Learning Transformational Invariants from Natural Movies

We describe a hierarchical, probabilistic model that learns to extract complex motion frommovies of the natural environment. The model consists of two hidden layers: the first layer produces a sparse representation of the image that is expressed interms of local amplitude and phase variables. The second layer learns the higher-order structure among the time-varying phase variables. After training onnatural movies, the top layer units discover the structure of phase-shifts within the first layer.