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Recently, deep learning has revolutionized the field of natural languageprocessing, with neural language models proving to be very effective fornext-word prediction. However, a rigorous theoretical explanation for theirsuccess in the context of formal language theory has not yet been developed, asit is unclear why neural language models can learn the combinatorial rules thatgovern the next-word prediction task. In this paper, we study a class of formallanguages that can be used to model real-world examples of English sentences.We construct neural language models can solve the next-word prediction task inthis context with zero error. Our proof highlights the different roles of theembedding layer and the fully connected component within the neural languagemodel.

Why can neural language models solve next-word prediction? A mathematical perspective