Extended Data Fig. 11: Additional properties of aVEVS invariance.

a, (Row 1) For same cells recorded in response to the movement of a green striped and green checkered bars of light, mean firing rates during stationary epochs (running speed< 5cm/sec), were significantly correlated (Pearson’s r = 0.48 p =  2 x 10⁻⁵). Preferred angles of aVEVS between the two stimulus patterns were also significantly correlated (circular correlation coefficient, r = 0.32 p = 5 x 10⁻³). Solid red dots denote preferred angles of cells tuned (sparsity (z) > 2) in both conditions; gray dots are for cells with significant tuning in one of the conditions. (Row 2) Same as a (Row 1), but for responses to changes of stimulus color, green and blue. Firing rate (r = 0.45 p = 1 x 10⁻⁴) & preferred angle (r = 0.36 p = 0.01) were correlated. (Row 3) Same as a (Row 1), but for changes to predictability of the stimulus, also called “random” vs “systematic”. Firing rate (r = 0.55 p = 2 x 10⁻¹³) & preferred angle (r = 0.27 p = 0.01) were significantly correlated between systematic and random stimuli movement. (Row 4) Same as a (Row 1), but for responses recorded across 2 days. Firing rate (r = 0.28 p = 3.2 x 10⁻⁵) & preferred angle (r = 0.22 p = 0.006) were correlated. b, Similar to Fig. 3, we computed the population remapping indices based on sparsity difference, preferred angle difference and peak value of cross correlation. The sparsity difference did not show a systematic pattern, but the other two metrics generally showed increasing remapping going from pattern (correlation = 0.68, angle difference = 30^o) to color (correlation = 0.64, angle difference = 46.5^o) to predictability (correlation = 0.55, angle difference = 66^o) and across days (correlation = 0.63, angle difference = 66^o). n indicates the number of responses measured in both conditions for each comparison, similar to Fig. 3h. Thick line – median, box – sem. c, Percentage of tuned responses in the random stimulus experiments, showing, comparable bi-directionality (10% here vs 13% for systematically moving bar). d, For same cells recorded in random and systematic stimulus experiments, the distributions of firing rates and selectivity, quantified by z-scored sparsity, were not significantly different (cyan-systematic, purple-random, KS-test for z-scored sparsity p = 0.14, for firing rate p = 0.27). e, Cross correlation between CCW and CW tuning curves showing lagged response for the majority of bidirectional cells in the random condition. f, Same as e, but for unidirectional cells. g, Cross correlation of tuning curves (for tuned cells in the random stimulus experiment) between fast- and slow-moving stimulus was calculated from the subsample of data for a particular speed in CW and CCW direction separately and stacked together after flipping the CCW data and was not significantly biased from zero (Circular median test at 0^o, p = 0.56). h, Example cell showing similar aVEVS for data within 1 s of stimulus direction change (top), or an equivalent, late subsample (bottom). i, Firing rate (KS-test p = 0.73) and sparsity (KS-test p = 0.87) were not significantly different for these two subsamples of experimental recordings. j, In the randomly moving stimulus experiments, we computed a stimulus speed modulation index (see Methods). This distribution was not significantly biased away from zero. k, This modulation index was z-scored (see Methods), and only 5.2% of cells had significant firing rate modulation beyond z of ±2.