Fig 8. Learning rate calibration affects both the transient and the steady-state performance of closed-loop BMI decoders with continuous neural activity.

(A) The evolution of the decoded trajectory as the adaptation time is increased under different learning rates s. Note that the decoder is fixed after a given adaptation time is completed (as noted on each row). The fixed decoder is then used to generate the displayed trajectories. Each color corresponds to one learning rate. Decoding performance is unstable when the learning rate is large (s = 5 × 10⁻¹) even at steady state; this means that depending on exactly when we stop the adaptation and fix the decoder, performance widely oscillates due to the large steady-state model parameter error. (B) RMSE of the decoded trajectory under different learning rates for different adaptation times. RMSE is computed for a fixed decoder that was obtained by stopping the adaptation at various times (different colors). RMSE converges faster as the learning rate is increased (s = 5 × 10⁻⁵ to 5 × 10⁻³, for example). However, if the learning rate is selected too large (s = 5 × 10⁻¹), RMSE oscillates depending on when adaptation is stopped, without converging to a stable number. These results show that appropriately calibrating the learning rate is important not only for encoding model estimation but also for a desired trade-off between convergence time and steady-state RMSE in decoding.