Extended Data Fig. 7: Velocity correction to leading eigenvalues of active submatrices. | Nature Neuroscience

Extended Data Fig. 7: Velocity correction to leading eigenvalues of active submatrices.

From: Maintaining and updating accurate internal representations of continuous variables with a handful of neurons

Extended Data Fig. 7

a, Leading eigenvalues λ of active submatrices as a function of input velocity vin for a network of size N = 6. Shown for 11 velocity values evenly spaced between (and including) vin = 0 and vin = 1 rad s−1 (darker colors indicate higher velocities). Eigenvalues were obtained by numerically diagonalizing active submatrices of the full connectivity W = ((Wsym + vin Wasym)/N − I)/τ. Red dashed line marks an optimal value of local excitation. b, Coefficients of the best-fitting 3rd order polynomial of the velocity correction λ − λ0 versus input velocity vin, where λ0 is the leading eigenvalue of the full connectivity in the absence of velocity input. c, Comparison of the velocity correction λ − λ0 (solid lines) and the best-fitting polynomial (dashed lines), including terms of order O(v2) and O(v3). Shown for 6 different values of local excitation marked by arrows in panel b.

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