Abstract
Neurons in the primary visual cortex (V1) of primates are selective for location, orientation, and spatial frequency. Among them, complex cells are characterized by their selectivity to orientation and spatial frequency while lacking sensitivity to position or phase tuning (dark/bright line center) within a restricted range. The development of the shift invariance property of complex cells has been successfully explained by the temporal trace learning which takes advantage of the temporal coherence of visual stimuli (P. FΓΆldiΓ‘k, Neural Computation 1991;3:194). We have carried out mathematical modeling of complex cell development without temporal trace mechanism. The model network consists of three layers of E, S, and C layer which model excitatory cells in LGN or V1, and simple cells, and complex cells in V1, respectively. Neurons in layer E have position selectivity, and neurons in layer S are line detectors for a specific position. During the learning phase, the network is exposed to randomly located short oriented bars, and neurons in layer C selfβorganize its selectivity to the inputs. The learning rules are Hebbian or SOM (selfβorganizing map) type between layers S and C, and antiβHebbian between layers E and C by which neurons are forced to represent uncorrelated aspect of the inputs. We demonstrate that neurons in layer C learn invariance to shift in input position. Our model explains complex cell development in terms of the principle of information separation. Β© 2007 Wiley Periodicals, Inc. Syst Comp Jpn, 38(7): 76β 83, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/scj.20483