What Languages are Easy to Language-Model? A Perspective from Learning Probabilistic Regular Languages

TL;DR

This paper empirically investigates how well neural language models, specifically RNNs and Transformers, learn probabilistic regular languages by analyzing factors like RLM rank and string length.

Contribution

It introduces an empirical framework for assessing the learnability of probabilistic regular languages by neural models, focusing on measurable complexity parameters.

Findings

RLM rank strongly predicts learnability for RNNs and Transformers.

Expected string length significantly influences model learnability.

Different predictors show varying importance between RNNs and Transformers.

Abstract

What can large language models learn? By definition, language models (LM) are distributions over strings. Therefore, an intuitive way of addressing the above question is to formalize it as a matter of learnability of classes of distributions over strings. While prior work in this direction focused on assessing the theoretical limits, in contrast, we seek to understand the empirical learnability. Unlike prior empirical work, we evaluate neural LMs on their home turf-learning probabilistic languages-rather than as classifiers of formal languages. In particular, we investigate the learnability of regular LMs (RLMs) by RNN and Transformer LMs. We empirically test the learnability of RLMs as a function of various complexity parameters of the RLM and the hidden state size of the neural LM. We find that the RLM rank, which corresponds to the size of linear space spanned by the logits of its conditional distributions, and the expected length of sampled strings are strong and significant predictors of learnability for both RNNs and Transformers. Several other predictors also reach significance, but with differing patterns between RNNs and Transformers.