Multi-stage cortical recurrent circuit implementing normalization

The brain relies on communication between cortical areas to achieve perceptual, cognitive, and motor functions. Communication is supported by long-range reciprocal connections and, crucially, feedback connections have been hypothesized to influence perception by mediating attentional modulation. Here, we present a hierarchical recurrent neural circuit model with feedback that implements divisive normalization exactly at each stage of its hierarchy. We consider a two-stage model comprised of a sensory module (V1) and a perception module (FEF), each normalized by local inhibitory signals modulated by the activity of principal neurons across areas. We observe that an increase in feedback from FEF to V1, increases the responses in both stages, consistent with experiments. Additionally, we investigate the coherence of neuronal activity between the areas and find a peak in the gamma band whose amplitude is positively correlated with the feedback. Our model also admits the existence of a low-dimensional communication subspace (within and across areas) and makes predictions of how the subspace varies with feedback. In summary, our hierarchical model provides a robust and analytically tractable framework for exploring normalization, attention, and inter-areal communication.