Error Geometry Shapes Modular Sensorimotor Representations

Sensorimotor learning requires transforming sensory errors into adaptive motor responses under delayed feedback. Here, we investigate whether the geometry of motor errors can itself organize learned sensorimotor representations. Inspired by theories of cerebellar error-based learning, we introduce a modular recurrent controller in which error direction determines which expert modules receive a learning signal, while error magnitude determines its strength. The update gate sparsely activates modules according to preferred directions in error space, producing a structured, microzone-like organization. Sparse top-2 gate reduces functional overlap between experts compared with unconstrained gate, yielding direction-selective representations and strong separation between opposing directions. Incorporating delayed sensory feedback further produces distinct adaptation timescales, combining rapid task-error correction with slower changes in feedforward behavior. These results suggest that gating of graded error signals provides a simple inductive bias for learning modular sensorimotor representations while linking the spatial organization of error processing to the temporal dynamics of motor adaptation.