Resonant Learning in Scale-free Networks

ABSTRACT Over the last decades, analyses of the connectivity of large biological and artificial networks have identified a common scale-free topology, where few of the network elements, called hubs, control many other network elements. In monitoring the dynamics of networks’ hubs, recent experiments have revealed that they can show behaviors oscillating between ‘on’ and ‘off’ states of activation. Prompted by these observations, we ask whether the existence of oscillatory hubs states could contribute to the emergence of specific network dynamical behaviors. Here, we use Boolean threshold networks with scale-free architecture as representative models to demonstrate how periodic activation of the network hub can provide a network-level advantage in learning specific new dynamical behaviors. First, we find that hub oscillations with distinct periods can induce robust and distinct attractors whose lengths depend upon the hub oscillation period. Second, we determine that a given network can exhibit series of different attractors when we sequentially change the period of hub pulses. Using rounds of evolution and selection, these different attractors could independently learn distinct target functions. We term this network-based learning strategy resonant learning , as the emergence of new learned dynamical behaviors depends on the choice of the period of the hub oscillations. Finally, we find that resonant learning leads to convergence towards target behaviors over an order of magnitude faster than standard learning procedures. While it is already known that modular network architecture contributes to learning separate tasks, our results reveal an alternative design principle based on forced oscillations of the network hub. SIGNIFICANCE Large networks of interconnected components such as genes or machines can coordinate complex behavioral dyamics. One outstanding question has been to identify the design principles that allow networks to learn new behaviors. Here, in simulating learning cycles, we randomly modify the interactions between components and select networks that exhibit a desired behavior. Surprisingly, we find that networks can learn new behaviors faster when the state of the most connected network component is forced to oscillate during learning. Remarkably, using distinct periods of oscillations allows a given network to learn distinct behaviors. While it is known that modular network architecture contributes to learning separate tasks, our results reveal an alternative design principle for which modules are not needed.