Comparing noisy neural population dynamics using optimal transport distances

Biological and artificial neural systems form high-dimensional neural representations that underpin their computational capabilities. Methods for quantifying geometric 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, and some artificial systems, are noisy and dynamically unfold over time. Furthermore, these characteristics can have substantial influence on a system's computational capabilities. Here, we demonstrate that existing metrics can fail to capture key differences between neural systems with noisy dynamic responses. We then propose a metric for comparing the geometry of noisy neural trajectories, which can be derived as an optimal transport distance between Gaussian processes. We use the metric to compare models of neural responses in different regions of the motor system and to compare the dynamics of latent diffusion models for text-to-image synthesis. Biological and artificial neural systems represent their environments and internal states as patterns of neural activity, or "neural representations". In an effort to understand general principals governing these representations, a large body of work has sought to quantify the extent to which they are similar across systems (Klabunde et al., 2023). Most of these existing (dis)similarity measures assume that neural activities are deterministic and static.