A Hopfield network model of neuromodulatory arousal state

Neural circuits display both input-driven activity that is necessary for the real-time control of behavior and internally generated activity that is necessary for memory, planning, and other cognitive processes. A key mediator between these intrinsic and evoked dynamics is arousal, an internal state variable that determines an animals level of engagement with its environment. It has been hypothesized that arousal state acts through neuromodulatory gain control mechanisms that suppress recurrent connectivity and amplify bottom-up input. In this paper, we instantiate this longstanding idea in a continuous Hopfield network embellished with a gain parameter that mimics arousal state by suppressing recurrent interactions between the networks units. We show that dynamics capturing some essential effects of arousal state at the neural and cognitive levels emerge in this simple model as a single parameter--recurrent gain--is varied. Using the models formal connections to the Boltzmann machine and the Ising model, we offer functional interpretations of arousal state rooted in Bayesian inference and statistical physics. Finally, we liken the dynamics of neuromodulator release to an annealing schedule that facilitates adaptive behavior in ever-changing environments. In summary, we present a minimal neural network model of arousal state that exhibits rich but analytically tractable emergent behavior and reveals conceptually clarifying parallels between arousal state and seemingly unrelated phenomena.