Generalizing Reasoning Problems to Longer Lengths

Changnan Xiao, Bing Liu

Keywords: length generalization, learning to reason, length extrapolation

TL;DR: This paper first introduces a theorem to show the length generalization (LG) problem’s root cause, highlighting what is necessary to resolve it. It then proposes and proves a sufficient condition to solve LG

Abstract: Length generalization (LG) is a challenging problem in learning to reason. It refers to the phenomenon that when trained on reasoning problems of smaller lengths/sizes, the model struggles with problems of larger sizes or lengths. Although it has been proven that reasoning can be learned if the intermediate reasoning steps (also known as chain-of-thought (CoT)) are given in the training data, existing studies only apply to within a given length (interpolation), while LG is about extrapolation beyond the given length. This paper begins by presenting a theorem that identifies the root cause of the LG problem. It then defines a class of reasoning problems for which achieving LG with Transformers can be theoretically guaranteed, provided the CoT schemes are constructed to meet a proposed condition called $(n,r)$-consistency.

Primary Area: other topics in machine learning (i.e., none of the above)

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Submission Number: 8618