Heterogeneous and higher-order cortical connectivity undergirds efficient, robust, and reliable neural codes

We hypothesized that the heterogeneous architecture of biological neural networks provides a substrate to regulate the well-known tradeoff between robustness and efficiency, thereby allowing different subpopulations of the same network to optimize for different objectives. To distinguish between subpopulations, we developed a metric based on the mathematical theory of simplicial complexes that captures the complexity of their connectivity by contrasting its higher-order structure to a random control and confirmed its relevance in several openly available connectomes. Using a biologically detailed cortical model and an electron microscopic dataset, we showed that subpopulations with low simplicial complexity exhibit efficient activity. Conversely, subpopulations of high simplicial complexity play a supporting role in boosting the reliability of the network as a whole, softening the robustness-efficiency tradeoff. Crucially, we found that both types of subpopulations can and do coexist within a single connectome in biological neural networks, due to the heterogeneity of their connectivity.