Advancing Regular Language Reasoning in Linear Recurrent Neural Networks

TL;DR

This paper investigates the ability of linear recurrent neural networks to learn regular language structures, identifies their limitations, and proposes a new LRNN model that successfully performs length extrapolation on such tasks.

Contribution

It introduces a novel LRNN with a block-diagonal, input-dependent transition matrix that overcomes previous limitations in modeling regular languages.

Findings

Theoretical analysis reveals limitations of existing LRNNs in regular language modeling.

The proposed LRNN can perform length extrapolation on tasks like Sum, Even Pair, and Modular Arithmetic.

Code for the new model is publicly available.

Abstract

In recent studies, linear recurrent neural networks (LRNNs) have achieved Transformer-level performance in natural language and long-range modeling, while offering rapid parallel training and constant inference cost. With the resurgence of interest in LRNNs, we study whether they can learn the hidden rules in training sequences, such as the grammatical structures of regular language. We theoretically analyze some existing LRNNs and discover their limitations in modeling regular language. Motivated by this analysis, we propose a new LRNN equipped with a block-diagonal and input-dependent transition matrix. Experiments suggest that the proposed model is the only LRNN capable of performing length extrapolation on regular language tasks such as Sum, Even Pair, and Modular Arithmetic. The code is released at \url{https://github.com/tinghanf/RegluarLRNN}.