Transformers Can Represent n-gram Language Models
Authors: name: Anej Svete, name: Ryan Cotterell

Plenty of existing work has analyzed the abilities of the transformer
architecture by describing its representational capacity with formal models of
computation. However, the focus so far has been on analyzing the architecture
in terms of language acceptance. We contend that this is an ill-suited
problem in the study of language models (LMs), which are definitionally
probability distributions over strings. In this paper, we focus on the
relationship between transformer LMs and n-gram LMs, a simple and
historically relevant class of language models. We show that transformer LMs
using the hard or sparse attention mechanisms can exactly represent any
n-gram LM, giving us a concrete lower bound on their probabilistic
representational capacity. This provides a first step towards understanding the
mechanisms that transformer LMs can use to represent probability distributions
over strings.