Complementary task representations in hippocampus and prefrontal cortex for generalizing the structure of problems

Humans and other animals effortlessly generalize prior knowledge to solve novel problems, by abstracting common structure and mapping it onto new sensorimotor specifics. To investigate how the brain achieves this, in this study, we trained mice on a series of reversal learning problems that shared the same structure but had different physical implementations. Performance improved across problems, indicating transfer of knowledge. Neurons in medial prefrontal cortex (mPFC) maintained similar representations across problems despite their different sensorimotor correlates, whereas hippocampal (dCA1) representations were more strongly influenced by the specifics of each problem. This was true for both representations of the events that comprised each trial and those that integrated choices and outcomes over multiple trials to guide an animal’s decisions. These data suggest that prefrontal cortex and hippocampus play complementary roles in generalization of knowledge: PFC abstracts the common structure among related problems, and hippocampus maps this structure onto the specifics of the current situation.

. Transfer learning in mice. A) Trial structure of the probabilistic reversallearning task. Mice poked in an initiation port (grey), then chose between two choice ports (green and pink) for a probabilistic reward. B) Block structure of the probabilistic reversal-learning task. Reward contingencies reversed after the animal consistently chose the high reward probability port. C) Example sequence of tasks used for training, showing different locations of the initiation (I) and two choice ports (A & B) in each task. D) Example behavioural session late in training in which the animal completed 12 reversals. Top panel shows which side has high reward probability; bottom panel shows exponential moving average of subjects' choices (tau=8 trials). E) Number of trials following a reversal taken to reach the threshold to trigger the next reversal, as a function of task number. F) Number of pokes per trial to a choice port that was no longer available because the subject had already chosen the other port, as a function of task number. G, I) Coefficients from a logistic regression predicting current choices using the history of previous choices (G), outcomes (not shown) and choice-outcome interactions (I). For each task and predictor the coefficients at lag 1-11 trials are plotted. H, J) Coefficients for the previous trial (lag 1, left) and average coefficients across lags 2-11 (right), as a function of task number. Error bars on all plots show mean ± SEM across mice.

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Fig: 2. Recording units across multiple tasks in a single session. A) Silicon probes targeting hippocampal dorsal CA1 and medial PFC were implanted in separate groups of mice. B) Diagram of task layouts types used during recording sessions. C) Example recording session in which a subject completed four reversals in each of three tasks. Top panel shows the ports participating in each task colour coded by layout type. Bottom panel shows the exponential moving average of choices, with the blocks shown above. D) Example PFC neurons. Cell 1 in PFC fired selectively to both choice ports (but not initiation) in each task, even though the physical location of the choice ports was different both within and across tasks. Cell 2 fired at the initiation port in every task, even when its physical location changed. Cell 3 fired at B choice ports in all tasks, but also gained a firing field when initiation port moved to the previous B choice port (showing PFC does have some port-specific activity). Cell 4 responded to reward at every choice port in every task. Cell 5 responded to reward omission, and had high firing during the ITI. Cell 6 responded to reward at B choice port (that switched location) in each task. E) Example CA1 neurons. Some CA1 cells also had task general firing properties (cell 1 and 2). Cell 1 fired at B choice that switched physical location between tasks. Cell 2 responded to the same port in all tasks and modulated its firing rate depending on whether it was rewarded or not. Cell 3 fired at the same port in all task layouts. Cell 4 switched its firing preference from initiation to B choice that shared physical locations, analogous to 'place cells' firing at a particular physical location. This port selectivity was more pronounced in CA1 than PFC (Supplementary Figure 4). Cell 5 and 6 'remapped' -showing interactions between task and space. Cell 5 fired at a given port in one layout but not when the same port was visited in a different layout. Cell 6 fired at choice time at a given port in one layout and changed its preferred firing time to pre-initiation in a different layout.

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was randomised in each recording session.
As animals transferred knowledge of the trial structure across tasks, we reasoned that neu-138 rons may exhibit 'task general' representations of the abstract stages of the trial (initiate, choose, outcome) divorced from the sensorimotor specifics of each task. On inspection, such 140 cells were common in PFC ( Figure 2D). To respond flexibly when a novel task with the same 141 trial structure is encountered, abstract knowledge should be mapped onto the sensorimotor 142 specifics of the new experience. In line with this, although we observed some task-general 143 firing in CA1, hippocampal cells were more likely to respond to the specifics of each task 144 ( Figure 2E). These single unit examples suggest that although task general representations 145 might exist in both regions, PFC activity appears to generalise more across tasks, while CA1 146 represents physical location more strongly, and additionally exhibits 'remapping' between 147 tasks in which neurons change their tuning to both physical location and task events.

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PFC population activity generalises more strongly across tasks than CA1

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To assess whether our single unit observations hold up at the population level, we sought 150 to characterise how neural activity in each region represented task events, and how these 151 representations generalised across tasks.

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We first assessed the influence of different task variables in each region using linear 154 regression to predict spiking activity of each neuron, at each time point across the trial, as a 155 function of the choice, outcome, and outcome x choice interaction on that trial ( Figure 3A). 156 We quantified how strongly each variable affected population activity as the population 157 coefficient of partial determination (i.e., the fraction of variance uniquely explained by each 158 regressor) at every time point across the trial ( Figure 3B). This analysis was run separately 159 for each task in the session and the results were averaged across tasks and sessions. Both 160 regions represented current choice, outcome, and choice x outcome interaction, but there 161 was regional specificity in how strongly each variable was represented. Choice (A vs B) 162 representation was more pronounced in CA1 than PFC (peak variance explained -CA1: 163 8.4 %, PFC: 4.8 %, p < .001), whereas outcome (reward vs no reward) coding was stronger 164 in PFC (peak variance explained -CA1: 7.1 %, PFC: 12.9 %, p < .001). Furthermore, 165 choice x outcome interaction explained more variance in CA1 than PFC (peak variance 166 explained -CA1: 3.7 %, PFC: 2.4 %, p <.001).

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Though highlighting some differences in population coding between regions, this approach 169 cannot assess the relative contribution of abstract representations that generalise across 170 tasks versus task specific features such as the physical port location. This requires 171 comparing activity both across time points in the trial and across tasks, which we did using 172 representational similarity analysis (RSA) 42 . We extracted firing rates around initiation 173 and choice port entries (40ms window) and categorised these windows by which task they 174 came from, whether they were initiation or choice, and -for choice port entries whether the  To quantify the factors influencing representation similarity, we created representational 184 similarity design matrices (RDMs) which each encapsulated the predicted pattern of 185 similarities under the assumption that activity was influenced by a single task feature 186 ( Figure 3D). For example, if the population activity represented only which physical port Fig: 3. Task-general and task-specific representations in PFC and CA1 population activity. A) Linear regression predicting activity of each neuron at each time point across the trial, as a function of the choice, outcome and outcome x choice interaction. B) Coefficients of partial determination from the linear model shown in A for choice, outcome and outcome x choice regressors in PFC and CA1. C) Representation similarity at 'choice time' (left) and 'outcome time' (right), quantified as the Pearson correlation between the demeaned neural activity vectors for each pair of conditions. D) Representational Similarity Design Matrices (RDMs) used to model the patterns of representation similarity observed in the data. Each RDM codes the expected pattern of similarities among categories in C under the assumption that the population represents a given variable. The Port RDM models a representation of the physical port poked (e.g., far left) irrespective of its meaning in the task. A vs B Choice models a representation of A/B choices irrespective of physical port. The Outcome RDM models representation of reward vs reward omission. The Outcome at A vs B RDM models separate representations of reward vs omission following A and B choices. Choice vs Initiation models representation of the stage in the trial. Choice A Task Specific models separate representation of the A choice in different tasks. E) Coefficients of partial determination in a regression analysis modelling the pattern of representation similarities using the RDMs shown in D. The time-course is given by sliding the windows associated with choices from being centered on choice port entry to 0.76 s after choice port entry, while holding time windows centered on trial initiations fixed. Stars indicated time points where regression weight for each RDM was significantly different between the two regions (p < .05 (small stars) and p < .001 (big stars), permutation test across sessions corrected for multiple comparison over time points. For more details on permutation tests see Methods.

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choice 'Outcome at A vs B'). Changes in activity across tasks might occur simply due to neurons being tuned for particular physical locations, which will be captured by the 'Port' 192 RDM. However, it is also possible that the changing context provided by different tasks 193 modifies the representation of choosing the same physical port at the same trial stage. To 194 assess such 'remapping', we included an RDM 'Choice A task specific' which modelled 195 task specific representations of the A choice, which shares the same physical location and 196 meaning across tasks. We modelled the observed pattern of similarities in the data as a 197 linear combination of these RDMs, quantifying the influence of each by its corresponding 198 weight in the linear fit. To be able to examine the temporal evolution of these effects we 199 run a series of regressions onto the data. In each, the data around initiation port entry was 200 the same but the data around the choice port entry progressed serially through time from 201 choice point until after the reward was delivered ( Figure 3E).

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Consistent with our single unit observations, both PFC and CA1 represented both task 204 specific and task general features to some extent. However, there was a marked regional 205 specificity in how strongly different features were encoded ( Figure 3E). PFC had stronger, 206 abstract, sensorimotor-invariant representation of trial stage (initiation vs choice) and trial 207 outcome (p < .001). In contrast, CA1 had stronger representation of the physical port 208 the subjects was poking, and whether it was an A vs B choice (p < .001). Additionally, 209 CA1 but not PFC showed a task specific representation of A choices (p < .001). This 210 is striking because during A choices both the physical port and its meaning are identical 211 across tasks, indicating that the changing task context alone induced some 'remapping' in 212 CA1 but not PFC. Finally, there was a regional difference in the representation of trial 213 outcome. PFC outcome representations were more general (the same neurons responded 214 to reward or reward omission across ports and tasks -p < .001). CA1 also maintained an 215 outcome representation, but this was more likely to be conjunctive than in PFC -different 216 neurons would respond to reward on A and B choices (p < .001). To exclude the possibility 217 that task specificity in CA1 might be driven by CA1 representations drifting slowly over 218 time we confirmed that task representation changed abruptly at transitions between tasks 219 (Supplementary Figure 5).

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Low dimensional temporal structure of activity is invariant across tasks 221 and regions, but cell assemblies generalise more strongly in PFC than CA1

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To further explore how the structure of population activity generalised between tasks, 223 we used singular value decomposition to compare the principal temporal and cellular 224 modes across the different tasks. We decomposed activity in each task into a set of 225 cellular (across neurons) and temporal modes (across trial and time). For each cell in 226 each task, we computed the average firing rate at each time point across the trial, for four 227 types of trials -rewarded A choices, A non-rewarded, B rewarded, and B non-rewarded. 228 We concatenated these four time series for each cell to create an activity matrix D 229 where each row contained the average activity of one neuron in one task across each 230 time point of the four trial types ( Figure 4A). Using SVD, we decomposed each activ-231 ity matrix into cellular and temporal modes U and V, linked by a diagonal weight matrix Σ. Diagram of singular value decomposition (SVD) analysis. A data matrix comprising the average activity of each neuron across time points and trial types was decomposed into the product of three matrices, where diagonal matrix Σ linked a set of temporal patterns across trial type and time (rows of V T ) to a set of cellular patterns across cells (columns of U ). B) First temporal mode in V T from SVD decomposition of data matrix from PFC plotted in each task separately for clarity and separated by A (green) and B (pink) rewarded (solid) non-rewarded (dashed) choices. C) First cellular mode from SVD decomposition of data matrix from PFC in each task showing similar pattern of cells participate in all tasks. D) Variance explained when using temporal activity patterns V T 1 from one task to predict either held out activity from the same task (solid lines) or activity from a different task (dash lines). E) Variance explained when using temporal activity patterns V T 1 to predict either activity from the same task and brain region (solid lines) or a different brain region and the same task (dash lines) D 2 . F) Variance explained when using cellular activity patterns U 1 from one task to predict either held out activity from the same task (solid lines) or activity from a different task (dash lines). G) Cumulative weights along the diagonal Σ using pairs of temporal V T 1 and cellular U 1 activity patterns from one task to predict either held out activity from the same task (solid lines) or activity from a different task (dash lines). Weights were normalised by peak cross-validated cumulative weight computed on the activity from the same task. H) To assess whether the temporal singular vectors generalised significantly better between tasks in PFC than CA1, we evaluated the area between the dash and solid lines in D for CA1 and for PFC separately, giving a measure for each region of how well the singular vectors generalised. We computed the difference in this measure between CA1 and PFC (pink line in H), and compared this difference to the null distribution obtained by permuting sessions between brain regions (grey histogram, black line shows 95 th percentile of distribution). For more details on permutation tests see Methods.Temporal singular vectors generalised equally well between tasks in the two regions. I) Cellular singular vectors generalised significantly better between tasks in PFC than CA1. Computed as in H but using the solid / dash lines from F. G) Pairs of cellular and temporal singular vectors generalised significantly better between tasks in PFC than CA1. Computed as in H but using the solid / dash lines from G. 9/23 peak at choice time, but strongly suppressed following reward (similar to cell 5 in Figure 2D). We reasoned that: (i) if the same events were represented across tasks (e.g. initiation, A/B 245 choice, reward), then the temporal modes would be exchangeable between tasks, no matter 246 whether these representations were found in the same cells; (ii) if the same cell assemblies 247 were used across tasks, then the cellular modes would be exchangeable across tasks, no 248 matter whether the cell assemblies played the same role in each task; and (iii) if the same 249 cell assemblies performed the same roles in each task, then pairs of cellular and temporal 250 modes would be exchangeable across tasks.

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To see whether the same representations existed in each task, we first asked how well the 253 temporal modes from one task could be used to explain recordings from other tasks. Since 254 V is an orthonormal basis, any data of the same rank or less can be perfectly explained 255 when using all the temporal modes. However, population activity in each task is low 256 dimensional so a small number of modes explain a great majority of the variance. Modes 257 that explain a lot of variance in one task will only explain a lot of variance in the other task 258 if the structure captured by the mode is prominent in both tasks. The question is therefore 259 how quickly variance is explained in data set B, when ordering the modes according to 260 variance explained in data set A. To assess this, we regressed the temporal modes from 261 one task onto the data matrix from the other, and plotted cumulative variance explained 262 ( Figure 4D). To control for drift in neuronal representations across time, we computed the 263 data matrices separately for the first and second halves of each task. We compared the 264 amount of variance explained using modes from the first half of one task to model activity 265 in the second half of the same task, with the variance explained using modes from the 266 second half of one task to model activity from the first half of the next task.

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In both PFC and CA1, the cumulative variance explained as a function of the number of 269 temporal modes used, did not depend on whether the two data sets were from the same 270 task (solid) or different tasks (dashed) ( Figure 4D, H, p > .05). This indicates that the 271 temporal patterns of activity, and therefore the trial events represented, did not differ 272 across tasks in either brain area. However, as this analysis used only the temporal modes, it 273 says nothing about whether the same or different neurons represented a given event across 274 tasks. In fact, we can even explain activity in one brain region using temporal modes from 275 another region and mouse. ( Figure 4E).

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The pattern was very different when we used cellular modes (i.e., assemblies of co-activating 278 neurons) from one task to explain activity in another. In both PFC and CA1, cellular 279 modes in U that explained a lot of variance in one task, explained more variance in the 280 other half of the same task than they did in an adjacent task ( Figure 4F -differences 281 between solid and dashed lines). However, the within task vs cross task difference was 282 larger in CA1 than PFC ( Figure 4I, p < .05). This indicates that PFC neurons whose 283 activity covaried in one task were more likely to also covary in another task, when compared 284 to CA1 neurons. As this analysis considered only the cellular modes it does not indicate 285 whether a given cell assembly carried the same task information across tasks.

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To assess how well the cellular-temporal activity patterns from one task explained activity 288 in another, we projected one data set D 2 onto the cellular and temporal mode pairs of the If the same cell assemblies perform the same roles in two different tasks, the temporal and 291 cellular modes will align, and Σ 2 will have high weights on the diagonal. We therefore plotted 292 the cumulative weight of the diagonal elements of Σ within and between tasks ( Figure 4G).

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In both PFC and CA1 cellular and temporal modes aligned better in different data sets from 294 10/23 the same task (solid lines), than for different tasks (dashed lines). However, this difference was substantially larger for CA1 than PFC ( Figure 4J, p < .05).

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These data show that although the temporal structure of activity in both regions generalises 297 perfectly across tasks, brain regions and subjects -a consequence of the same set of trial 298 events being represented in each, the cell assemblies used to represent them generalised more 299 strongly in PFC than CA1. To quantify whether policy generalised more strongly between tasks in PFC than CA1, we computed the between region difference in the sum along the diagonal of the correlation matrices in C), separately for A and B choices, and compared it against the null distribution obtained by permuting sessions between brain regions. Policy representation on both A and B choices generalised more strongly in PFC than CA1. E) Slices through the correlation matrices at initiation (left), choice (center) and outcome (right) times for A (solid) and B (dash line) choices. Significant differences between conditions are indicated by stars as shown in legend.

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motor specifics in CA1. A portion, but not all, of this task specificity in CA1 was accounted for by the port identity. Recent data have highlighted the low dimensional structure of task representations in rodent 368 OFC 8 . We show that these low dimensional temporal modes are also consistent across tasks 369 in both mPFC and CA1. We also confirm that they are consistent between animals and 370 further demonstrate they are consistent between different brain areas (mPFC and CA1), 371 suggesting this low dimensional structure does not reflect the unique representational 372 properties of a particular brain area. Our manuscript makes further unique contributions.

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Because we record across the same neurons in different tasks, we are able to ask not only 374 whether the temporal dimensions are preserved across tasks, but whether these temporal 375 modes align to the same neurons in each task, i.e., whether the same neurons represent the 376 same trial events across tasks. They do so significantly more in PFC than CA1. Whilst 377 transfer learning relies on building abstractions, it must also tie these abstractions to 378 the sensorimotor properties of each new task. In this context it is intriguing that CA1 379 representations contained distinct portions of variance aligned to abstract task coordinates, 380 to sensorimotor coordinates and to the interaction of the two coordinate sets. Lastly, our 381 paper extends these ideas to variables that must integrate information over many different 382 experiences (such as the animals' choice policy) and shows a similar distinction between 383 mPFC and CA1 in performing such computations. We would like to thank Tom Jahans-Price for his help with setting up electrophysiology in 451 our lab and training us to conduct our first recordings. We would also like to thank Tom  , and a ground screw was implanted above the cerebellum.

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Both of the DV coordinates are relative to the brain surface. Mice were given additional 700 doses of meloxicam each day for 3 days after surgery, and were monitored carefully for 7 days 701 post-surgery, then placed back on water restriction 24 hours before restarting task behaviour.

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At the end of the experiment, electrolytic lesions were made under terminal pentobarbital 703 anaesthesia to mark the probe location, animals were perfused, and the brains fixed in 704 formal saline for subsequent histology to identify lesion locations.

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Data analysis

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All analyses were carried out using custom written code in Python. The significance of the differences between brain areas in analyses reported throughout the We created representational similarity matrices which consisted of the Pearson correlation coefficients of neurons in 15 different task condition, defined by the trial stage, choice, outcome and task number (see Results section and Figure 3). Because neurons were not simultaneously recorded, we collapsed data across recording sessions for each brain region into a single matrix (cells x task events) and then calculated the correlation matrix across cells between different task events (i.e., representational similarity). We used a linear regression to model the patterns of representation similarity in the data as a linear combination of representation similarity design matrices (RDMs): Where r (i,j) are elements of the RSA matrix and RDM n(i,j) are elements of the nth RDM.

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The set of RDMs used is shown in Figure 3D. Before regressing the correlation matrices onto 731 the RDMs the diagonal elements from both were deleted and a constant matrix of ones was added to the design matrix to account for any condition independent correlation between model described above. to layout changes (Supplementary Figure 4), we used the 'surprise' measure from the infor-742 mation theory: where x ij is the firing rate of one neuron on a given trial i and task layout j, µ k and σ k 744 are the baseline mean and the standard deviation of the firing rate of that neuron on a 745 particular task layout. If j = k, then the s(x ij ) on each trial i is calculated based on the 746 mean firing rate µ and standard deviation σ of the withheld trials from the same task. More 747 precisely, to calculate how much the firings rates change during the same task layout s(x ij ) 748 was calculated on the 10 trials before the task layout switch ('test' within task), where µ k 749 and σ k were calculated on the 10 trials before those 'test' trials ('train' within task). If 750 j = k, then the s(x ij ) on each trial i was calculated based on the mean firing rate µ and 751 standard deviation σ of the withheld trials from a different task. So, to estimate how much 752 the firings rates change after the task layout switch s(x ij ) was calculated on the 20 trials 753 after the task layout switch ('test' between tasks), where µ k and σ k were calculated from 754 the 'train' trials from a different task layout. This measure was calculated for each neuron 755 separately and then averaged across all neurons for each brain region.

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Singular value decomposition (SVD) was performed using the numpy linalg.svd function in Python. SVD is a principal component analysis technique that decomposes any n x m matrix into a product of three matrices: where D comprises the data matrix to be decomposed and the U Σ and V T matrices have specific interpretations depending on the type and organisation of data in matrix D. The U Σ and V T are computed based on the non-normalised covariances in the column space: and row space: where DD T U = U Σ 2 and D T DV = V Σ 2 are analogous to eigenvalue decomposition 758 AQ = Q. These equations provide an intuition for what the U , Σ and V T matrices mean.

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In the analyses of our data, matrices D were of neuron x timepoints* trial type dimensions.

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As DD T is a non-normalised covariance in the column space, this means that the U 761 singular vectors come from the eigendecomposition of the covariances between neurons 762 (as column space in D is neuron number) and thus describe the neural patterns in the 763 data (i.e., neurons that are active/silent together). D T D is non-normalised covariance 764 in the row space, meaning the V singular vectors come from the eigen decomposition 765 21/23 of the covariances between time and trial type (as D row space is time and trial type) 766 and thus describe the trial and time modes in the data (i.e., trial times/types that are 767 represented similarly). The Σ is diagonal matrix and captures the overall strength of 768 association between each U and V T vectors in the data matrix D, hence how much loading 769 there is of a particular neural mode together with its respective trial x time mode in the data.

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Our goal was to use the SVD to test how well cellular and temporal patterns generalise across different tasks. To make the D matrix we averaged time warped trial firing rates for each neuron in A choice rewarded, A choice non-rewarded, B choice rewarded and B choice non-rewarded conditions and concatenated the data from all sessions for each region separately such that each matrix was had the neurons x time point in trial and condition dimensions. We performed the SVD on demeaned firing rates separately for each task and for cross-validation purposes performed the decomposition separately on the first half and second half of the task: where i is the task number i = 1, 2, 3 and j is the half of the task the data is taken from 772 j = 1, 2.

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To test how well the neural and temporal patterns generalised between pairs of tasks we used the U i2 , V T i2 from the second half of the first task but the activity matrix from the first half of the next task D i+11 to compute the Σ pred i+1 : Cross-validation was computed in an analogous manner but based on the data from the 774 same task. Selecting the second versus first half of the task data ensured there was no time 775 confound in cross-validated results, as the between task analysis would have analogous time 776 effects.

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Since we had different number of neurons in each brain region, each Σ was normalised by 779 the number of neurons recorded from the respective brain region. Computing the Σ pred i 780 for the new D using U T and V from a decomposition of a different D matrix results in a 781 Σ matrix that is no longer diagonal. However, by looking at the diagonal elements we can 782 estimate how much the U T and V from one task explain the activity of neurons from a 783 different layout or in the cross-validated version -same layout but second half of the task.

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More specifically, the diagonal elements tell us how strong the association between each U T 785 and V vectors computed on one of the D matrix is in a different data matrix D.

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Hence, when we looked at how much variance the combination of neural and temporal 788 components from one task explain in a different task, we looked at the cumulative diagonal 789 elements in Σ pred . Selecting only the diagonal elements from the Σ pred also means that the 790 meaningful comparison is between the cross-validated within task Σ pred i and between task 791 Σ pred i+1 as the cumulative sum of the singular values in either Σ pred i+1 or Σ pred i will not 792 add up to a 100 % because the matrix is no longer diagonal in either cross-validated or 793 cross-layout conditions because the singular vectors U and V were computed on a different 794 data matrix data matrix D. Thus, we normalised the test weights by the peak of the 795 cross-validated cumulative weights.

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To investigate how much variance either U or V singular vectors independently explain in the data matrix from a different task we removed the constraint for any U s or V s to be linked to each other. We estimated how much variance the temporal components V on their own explain in the new task: M pred i+1= D i+11 V i2 and cross-validated analogously: M pred i= D i2 V i1 Similarly, to estimate how much variance the neural components U explained in a different task we computed:

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And cross-validated analogously: To determine the significance of the differences between two regions we compared differences 797 in the data between PFC and CA1 against a null distribution of differences between areas 798 under the curve by shuffling the sessions between CA1 and PFC animals.