Wiring minimization of deep neural networks reveal conditions in which multiple visuotopic areas emerge

Abstract

The visual system is characterized by multiple mirrored visuotopic maps, with each repetition corresponding to a different visual area. In this work we explore whether such visuotopic organization can emerge as a result of minimizing the total wire length between neurons connected in a deep hierarchical network. In particular we ask, given N neurons with a given connectivity and a 2-d grid with N locations, how will the neurons be placed on the grid such that the total distance between the connected neurons is minimized? This problem is an NP-hard combinatorial problem which we solve using simulated annealing. We first construct multi-layer feedforward hierarchical networks, and examine how different parameters of the network such as filter size, number of channels, and stride affect the placement of the neurons on the grid. By introducing visual input to the network we can visualize the resulting visuotopic organization on the 2-d grid. Our results show that networks with purely feedforward connectivity typically result in a single visuotopic map, and in certain cases no visuotopic map emerges. However, when we modify the network by introducing lateral connections, with sufficient lateral connectivity among neurons within layers, multiple visuotopic maps emerge, where some connectivity motifs yield mirrored alternations of visuotopic maps–a signature of biological visual system areas. These results demonstrate that different connectivity profiles have different emergent organizations under the minimum wiring hypothesis, and highlight that characterizing the large-scale spatial organizing of tuning properties in a biological system might also provide insights into the underlying connectivity.