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

Simplified models of neural networks have demonstrated the importance of establishing a reasonable tradeoff between memory capacity and fault-tolerance in cortical coding schemes. The intensity of the tradeoff is mediated by the level of neuronal variability. Indeed, increased redundancy in neuronal activity enhances the robustness of the code at the cost of the its efficiency. We hypothesized that the heterogeneous architecture of biological neural networks provides a substrate to regulate this tradeoff, 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. To confirm the relevance of our metric we analyzed several openly available connectomes, revealing that they all exhibited wider distributions of simplicial complexity across subpopulations than relevant controls. Using a biologically detailed cortical model and an electron microscopic data set of cortical connectivity with co-registered functional data, 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 neuronal networks, due to the heterogeneity of their connectivity. Our work thus suggests an avenue for resolving seemingly paradoxical previous results that assume homogeneous connectivity.