Extended Data Fig. 2: Tuning entanglement decoupling analysis.

(A) Left, plot illustrating a driver variable (v₁) and a correlated passenger variable (v₂; Pearson’s correlation coefficient = 0.45). v₁ samples are drawn from a normal distribution of mean 0 and standard deviation 1. The j^th sample of v₂ is computed as v_2, j = 0.5× v_1,j+ε_j, where each ε_j is drawn from a second normal distribution with mean 0 and standard deviation 1. Right, v₁ is used to simulate the spiking of a neuron such that the probability of firing is equal to 0.1 × v₁ if v₁ > 1 and 0 if v₁ ≤ 1. TunED analysis was then applied to v₁, v₂ and simulated spiking data as described in Methods to compute observed and expected tuning curves to v₁ and v₂. The method correctly identifies v₁ as the driver variable. The observed tuning curve to the passenger variable v₂ (dark yellow) can be fully explained by the tuning to the driver variable (brown). In contrast, the observed tuning to driver variable (dark blue), cannot be explained by the tuning to the passenger variable (light blue). (B) Left, schematic of head–shelter angle and head direction variables during the experiment. Right, correlation between head–shelter angle and head direction in our experimental setting plotted for eight values of head direction for each grid ___location. (C) Left, tuning curves of neurons for which the driver variable was head direction (top) or head–shelter angle (bottom). Right, illustration of the statistical method used to determine whether the driver variable of the neuron was head shelter offset, head direction or none of them (see Methods for details). Briefly, the distribution of dHSA - dHD (dark grey histogram) indicates whether the expected and observed tuning curves are more similar for head–shelter angle or for head direction. If the dHSA - dHD distribution is significantly smaller than zero (both 2.5^th and 97.5^th percentile <0, vertical dotted lines) the cell is classified as a head direction cell; if the distribution of dHSA - dHD is significantly larger than zero (both 2.5^th and 97.5^th percentile > 0) the cell is classified as a head-shelter angle cell; otherwise the cell is not considered a shelter-direction nor head direction cell.