Misinterpreting the horseshoe effect in neuroscience

Dimensionality reduction methods are frequently used to analyze high-dimensional activity of cortical neuron populations during behavior. The resulting oscillatory trajectories that consistently emerge from this analysis have been interpreted as a signature of latent dynamical systems. Here, we show that these oscillatory trajectories necessarily result from applying dimensionality reduction methods on recordings that approximately exhibit continuous variation in time, regardless of whether or not the recorded system incorporates latent dynamics.