AI RESEARCH
Rethinking State Tracking in Recurrent Models Through Error Control Dynamics
arXiv CS.LG
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ArXi:2605.07755v1 Announce Type: new The theory of state tracking in recurrent architectures has predominantly focused on expressive capacity: whether a fixed architecture can theoretically realize a set of symbolic transition rules. We argue that equally important is error control, the dynamics governing hidden-state drift along the directions that distinguish symbolic states. We prove that affine recurrent networks, a class of models encompassing State-Space Models and Linear Attention, cannot correct errors along state-separating subspaces once they preserve state representations.