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Learning divisive normalization in primary visual cortex
Fig 5
Structure of divisive normalization.
A. The matrix shows the average strength of the normalizing inputs (products 
in denominator of Eq (1) averaged across images; see Methods) for each combination of filter response being normalized (rows) and filter response providing normalizing input (columns). Darker shades of blue indicate stronger normalization. Orientation-selective filters are grouped at the top, ordered by preferred orientation and marked by the black square. The dashed black lines within the square separate pairs of filters with similar (< 45°) and dissimilar (≤ 45°) orientations. Normalizing inputs are stronger for similarly tuned filters. Unoriented filters mainly accounting for orientation-unspecific contrast are sorted by total normalization input. Darkest blue color corresponds to the maximum normalization input for the group of oriented filters, higher normalization input values for the unoriented filters are clipped to that value. Data of the model with highest accuracy on the validation set is shown. B. Normalization input from similar orientations (< 45°) compared to the normalization input from dissimilar orientations (≥ 45°) for each oriented linear filter. Grey line: identity. Most features are normalized preferentially by the responses of filters with similar preferred orientations. Data of the model with highest accuracy on the validation set is shown. C. Normalization input, binned into orientation difference of 10°. Each bin was averaged over the top-10 models (assessed on the validation set). The shaded area depicts the standard deviation per bin. C inset. Normalization input (norm. input) vs. cosine similarity between linear filters (cos. sim.) averaged across the top-10 models (assessed on the validation set). A cosine similarity greater than zero corresponds to similar features. Error bars: standard error of the mean. D. Histogram of DN exponents (nl in Eq 1) of the ten best performing models in terms of validation set accuracy. Darker/lighter color: exponents corresponding to driving inputs due to oriented/unoriented linear filters. Most values are larger than one, with a few exceptions mainly corresponding to unoriented filters.
doi: https://doi.org/10.1371/journal.pcbi.1009028.g005