linear and recurrent architectures, the Transformer, and state space models to understand the architectures' influence on rule extrapolation. We also lay the first stones of a normative theory of rule extrapolation, inspired by the Solomonoff prior in algorithmic information theory.