Fig. 5: Interplay between input and processing dimensionality.
From: Fast nonlinear integration drives accurate encoding of input information in large multiscale systems
a Mutual information between input and output IIO for nonlinear integration and a fast processing unit. For a given input dimension MI, there exists an optimal processing dimensionality \({M}_{P}^{* }\) that maximizes the IIO (dashed lines). The coupling strength between processing and output is gOP = 10. b, c Optimal processing dimensionality as a function of the input dimension MI for two different values of interaction heterogeneity σOP. Error bars represent one standard deviation over realizations of the random interaction matrices. The emergence of an optimal processing dimension is more evident at sufficiently strong couplings and is characterized by a decrease of \({M}_{P}^{* }\) as MI increases. The optimal processing dimension \({M}_{P}^{* }\) also increases with σOP. d, e Same as (a) for smaller gOP and different interaction heterogeneity σOP. At intermediate values (gOP = 5) and low heterogeneity (σOP = 1), \({I}_{IO}^{{{\rm{int}}}}\) is higher for smaller input dimensions and \({M}_{P}^{* }\) stays almost unchanged independently of MI. Increasing σOP to 2, large processing units become favored at small input dimensions and vice-versa. In this Figure, the standard deviations of the interaction matrices are σPI = 1, σI = σP = 0.9, and the input-processing coupling is gPI = 10. Results are obtained by averaging over 2 × 104 realizations of the random interaction matrices.
