  Predictive coding is a promising theoretical framework in neuroscience for
understanding information transmission and perception. It posits that the brain
perceives the external world through internal models and updates these models
under the guidance of prediction errors. Previous studies on predictive coding
emphasized top-down feedback interactions in hierarchical multi-layered
networks but largely ignored lateral recurrent interactions. We perform
analytical and numerical investigations in this work on the effects of
single-layer lateral interactions. We consider a simple predictive response
dynamics and run it on the MNIST dataset of hand-written digits. We find that
learning will generally break the interaction symmetry between peer neurons,
and that high input correlation between two neurons does not necessarily bring
strong direct interactions between them. The optimized network responds to
familiar input signals much faster than to novel or random inputs, and it
significantly reduces the correlations between the output states of pairs of
neurons.
