Extended Data Fig. 5: Effect of correlated noise on the toy model of temporal dimensionality (see ^{Supplemental Note 1} for a detailed interpretation of this figure).

a, Example noise vectors and covariance matrix for temporally correlated noise. On the left, example noise vectors are plotted (each line depicts a single example). Noise vectors are shown for all 100 time steps of neuron 1. On the right, the covariance matrix used to generate temporally correlated noise is plotted (dimensions = 200 × 200). The first 100 time steps describe neuron 1’s noise and the last 100 time steps describe neuron 2’s noise. The diagonal band creates noise that is temporally correlated within each simulated neuron (but the two neurons are uncorrelated with each other). b, Classification accuracy when using a maximum likelihood classifier to classify between all four possible trajectories in the presence of temporally correlated noise. Even in the presence of temporally correlated noise, the time-varying trajectories are still much easier to classify. c, Example noise vectors and noise covariance matrix for noise that is correlated with the signal (i.e., noise that is concentrated only in spatiotemporal dimensions that span the class means). Unlike the temporally correlated noise, this covariance matrix generates spatiotemporal noise that has correlations between time steps and neurons. d, Classification accuracy in the presence of signal-correlated noise. Again, time-varying trajectories are easier to classify than constant trajectories.