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.
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General criteria for minimal models of streaming transducers are established, yielding effective minimization for variants of streaming string-to-tree transducers that build terms at leaves or roots.
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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.
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Minimization of Streaming Transducers
General criteria for minimal models of streaming transducers are established, yielding effective minimization for variants of streaming string-to-tree transducers that build terms at leaves or roots.