Extended Data Fig. 8: Anchoring analysis using linear and non-linear models.

a) Histogram showing the right shifted distribution of mean cross-validated correlation values between model-predicted (from training tasks) and actual activity (from a left out test task) for only non-zero lag state-tuned neurons with the maximum regression coefficient value a whole state (90 degrees) or more either side of the anchor. To avoid contamination due to potential residual spatial-tuning, only regression coefficient values more than 90 degrees in task space either side of the anchor point are used for the prediction. T-test (two-sided) against 0: N = 224 neurons, statistic=2.53, P = 0.012, df = 223. b) Histograms showing the right-shifted distribution of mean cross-validated correlation values between model-predicted (from training tasks) and actual activity (from a left out test task) for state neurons that are defined using a stricter threshold (z-score >99th percentile of permuted distribution). Left: this correlation is shown for all state-tuned neurons; Middle: only state-tuned neurons with non-zero-lag firing from their anchors; and Right: non-zero lag state-tuned neurons with the maximum regression coefficient value a whole state (90 degrees) or more either side of the anchor. T-test (two-sided) against 0: All state-tuned neurons N = 349 neurons, statistic=8.70, P = 1.34 × 10⁻¹⁶, df = 348; Non-zero lag state-tuned neurons N = 227 neurons, statistic=2.83, P = 0.005, df = 226; distal (90 degrees) non-zero lag neurons: N = 154 neurons, statistic=1.94, P = 0.054, df = 153. c) Histogram showing the right shifted distribution of mean cross-validated correlation values between model-predicted (from training tasks) and actual activity (from a left out test task) for state neurons that are not tuned to the animal’s current trajectory. Note that we use a permissive threshold for trajectory tuning here to ensure we exclude any neurons with even weak/residual tuning for trajectory. Any neuron that had a trajectory regression coefficient above the 95th percentile of the null distribution was excluded from this analysis. T-test (two-sided) against 0: N = 112 neurons, statistic=4.27, P = 4.13 × 10⁻⁵, df = 111). d) Histograms showing the right-shifted distribution of mean cross-validated correlation values between model-predicted (from training tasks) and actual activity (from a left out test task) for state neurons using a Poisson regression model. Left: this correlation is shown for all state-tuned neurons; Middle: only state-tuned neurons with non-zero-lag firing from their anchors; and Right: non-zero lag state-tuned neurons with the maximum regression coefficient value a whole state (90 degrees) or more either side of the anchor. T-test (two-sided) against 0: All state-tuned neurons N = 489 neurons, statistic=10.7, P = 2.86 × 10⁻²⁴, df = 488; Non-zero lag state-tuned neurons N = 346 neurons, statistic=4.74, P = 3.09 × 10⁻⁶, df = 345; distal (90 degrees) non-zero lag neurons: N = 229 neurons, statistic=2.81, P = 0.005, df = 228. e) Mean, per mouse distribution of cross-validated correlation values between model-predicted (from training tasks) and actual activity (from a left out test task) for: Top: All state-tuned neurons, Middle: non-zero lag state-tuned neurons (30 degrees or more away from anchor), Bottom: distal non-zero lag state-tuned neurons (90 degrees or more away from anchor). One-sided binomial test against chance (chance being mean values equally likely to be above or below 0): All state-tuned neurons: 6/7 mice with mean positive correlation P = 0.063; Non-zero lag state-tuned neurons: 7/7 mice with mean positive correlation P = 0.008; Distal Non-zero-lag state-tuned neurons: 6/7 mice with mean positive correlation P = 0.063). All error bars represent the standard error of the mean.