Fig. 2: Network gain covaries with resetting dynamics.

a, Experimental protocol (top). Middle, example session showing the offset obtained by subtracting decoded from measured HD (blue dots). Red, smoothed offset. Darkness periods are shaded in grey. Bottom, measured (blue) and decoded (green) HD. b, Example fast (top) and slow (bottom) resets. The horizontal solid line indicates the cue location. The offset is relative to its angle at the cue onset. c, Projection of population activity onto the polar plane for the baseline (left) and the entire session (right). d, The same as in c; however, points are shaded by their radius (left). Right, mean bump of activity in the internal reference frame across radius ranges. e, The relationship between network gain and state radius (n = 42 × L datapoints, where L is the number of frames in a session). R² value of linear regression model fit. Data are mean ± s.d. f, Triggered average of network gain (n = 168 = 4 × 42 cue events). The dashed red line indicates the cue display. g, Mean offsets for fast (light blue; n = 22 resets) and slow (dark blue; n = 20 resets) resets. Both groups have similar ranges (two-sided Wilcoxon rank-sum test, P = 0.4131, Z = 0.82), yet their speeds are different (two-sided Wilcoxon rank-sum test, P = 1.0982 × 10⁻⁶, Z = 4.87; 150 frames (~5 s) after the cue). h, Network gains of fast and slow reset groups have similar amplitudes before cue display (two-sided Wilcoxon rank-sum test, P = 0.6234, Z = 0.49; 50 frames (~1.67 s) before the cue), yet are different after cue display (two-sided Wilcoxon rank-sum test, P = 0.0085, Z = 2.63; 150 frames (~5 s) after the cue). The same data as in g. i, The relationship between gain and reset speed within 150 frames (~5 s) after the cue (n = 42 × 150 datapoints). The P value was calculated using an F-test on a linear model fit. j, Simulation of the bump of activity showing gain control of reset speed. The gain remains constant after cue display (dashed red). The solid white lines show the relative cue location. k, Model-based prediction (red) and true reset (blue). The dashed black lines indicate the cue display. The solid yellow lines indicate the relative cue location. All clockwise sessions were reflected across the x axis and transformed into counter-clockwise ones. Time-dependent signals in f–h are shown as mean ± s.e.m. Bar graphs and error bars, except in e, show mean ± s.e.m. with individual datapoints.