A unified algebraic account reduces RNN expressivity to syntactic monoid division in wreath products and shows diagonal state-space models realize every even-modulus counter under unsigned-integer quantization but none under floating-point recurrences.
arXiv preprint arXiv:2109.09828 , year=
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An Algebraic View of the Expressivity of Recurrent Language Models
A unified algebraic account reduces RNN expressivity to syntactic monoid division in wreath products and shows diagonal state-space models realize every even-modulus counter under unsigned-integer quantization but none under floating-point recurrences.