Generalizing biological surround suppression based on center surround similarity via deep neural network models
Fig 7
The most suppression by the homogeneous surround can be achieved by two layers with nonlinear activation, as shown in a conceptual model and toy model simulation.
A. A conceptual model. Top: The model has two input neurons with center-surround receptive fields, i.e. the optimal pattern in the center elicits a response of 1; the optimal pattern in the surround elicits a response of -0.8. We further assume that the optimal patterns for two neurons are orthogonal, i.e. the optimal pattern of one neuron does not elicit responses of the other neuron. The response of the output neuron, i.e. neuron 3, is the weighted sum of rectified responses of the two neurons. Neuron 1 has a higher weight than neuron 2. Bottom: input patterns that are created from combining optimal patterns of neuron 1 and 2. Activations of three neurons are computed as defined. The maximum surround suppression happens when the surround pattern matches the center. This is due to the nonlinear ReLU blocking the excessive suppression from the unmatched neuron. B. In a toy model simulation, the visualization results show similar behavior to the conceptual model. The two neurons are constructed by first taking two simple orientated filter maps, then convolving with a kernel with center weight 1 and surround weight -1. Equivalent filters for the two neurons are also shown as “deconvolved” input images. We simulated the visualization experiment in neuron 3. The optimal center for neuron 3 is horizontal and the most suppressive surround matches the optimal center. When the center is replaced by the neuron 2’s optimal pattern, the most suppressive surround looks vertical which is close to the optimal pattern of neuron 2, unlike the most suppressive pattern when the center is fixed to the optimal.