Modelling Retinal Activity with Restricted Boltzmann Machines: a Study on the Inhibitory Circuitry

Being the first stage of the visual system, the retina performs an extremely important task: encoding visual information and making it available to higher visual areas. In order to be effective, the encoding should be rich enough to capture the information of different stimuli, and stable enough to show small variations across repeated presentations of the same stimulus. This should arguably be achieved as a collective behaviour, capable of subduing the variability in the response of single Retinal Ganglion Cells (RGCs). In this work we study the statistical structure of the signal produced by a large population of RGCs, looking for prototypical activation modes of the retina subject to photostimulation. RGCs are modelled as logGaussian Cox Processes and a mean covariance Restricted Boltzmann Machine (mcRBM) is used to model the joint distribution of the firing rates of all the neurons in the recorded population. Due to its formulation, the mcRBM allows to infer a set of activation modes of the retina defined by the configuration of the model's latent variables. These activation modes are obtained in a fully unsupervised way using no information about the input and thus reflect the regularities of RGCs signal. In our work we show that the activity modes found through the mcRBM map reliably to different visual stimuli. Moreover, we show that the inferred modes can be used to evaluate the information content of the retinal signal. As a case study, we evaluate the information carried by the concurrent firing rates of RGCs of a retina in normal conditions and after pharmacologically blocking GABAC, at first, and then GABAC plus GABAA and GABAB receptors. As expected from physiology, blocking the inhibitory circuitry disrupts the spatiotemporal precision of retinal encoding, resulting in a reduced Mutual Information between the inferred activation modes and the presented visual stimuli.