Figure 3

Eigenspectrum and rotational modes. (a) Eigenvalue spectrum of the remembered dynamics matrix used for decoder hysteresis (red) and an example eigenvalue spectrum of re-learned neural dynamics (blue) with the simulated loss of 140 electrodes in Monkey J. The frequencies used by the re-learned dynamics are smaller than those of the remembered dynamics. (b) Eigenvalue spectrum of the remembered dynamics matrix used for decoder hysteresis (red) and an example eigenvalue spectrum of re-learned neural dynamics (blue) with the simulated loss of 60 electrodes in Monkey L. (c) The max frequency of the dynamical system versus the number of electrodes used to infer the dynamics in Monkey J. We only considered oscillation frequencies for modes which had a time constant of decay greater than 20 ms, since the timescale of the exponential decay would be faster than any oscillation. The oscillation frequencies of the neural dynamics decrease as the number of electrodes decreases (linear regression r ² = 0.59, slope significantly different than 0 at p < 0.01). This trend also held up using the average frequency of the eigenvalues of the dynamical system. (d) Same as (c) but for Monkey L (linear regression r ² = 0.48, slope significantly different than 0 at p < 0.01). (e) The R ² ratio quantifies the ratio in describing the neural population activity with a skew symmetric dynamics matrix (having purely imaginary eigenvalues) vs the least-squares optimal dynamics matrix (having complex eigenvalues) as further described in the Methods. If the R ² ratio is large, it signifies that much of the dynamical variance can be captured by a purely rotational dynamics matrix. As electrodes are lost in Monkey J, the R ² ratio significantly declines (linear regression r ² = 0.13, slope significantly different than 0 at p < 0.01), indicating that the neural activity is less well-described by rotational modes. (f) Same as (e) but for Monkey L (linear regression r ² = 0.43, slope significantly different than 0 at p < 0.01).