An Algorithmic Barrier to Neural Circuit Understanding

Neuroscience is witnessing extraordinary progress in experimental techniques, especially at the neural circuit level. These advances are largely aimed at enabling us to understand how neural circuit computations mechanistically cause behavior. Here, using techniques from Theoretical Computer Science, we examine how many experiments are needed to obtain such an empirical understanding. It is proved, mathematically, that establishing the most extensive notions of understanding need exponentially-many experiments in the number of neurons, in general, unless a widely-posited hypothesis about computation is false. Worse still, the feasible experimental regime is one where the number of experiments scales sub-linearly in the number of neurons, suggesting a fundamental impediment to such an understanding. Determining which notions of understanding are algorithmically tractable, thus, becomes an important new endeavor in Neuroscience.