Extended Data Fig. 4: Quasi-coherent task-space remapping of mFC neurons.

a) Three example state-tuned neurons remapping across tasks. The top two neurons remap in a way that is not related to their spatial maps in any given task. The bottom neuron remaps in accordance to its spatial map. Angles (in degrees) of each cell’s rotation relative to its tuning in session X are shown to the right of each session’s polar plot. Note that these are not all simultaneously recorded neurons. b) Remapping of state neurons that are defined using a stricter threshold (z-score >99th percentile of permuted distribution). Top: A schematic showing how the difference in tuning angles for the same neuron across sessions is quantified. Bottom left: Polar histograms show that state-tuned neurons remap by angles close to multiples of 90 degrees, as a result of conserved goal-progress tuning and the 4 reward structure of the task. No clear peak at zero is seen relative to the other cardinal directions when comparing sessions spanning separate tasks (Two proportions test against a chance level of 25% N = 1061 neurons; mean proportion of generalising neurons across one comparison (mean of X vs Y and X vs Z) = 24%, z = 0.59, P = 0.552. Bottom right: Neurons maintain their state preference across different sessions of the same task (X vs X’ Two proportions test against a chance level of 25% N = 770 neurons; proportion generalising=80%, z = 21.5, P = 0.0). c) Remapping when using only state-neurons with concordant remapping angles across two methods (i.e. using the best-rotation analysis method and peak-to-peak changes method). This analysis would for example exclude neuron 3 in Fig. 3a. Left: Polar histograms show that state-tuned neurons remap by angles close to multiples 90 degrees, as a result of conserved goal-progress tuning and the 4 reward structure of the task. No clear peak at zero is seen relative to the other cardinal directions when comparing sessions spanning separate tasks (Two proportions test against a chance level of 25% N = 369 neurons; mean proportion of generalising neurons across one comparison (mean of X vs Y and X vs Z) = 24%, z = 0.41 P = 0.684. Right: state-tuned neurons maintain their state preference across different sessions of the same task (bottom right). Two proportions test against a chance level of 25% N = 240 neurons; proportion generalising=84%, z = 13.0, P = 0.0). d) Remapping of non-spatial neurons. Note that we use the most permissive threshold for spatial tuning here to ensure that we exclude even neurons with weak/residual spatial tuning. Any neuron that had a spatial regression coefficient above the 95th percentile of the null distribution was excluded from this analysis. Left: Polar histograms show that non-spatial state-tuned neurons remap by angles close to multiples 90 degrees, as a result of conserved goal-progress tuning and the 4 reward structure of the task. No clear peak at zero is seen relative to the other cardinal directions when comparing sessions spanning separate tasks (Two proportions test against a chance level of 25% N = 704 neurons; mean proportion of generalising neurons across one comparison (mean of X vs Y and X vs Z) = 22%, z = 1.19 P = 0.233). Right: Non-spatial state-tuned neurons maintain their state preference across different sessions of the same task (bottom right). Two proportions test against a chance level of 25% N = 507 neurons; proportion generalising=68%, z = 13.9, P = 0.0). e) Pairwise coherence of state neurons that are defined using a stricter threshold (z-score >99th percentile of permuted distribution). Top: A schematic showing how the difference in relative angles between pairs of neurons across sessions is quantified. Bottom left: Polar histograms show that the proportion of coherent pairs of state-tuned neurons (comprising the peak at zero) is higher than chance but less than 100%, indicating that the whole population does not rotate coherently. Two proportions test against a chance level of 25% N = 17671 pairs; mean proportion of coherent neurons across one comparison (mean of X vs Y and X vs Z) = 29%, z = 8.9, P = 0.0). Bottom right: As expected from panel b, the large majority of state-tuned neurons keep their relative angles across sessions of the same task (X vs X’; Two proportions test against a chance level of 25% N = 11716 pairs; proportion coherent=64%, z = 59.3, P = 0.0). f) Coherence of state-neuron pairs using only state-neurons with concordant remapping angles across two methods (i.e. using the best-rotation analysis method and peak-to-peak changes method). Left: Polar histograms show that the proportion of coherent pairs of state-tuned neurons (comprising the peak at zero) is higher than chance but far from 1, indicating that the whole population does not rotate coherently (Two proportions test against a chance level of 25% N = 1642 pairs; mean proportion of coherent neurons across one comparison (mean of X vs Y and X vs Z = 30%, z = 3.32, P = 9.04 × 10⁻⁴). Right: As expected from panel b, the large majority of state-tuned neurons keep their relative angles across sessions of the same task (X vs X’; Two proportions test against a chance level of 25% N = 657 pairs; proportion coherent=72%, z = 17.1, P = 0.0). g) Coherence of non-spatial neuron pairs. Note that we use the most permissive threshold for spatial tuning here to ensure that we exclude even neurons with weak/residual spatial tuning. Any neuron that had a spatial regression coefficient above the 95th percentile of the null distribution was excluded from this analysis. Left: Polar histograms show that the proportion of coherent pairs of non-spatial state-tuned neurons (comprising the peak at zero) is higher than chance but far from 1, indicating that the whole population does not rotate coherently (Two proportions test against a chance level of 25% N = 6996 pairs; mean proportion of coherent neurons across one comparison (mean of X vs Y and X vs Z = 30%, z = 3.49, P = 4.74 × 10⁻⁴). Right: As expected from panel b, the large majority of non-spatial state-tuned neurons keep their relative angles across sessions of the same task (X vs X’; Two proportions test against a chance level of 25% N = 4822 pairs; proportion coherent=54%, z = 29.2, P = 0.0). h) Proportion of coherent pairs per recording day (pairs of state-tuned neurons where the relative angle doesn’t change by more than 45 degrees across both X to Y and X to Z comparisons) relative to all pairs across different pairwise task space angles. T-tests (two-sided) with Bonferroni correction against chance level of 1/16 (probability of neuron pair rotating coherently across two comparisons (i.e. 1/4²)): N = 38 recording days, pairwise circular distance difference: 0-45 degrees statistic=8.17, P = 3.33 × 10⁻⁹, df = 37; 45-90 degrees statistic=2.84, P = 0.013, df = 37; 90-135 degrees statistic=3.88, P = 0.001, df = 37; 135-180 degrees statistic=2.89, P = 0.013, df = 37. Top: bar graph, bottom: individual points (recording days). i) Coherent pairs are slightly closer anatomically than incoherent pairs. Mann-Whitney U-test (Two-sided): N = 3567 pairs (53 coherent; 3514 incoherent), statistic=72872, P = 0.006. Note that, to minimise the effect of noise, this analysis uses only double days and only considers a pair of neurons coherent if they show perfect coherence across all combinations of 6 tasks. Top: bar graph, bottom: kernel density estimate of data distribution. j) The subregional distribution of single neuron generalisation (averaged across X vs Y and X vs Z comparisons) along the medial wall of frontal cortex in neuropixels recordings. One-way ANOVA: F = 1.59, P = 0.323, df = 3. k) The subregional distribution of neuron pair coherence. Coherence is calculated across both X vs Y and X vs Z comparisons along the medial wall of frontal cortex in neuropixels recordings: One-way ANOVA: F = 4.76, P = 0.083, df = 3. l) Top: Visualisation of tuning relationships between two clusters computed in a single recording day. Each dot is a neuron (numbered in correspondence to the polar plots below) and each ring is a cluster derived from the analysis in panel d. The colour code represents the tuning of the neurons in task X. The x,y position defines the tuning in each task. The z position corresponds to cluster ID. Note that the ordering along the z axis is arbitrary. Neurons rotate (remap) in task space while maintaining their within-cluster tuning relationships but not cross-cluster relationships across tasks. Bottom: polar plots for all of the (seven) neurons assigned to each of the two clusters in the above plot. Angles (in degrees) of each cell’s rotation relative to its tuning in session X are shown to the right of each session’s polar plot. All error bars represent the standard error of the mean.