Estimating the amount of computation done by a brain using population neural activity

Many dynamical systems, ranging from genetic circuits to the human brain to human social systems, are often characterized as computational. Although extensive research has explored their dynamics, the computations underlying often remain elusive. Even the fundamental task of quantifying the amount of computation underlying a dynamical system remains underinvestigated. In this study we introduce a task-independent framework to estimate the amount of computation implemented by an observed system based on empirical time-series of its dynamics. This framework works by forming a statistical reconstruction of that dynamics, and defining the amount of computation in terms of both the complexity and fidelity. We validate our framework by showing it appropriately distinguishes the relative amount of computation across different regimes of Lorenz dynamics and various computation classes of cellular automata. We then apply this framework to whole-brain neural recordings of Caenorhabditis elegans and large scale population recordings of the mouse cortex. We find that high and low amounts of computation underlie the neural dynamics of freely moving and immobile worms. Our analysis further sheds light on the amount of computation C. elegans performs in various locomotion states. When applied to large-scale electrophysiological recordings from the mouse cortex during a visual decision-making task, our framework recovers the ground-truth difficulty of the task, assigning higher amounts of computation to more difficult trials where sensory inputs are ambiguous. In sum, our study explores a powerful framework for quantifying the amount of computation performed by a system based on time-series data of its dynamics, and highlights neural computation in both simple and complex organisms.