Modeling the development of maps of complex cells in V1

Hubel and Wiesel classified primary visual cortex (V1) neurons as either simple, with responses strongly modulated by the spatial phase of a sine grating, or complex, largely phase invariant [1]. Much progress has been made in understanding how simple cells develop, with detailed computational models establishing how they can form topographic maps ordered by orientation preference. There are also models of how individual complex cells can develop using outputs from simple cells with different phase preferences, but no model of how a realistic topographic orientation map of complex cells could be formed based on the actual connectivity patterns found in V1. Addressing this question is important, because a majority of existing simple-cell models produce maps that group similar spatial phases together, which is contrary to experimental evidence, and makes it difficult to construct complex cells. Overcoming this limitation is not trivial, because the simple-cell models are driven by correlations in the input, and phase is more highly correlated than orientation in natural images.