Exploring Length Generalization in Large Language Models

TL;DR

This paper investigates how large language models generalize to longer reasoning problems, finding that in-context learning with scratchpad prompting significantly improves their ability to extrapolate to longer instances.

Contribution

The study demonstrates that combining pretrained models' in-context learning with scratchpad prompting enhances length generalization in transformer-based language models.

Findings

Naive finetuning shows poor length generalization regardless of model size.

Scratchpad prompting dramatically improves length generalization.

Failure analyses reveal common sources of mistakes and opportunities for improvement.

Abstract

The ability to extrapolate from short problem instances to longer ones is an important form of out-of-distribution generalization in reasoning tasks, and is crucial when learning from datasets where longer problem instances are rare. These include theorem proving, solving quantitative mathematics problems, and reading/summarizing novels. In this paper, we run careful empirical studies exploring the length generalization capabilities of transformer-based language models. We first establish that naively finetuning transformers on length generalization tasks shows significant generalization deficiencies independent of model scale. We then show that combining pretrained large language models' in-context learning abilities with scratchpad prompting (asking the model to output solution steps before producing an answer) results in a dramatic improvement in length generalization. We run careful failure analyses on each of the learning modalities and identify common sources of mistakes that highlight opportunities in equipping language models with the ability to generalize to longer problems.