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Maximally Informative “Stimulus Energies” in the Analysis of Neural Responses to Natural Signals

Figure 3

Core of the method.

(a) A general implementation is shown here. The stimuli are natural image clips which are pixel patches resized from a natural image database, as described in [36]. spikes are generated with a probability per time bin of from the model neuron by a thresholding the term, where the matrix is the receptive field of the neuron. (b) Mutual information between the spiking response of the model neuron and the quadratic stimulus projection is plotted as a function of the number of learning steps. Information, normalized by its value when , peaks at the learning step and then plateaus. The black dots on the trace denote the points at which we extract the initial, the intermediate and the optimal matrices for comparison. The maximally informative matrix reconstructed at the step, agrees well with , indicating convergence. For this implementation the step size at the start and at the end of the algorithm. (c) Root–mean–square (RMS) reconstruction error calculated as , is plotted as a function of the number of learning steps. This error decreases steadily until either the randomly initialized matrix (solid line) or the matrix initialized to the spike–triggered covariance matrix (dashed line) matches . If is initialized to the covariance matrix, the initial RMS error is smaller and the convergence is faster ( learning step) compared to that for a randomly initialized . For this example, both and are matrices and the black dot on the solid trace is at the same learning step as in panel (b).

doi: https://doi.org/10.1371/journal.pone.0071959.g003