Can grid cells produce hexadirectional signals?

Hexadirectional analysis is widely used to infer population-level grid cell activity in humans, yet this signature has not been reproduced in rodent electrophysiology, where grid cells are best characterized. Moreover, it remains unclear how grid cell populations could generate such a signal. We address this issue theoretically and empirically by evaluating three prevailing hypotheses and the null model, while critically examining the analysis framework itself. We show that the standard approach is insensitive to grid firing per se. Instead, hexadirectional modulation emerges in firing variance, which we find in ratemaps of single-cell, MEC recordings of freely moving rats. Empirically, conjunctive grid-by-head-direction tuning does not produce hexadirectional signals, whereas specific nonlinear transformations can. We argue that false positive inferences can occur and suggest approaches for improved robustness and confidence. This work has critical implications for studies on hexadirectional signals and sheds light on the neural basis of fMRI.