Neurons in the primary visual cortex (V1) encode natural images that are exposed. As a candidate encoding principle, the efficient coding hypothesis was proposed by Attneave (1954) and Barlow (1961). This hypothesis emphasizes that the primary role of neurons in the sensory area is to reduce the redundancy of the external signal and to produce a statistically efficient representation. However, the outputs of neurons in V1 are statistically dependent because their classical receptive fields largely overlap and natural images have structures such as edges and textures. As described in this paper, we propose that the computational role of horizontal connections (HCs) is to decrease statistical dependency and attempt to self-organize the spatial distribution of HCs from natural images. In addition, we show that our neural network model with self-organized HCs can reproduce some nonlinear properties of V1 neurons,
size-tuning and contextual modulation. These results support the efficient coding hypothesis and imply that HCs serve an important role in decreasing statistical dependency in V1.