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We introduce a new neural architecture and an unsupervised algorithm forlearning invariant representations from temporal sequence of images. The systemuses two groups of complex cells whose outputs are combined multiplicatively:one that represents the content of the image, constrained to be constant overseveral consecutive frames, and one that represents the precise location offeatures, which is allowed to vary over time but constrained to be sparse. Thearchitecture uses an encoder to extract features, and a decoder to reconstructthe input from the features. The method was applied to patches extracted fromconsecutive movie frames and produces orientation and frequency selective unitsanalogous to the complex cells in V1. An extension of the method is proposed totrain a network composed of units with local receptive field spread over alarge image of arbitrary size. A layer of complex cells, subject to sparsityconstraints, pool feature units over overlapping local neighborhoods, whichcauses the feature units to organize themselves into pinwheel patterns oforientation-selective receptive fields, similar to those observed in themammalian visual cortex. A feed-forward encoder efficiently computes thefeature representation of full images.

Emergence of Complex-Like Cells in a Temporal Product Network with Local Receptive Fields