Transformers Can Represent $n$-gram Language Models
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929391727017984 |
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| author | Svete, Anej Cotterell, Ryan |
| author_facet | Svete, Anej Cotterell, Ryan |
| contents | Existing work has analyzed the representational capacity of the transformer architecture by means of formal models of computation. However, the focus so far has been on analyzing the architecture in terms of language \emph{acceptance}. We contend that this is an ill-suited problem in the study of \emph{language models} (LMs), which are definitionally \emph{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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_14994 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Transformers Can Represent $n$-gram Language Models Svete, Anej Cotterell, Ryan Computation and Language Artificial Intelligence Computational Complexity Formal Languages and Automata Theory Machine Learning Existing work has analyzed the representational capacity of the transformer architecture by means of formal models of computation. However, the focus so far has been on analyzing the architecture in terms of language \emph{acceptance}. We contend that this is an ill-suited problem in the study of \emph{language models} (LMs), which are definitionally \emph{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. |
| title | Transformers Can Represent $n$-gram Language Models |
| topic | Computation and Language Artificial Intelligence Computational Complexity Formal Languages and Automata Theory Machine Learning |
| url | https://arxiv.org/abs/2404.14994 |