Recurrent Dynamics and State Geometry of Echo State Networks in Robotic Imitation Learning

Echo State Networks (ESNs), a standard form of reservoir computing, use a fixed nonlinear reservoir while training only a readout. We apply this structure to a visuomotor policy trained on expert demonstrations to predict future actions from visual observations. We characterize its recurrent dynamics by sweeping the spectral radius and estimating maximum Lyapunov exponents. High-performing reservoirs tend to operate near a stability boundary. Near this boundary, state trajectories remain low-dimensional, while residual variability concentrates in fewer directions. Action variation across episodes remains linearly decodable from these residual directions under stronger ridge regularization. Together, these results characterize the dynamical regime and state geometry associated with successful ESN-based visuomotor policies.