Learning transformational invariants from natural movies

We describe a hierarchical, probabilistic model that learns to extract complex mo-tion from movies of the natural environment. The model consists of two hidden layers: the first layer produces a sparse representation of the image that is ex-pressed in terms of local amplitude and phase variables. The second layer learns the higher-order structure among the time-varying phase variables. After train-ing on natural movies, the top layer units discover the structure of phase-shifts within the first layer. We show that the top layer units encode transformational invariants: they are selective for the speed and direction of a moving pattern, but are invariant to its spatial structure (orientation/spatial-frequency). The diver-sity of units in both the intermediate and top layers of the model provides a set of testable predictions for representations that might be found in V1 and MT. In addition, the model demonstrates how feedback from higher levels can influence representations at lower levels as a by-product of inference in a graphical model.