Spontaneous emergence of topographic organization in a multistream convolutional neural network

Neurons in the cerebral cortex are organized topographically. In the primate visual cortex, neighboring neurons often respond to similar stimulus parameters, such as receptive field position, orientation, color, and spatial frequency. Preferred stimulus parameters change smoothly across the cortical surface. If such topographic organization plays an important role in computation, it is likely to emerge in artificial neural networks. In this study, a multistream convolutional neural network was constructed in which filters in the first convolutional layer were arranged in a two-dimensional filter matrix according to their output connections. The network was trained using supervised learning for image classification. Although adjacent filters in the filter matrix can develop any structure in principle, they acquire similar degrees of orientation and color selectivity. Moreover, they prefer similar orientations, hues, and spatial frequency. The similarity decreases with distance between filters in the matrix. Furthermore, neural-network model instances that have a strong relationship between filter distance and filter-property similarity performed better than those with a weak relationship. These results suggest that topographic organization emerges spontaneously in an artificial neural network and plays an important role in model performance, suggesting the importance of topographic organization for computations performed by artificial and biological neural networks.