The power of connectivity: identity preserving transformations on visual streams in the spike domain.

We investigate neural architectures for identity preserving transformations (IPTs) on visual stimuli in the spike domain. The stimuli are encoded with a population of spiking neurons; the resulting spikes are processed and finally decoded. A number of IPTs are demonstrated including faithful stimulus recovery, as well as simple transformations on the original visual stimulus such as translations, rotations and zoomings. We show that if the set of receptive fields satisfies certain symmetry properties, then IPTs can easily be realized and additionally, the same basic stimulus decoding algorithm can be employed to recover the transformed input stimulus. Using group theoretic methods we advance two different neural encoding architectures and discuss the realization of exact and approximate IPTs. These are realized in the spike domain processing block by a "switching matrix" that regulates the input/output connectivity between the stimulus encoding and decoding blocks. For example, for a particular connectivity setting of the switching matrix, the original stimulus is faithfully recovered. For other settings, translations, rotations and dilations (or combinations of these operations) of the original video stream are obtained. We evaluate our theoretical derivations through extensive simulations on natural video scenes, and discuss implications of our results on the problem of invariant object recognition in the spike domain.