  Lateral connections play an important role for sensory processing in visual
cortex by supporting discriminable neuronal responses even to highly similar
features. In the present work, we show that establishing a biologically
inspired Mexican hat lateral connectivity profile along the filter domain can
significantly improve the classification accuracy of a variety of lightweight
convolutional neural networks without the addition of trainable network
parameters. Moreover, we demonstrate that it is possible to analytically
determine the stationary distribution of modulated filter activations and
thereby avoid using recurrence for modeling temporal dynamics. We furthermore
reveal that the Mexican hat connectivity profile has the effect of ordering
filters in a sequence resembling the topographic organization of feature
selectivity in early visual cortex. In an ordered filter sequence, this profile
then sharpens the filters' tuning curves.
