Comparing noisy neural population dynamics using optimal transport distances

Neural systems form high-dimensional representations that underpin their computational capabilities. Consequently, methods for quantifying representational similarity in neural representations have become a popular tool for identifying computational principles that are potentially shared across neural systems. These methods generally assume that neural responses are deterministic and static. However, responses of biological systems are noisy and dynamically unfold over time and these characteristics can have substantial influence on a system’s computational capabilities. We first show that existing methods can fail to capture differences between noisy neural population dynamics. This failure can be attributed to ignoring either stochastic or dynamic aspects of neural responses. We then propose a novel metric that captures differences in the stochastic and dynamic aspects of neural responses. Our method is based on optimal transport distances between Gaussian processes and is readily computed using an alternating minimization algorithm. We illustrate our method by comparing models of neural trajectories in different regions of the motor system.