Learning the invariance properties of complex cells from their responses to natural stimuli

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Abstract
Neurons in primary visual cortex are typically classified as either simple or complex. Whereas simple cells respond strongly to grating and bar stimuli displayed at a certain phase and visual field location, complex cell responses are insensitive to small translations of the stimulus within the receptive field [Hubel & Wiesel (1962)J. Physiol. (Lond.), 160, 106–154; Kjaer et al. (1997)J. Neurophysiol., 78, 3187–3197]. This constancy in the response to variations of the stimuli is commonly called invariance. Hubel and Wiesel's classical model of the primary visual cortex proposes a connectivity scheme which successfully describes simple and complex cell response properties. However, the question as to how this connectivity arises during normal development is left open. Based on their work and inspired by recent physiological findings we suggest a network model capable of learning from natural stimuli and developing receptive field properties which match those of cortical simple and complex cells. Stimuli are drawn from videos obtained by a camera mounted to a cat's head, so they should approximate the natural input to the cat's visual system. The network uses a competitive scheme to learn simple and complex cell response properties. Employing delayed signals to learn connections between simple and complex cells enables the model to utilize temporal properties of the input. We show that the temporal structure of the input gives rise to the emergence and refinement of complex cell receptive fields, whereas removing temporal continuity prevents this processes. This model lends a physiologically based explanation of the development of complex cell invariance response properties.