Multilayer generative models can be learned one layer at a time by using a restricted Boltzmann machines as the basic learning module. Restricted Boltzmann machines only have pairwise interactions between units, but for many vision applications, three-way, multiplicative interactions are more appropriate. If these interactions are parameterized in the obvious way, the number of parameters becomes cubic in the number of units. The talk will describe a way of factoring the three-way interactions so that there are only quadratically many parameters. The resulting factors have many similarities to a popular models of cortical “simple” cells and the learning and inference procedures for restricted Boltzmann machines are easy to extend to this more powerful type of module. Using a module of this type it is possible to learn generative models in which the variables in one layer control the correlations between variables in the layer below.
Some preliminary simulations of this type of learning module show that it can learn to represent the motion of a field of random dots. After learning on images that only contain a single coherent motion, the model correctly perceives “transparent” motion in which a random subset of the dots move in one direction and the rest move in another direction.