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Under review as a conference paper at ICLR 2027

Learning to Route Recurrent State from Input History

Abstract

Can input history improve recurrent computation by controlling how stored state coordinates interact? We introduce Input-Conditioned Graph Routing (ICGR), a recurrent cell whose compact controller summarizes the input prefix and selects a graph-supported skew-symmetric operator from shared learned factors. The routed state current and encoded input form a bounded drive, combined with a contextual correction under an exponential retention update. Saturation and convex retention guarantee bounded main-state activations for arbitrary sequence length, without guaranteeing gradient stability. We study the mechanism through paired controls and routing interventions. Under identical parameter instantiation—not necessarily equal effective capacity—history conditioning outperforms learned time schedules and current-input-only conditioning on permuted sequential MNIST and character-level Penn Treebank. A symmetric routing control with matched support and prior spectral norm performs worse under the tested pSMNIST protocol. Donor trajectories and training-derived class templates redirect predictions toward the supplied class, while a frozen linear probe decodes class labels from the complete routing trajectory near complete-model accuracy. ICGR is competitive across four benchmarks under our evaluated configurations, although several pSMNIST baseline reruns fall below their published results and Penn Treebank shows mixed parameter efficiency. These findings identify class-bearing, history-conditioned routing signals as a task-relevant information pathway in the trained models, without establishing improved retention of target input history.

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