Biological learning of local motion detectors

Motion detectors in the brain are typically localized, using correlations between light intensities at nearby locations processed using different temporal dynamics. If motion is global, however, in the sense that the same transformation is applied uniformly across the entire field of view, locations arbitrarily far apart can in principle be used for motion detection. Here we provide a normative model to explain why more distant connections are not used. Specifically, we show that if the brain is adapted to natural visual statistics, this leads to localized interactions even if we ignore the costs implied by long-range connections. Our model further provides a biologically plausible mechanism that can be used to learn the connectivity pattern for local motion detectors. We adapt a method initially designed for learning infinitesimal generators for global motion, and show that, when the training data contains localized patterns and/or localized motion, the learned generators naturally cluster into groups involving small sets of nearby pixels. Our proposed learning algorithm is based on non-negative similarity matching, a normative approach that allows us to use an objective function to derive a biologically plausible circuit that solves the task.