Extended Data Fig. 5: Effect of different spike-train smoothing methods.

a, Gaussian smoothing with a kernel width of σ = 25 ms for the reach–no-reach experiment, as shown in Fig. 2b. Note that the activity appears to change from the constant perturbed state slightly before the end of the laser. This is because the kernel smooths forward into the post-laser epoch. b, Gaussian smoothing with σ = 50 ms. The divergence from the perturbed state begins earlier owing to a higher level of smoothing. c, Causal smoothing with a half-Gaussian kernel, truncated to use samples only from the past. Neural activity diverges from the perturbed state only after the end of the laser. d, Acausal smoothing with a half-Gaussian kernel, truncated to use samples only from the future. e, Gaussian smoothing in the sequential inactivation experiment with a kernel width of σ = 25 ms, as shown in Fig. 3f. Note that the activity appears to change from the constant perturbed state slightly before the end of the cortical inactivation. There is also a delay from the start of the cortical inactivation to the arrival of the neural state at the constant value. f, Gaussian smoothing with σ = 50 ms. g, Causal smoothing with a half-Gaussian kernel, truncated to use samples only from the past. Neural activity diverges from the perturbed state only after the end of the laser. However, there is still a lag from the start of cortical inactivation to the arrival of neural activity at the constant perturbed state. h, Acausal smoothing with a half-Gaussian kernel, truncated to use samples only from the future. Neural activity again diverges from the perturbed state before the end of the cortical inactivation. At the start of the cortical inactivation, neural activity has already arrived at the perturbed state.