Disparity tuning as simulated by a neural net

Previous research has suggested that the processing of binocular disparity in complex cells may be described with an energy formalism. The energy formalism allows for a representation of disparity by differences in the position or in the phase of monocular receptive subfields of binocular cells, or by combination of these two types. We studied the coding of disparities with an approach complementary to previous algorithmic investigations. Since realization of these representations is probably not genetically determined but learned during ontogeny, we used backpropagation networks to study which of these three possibilities were realized within neural nets. Three types of networks were trained with noise patterns in analogy to the three types of energy models. The networks learned the task and generalized to untrained correlated noise pattern input. Outputs were broadly tuned to spatial frequency and did not respond to anti-correlated noise patterns. Although the energy model was not explicitly implemented, we could analyze the outputs of the networks using predictions of the energy formalism. After learning was completed, the model neurons preferred position shifts over phase shifts in representing disparity. We discuss the general meaning of these findings and the correspondences and deviations between the energy model, V1 neurons, and our networks. Received: 6 August 1999 / Accepted in revised form: 26 January 2000