Quantifying the Controllability of Computations on Networks

Many complex biological and physical systems perform computations on an underlying network. While both structure and dynamics shape computational properties of these systems, how network architecture quantitatively shapes the ease with which specific computations can be enacted remains less understood. Here, we view computation as a controlled transformation of activity on a network, formalized using network control theory. We use this framework to examine how network structure influences the control inputs required to implement simple operations, such as superposition (to model modulatory effects of the Locus Coeruleus) and rotation (to model the head direction system in Drosophila) on synthetic networks. We then extend our analysis to empirical subnetworks in the brain, where we find that structural heterogeneity across subnetworks leads to systematic differences in controllability landscapes that reflect distinctions in the range of computations that can be efficiently supported. Sensory networks display more heterogeneous, specialized landscapes, whereas multimodal association networks display more homogeneous landscapes, suggesting a tradeoff between computational specialization and flexibility. Together, these results provide a quantitative link between structure, control, and computation. Building on this link, we explore how network architectures may be designed to favor specific operations. Our framework contributes to efforts aimed at understanding structure–function relationships in natural and artificial systems.