SD-SSM, a single-layer selective SSM with softmax-weighted dense transition matrices, achieves near-perfect length generalization on seven finite-state automaton tasks, while diagonal selective SSMs are shown to be limited to commutative automata under a stated mapping assumption.
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On the Expressiveness and Length Generalization of Selective State-Space Models on Regular Languages
SD-SSM, a single-layer selective SSM with softmax-weighted dense transition matrices, achieves near-perfect length generalization on seven finite-state automaton tasks, while diagonal selective SSMs are shown to be limited to commutative automata under a stated mapping assumption.