In early sensory systems, such as retina and olfactory bulb in vertebrates or optic and antennal lobes in invertebrates, information about the world converges from a large number of receptors onto a much smaller number of projection neurons. Such bottleneck in the communication channel to the higher brain areas (Attneave, 1954, Barlow & Levick, 1976) can be overcome for sensory stimuli containing correlations by the predictive coding strategy (Srinivasan et al, 1982). In case of the retina, instantaneous subtraction of the least squares prediction compresses information and results in center-surround biphasic receptive fields. However, explaining variation of receptive fields with SNR (Srinivasan et al, 1982, Van Hateren, 1992, Atick & Redlich, 1990) would require circuit re-wiring which is unlikely on short time scales. Here we develop the predictive coding idea by proposing that a non-linear recurrent neuronal circuit can implement predictive coding adaptively: stimuli of different SNR result in different inhibitory surrounds. We solve the transient dynamics of this circuit in response to a step-like stimulus and demonstrate that it communicates a residual of the regularization path to higher brain areas. Thus, we are able to map a non-trivial computation on a concrete neuronal circuit and provide a theoretical framework to understand neural coding for many physiological experiments.
