Experience-dependent contextual codes in the hippocampus

Abstract

The hippocampus contains neural representations capable of supporting declarative memory. Hippocampal place cells are one such representation, firing in one or few locations in a given environment. Between environments, place cell firing fields remap (turning on/off or moving to a new location) to provide a population-wide code for distinct contexts. However, the manner by which contextual features combine to drive hippocampal remapping remains a matter of debate. Using large-scale in vivo two-photon intracellular calcium recordings in mice during virtual navigation, we show that remapping in the hippocampal region CA1 is driven by prior experience regarding the frequency of certain contexts and that remapping approximates an optimal estimate of the identity of the current context. A simple associative-learning mechanism reproduces these results. Together, our findings demonstrate that place cell remapping allows an animal to simultaneously identify its physical location and optimally estimate the identity of the environment.

Extended Data Fig. 1 ∣. Licking behavior and number of cells recorded per session.

a, The number of cells identified per session is plotted for each rare morph animal individually. Each mouse shown as a different color. b, Same as (a) for all frequent morph animals. c, Single trial lick rate as a function of position is shown for an example rare morph session (R3, session 8; n = 120 trials). Left: Each row indicates the smoothed lick rate across positions for a single trial. The color of the row indicates the morph value (colormap in Fig. 1c). The grey shaded region indicates possible reward locations. Trials are shown in the order in which they occurred during the experiment. Right: Trials are sorted by the location of the reward cue. The color code also indicates increasing reward distance from the start of the track (green to yellow). Black trials are those in which the reward cue was omitted. d, Same as (c) for an example frequent morph session (F5, session 8; n = 120 trials). e, Across session mean lick rate (licks/sec) as a function of position (see [a-b] for number of sessions and color code) is plotted as a separated line for each mouse (R1-R6 & F1-F6; mean ± SEM). The color scheme for each mouse is the same as in the rest of the manuscript. Grey shaded region indicates possible reward location as in (c-d). f, The same data as (e) is normalized by the animal’s overall mean lick rate. g, Normalized mean lick rates were combined across rare and frequent morph animals. Trials were then binned by reward location (50 cm bins) and plotted as a function of position (across animal mean ± SEM). Color code is the same as (c-d).

Extended Data Fig. 2 ∣. Across Virtual Reality (VR) scene variance is best predicted by the horizontal component of the frequency of wall cues.

a, Schematic of how across scene covariance was determined. Screenshots of the virtual scene were taken at every 10 cm for the range of possible wall, tower, and background morph parameter settings. Translation invariant representations of these VR scenes were acquired by calculating the two-dimensional Fast Fourier Transform (FFT) of every screenshot on each color channel (RGB). Discarding phase information, we took the power spectrum for each channel and each screenshot. We flattened each of the FFT power spectrums into a column vector. Column vectors for every color channel and every position along the track were concatenated for a given morph parameter setting. This procedure gives one column vector for each morph parameter setting. We then horizontally stacked these column vectors for each morph parameter setting to give a matrix that we used to calculate a morph by morph covariance matrix. We then performed Principal Components Analysis (PCA) on this matrix. b, The eigenvalues of the morph by morph covariance matrix are plotted. c, The projection of each morph parameter setting onto the first principal component (PC1) from (a) plotted as a function of the wall morph value ($\tilde{S}$ + wall jitter)(left vertical axis, blue points). The horizontal component of the frequency of the wall cues, f_h, is also plotted (right vertical axis, red points). d, The projection of each morph parameter setting onto PC1 is plotted as a function of wall morph value (left vertical axis, blue points). The vertical component of the frequency of the wall cues, f_v, is also shown (right vertical axis, red points). e, The projection of each morph parameter setting onto PC1 is plotted as a function of tower morph value ($\tilde{S}$+ tower jitter)(left vertical axis, blue points). The normalized blue color channel pixel value of the towers is also plotted (right vertical axis, red points). The normalized green color channel pixel value of the tower is one minus the blue color channel. f, The projection onto PC1 is plotted as a function of background morph value ($\tilde{S}$+ background jitter). The normalized background color pixel intensity is also plotted (right vertical axis, red points). g, The log of the mean squared error (log(MSE)) of a linear regression to predict the projection of morph parameter settings onto PC1 is plotted for models using different sets of predictors. The ‘all’ model uses f_h, f_v, background pixel value (b), tower blue pixel value (t), and the angle of the wall cues (angle) as predictors of the projection onto PC1. The failure of this model is likely due to the strong correlation among stimulus values. Every other model uses only a single aspect of the stimulus to predict the projection onto PC1. The horizontal component of wall frequency, f_h, is the strongest predictor of the projection onto PC1. h, Ideal rare morph log posterior distribution as plotted Fig. 1f. i. Ideal frequent morph log posterior distribution as plotted Fig. 1f.

Extended Data Fig. 3 ∣. Remapping patterns for a simulated population designed to stochastically encode the posterior distribution reproduces our recorded remapping patterns.

a, Schematic for model of a ‘neural posterior’. Left: As the animal runs down the track, it tries to infer the identity of the environment it is occupying. The probability of the environment is given by the posterior distribution. Right: We assume that the activity of the neurons we are observing is governed by radial basis function tuning curves for distinct values of the inferred stimulus. b, Process for generating activity. Left: As the animal runs down the track, a process generates several random samples from the posterior distribution. Middle: Each of these samples is filtered through the deterministic neural tuning curves shown in (a). Right: Cellular activity rates are generated by a gamma process with parameters determined by the neural activation. Gamma processes were chosen, as calcium activity rate is a continuous variable. Mean and variance of gamma processes were chosen to be identical so they were more Poisson-like. c, Left: The ideal rare morph posterior distribution as plotted in Fig. 1f (top right) and elsewhere. Right: The activity of a simulated population that encodes samples from the rare morph posterior is shown for different f_h values. Each row of the heat map is the activity of a single cell sorted by the f_h values for which it has peak selectivity. Each column is the value of f_h used to generate a draw from the posterior distribution. Color (white to purple) indicates the average activity of the cell across 1000 draws from the posterior distribution. Yellow points show the index in the population that has the highest average activity rate. Maroon points indicate the ideal rare morph MAP estimates as in left. Note the similarity between the ideal posterior distribution (left) and the activity of the population designed to encode it (right). d, Same as (c) for simulations using the ideal frequent morph posterior distribution. e, Example trial by trial similarity matrices for simulated populations encoding the rare morph posterior. f, Same as (e) for simulated populations encoding the frequent morph posterior. g, Average rare morph trial x trial similarity matrix (n = 1,000 simulations). h, Average frequent morph trial x trial similarity matrix (n = 1,000 simulations). i, Difference in mean trial x trial similarity matrices (rare [g] - frequent [h]). j, Same as (i) but similarity matrices are z-scored prior to averaging (diagonal elements excluded).

Extended Data Fig. 4 ∣. Analysis of place cells with place fields in both S~=0 and S~=1 environments, and analysis of posterior distribution entropy.

a, Fraction of cells classified as place cells in the $\tilde{S}=0$ trials (magenta), $\tilde{S}=1$ trials (cyan), and both $\tilde{S}=0$ and $\tilde{S}=1$ trials (intersection of the sets of cells; navy). The number of cells expected to be classified as place cells in both environments if cells were chosen randomly with replacement is also shown (red). b, For cells that were classified as place cells in both $\tilde{S}=0$ and $\tilde{S}=1$ trials (n = 2,219 cells) in rare morph animals, we plotted the location of peak activity for $\tilde{S}=0$ trials against the location of peak activity for $\tilde{S}=1$ trials. Marginal histograms are shown for occupancy of position bins in the $\tilde{S}=0$ trials (bottom) and $\tilde{S}=1$ trials (right). Shaded regions indicate possible reward locations. c, Same as (b) for all frequent morph animals (n = 594 cells). d, Same as Fig. 2b (rare morph condition) but only cells that had place fields in both $\tilde{S}=0$ and $\tilde{S}=1$ trials are plotted (n = 2,219 cells). e, Same as Fig. 2d (frequent morph condition) but only cells that had place fields in both $\tilde{S}=0$ and $\tilde{S}=1$ trials are plotted (n = 594 cells). f, Example posterior distributions (rare morph-maroon, frequent morph-blue) for different values of ${\widehat{f}}_h$ (that is columns of Fig. 1f). g, Entropy of the posterior distribution as a function of ${\widehat{f}}_h$ (rare morph-maroon, frequent morph-blue).

Extended Data Fig. 5 ∣. Unsupervised confirmation of discrete vs continuous remapping.

a, Schematic of nonlinear dimensionality reduction. Morph-binned spatial activity rate maps were generated for cells with significantly different activity rate maps between $\tilde{S}=0$ and $\tilde{S}=1$. Morph by position maps were flattened and then stacked to form a cells x (position bins*morph bins) matrix. We performed UMAP dimensionality reduction on this matrix. This produces an embedding space for plotting individual cells. In this space, cells with similar activity rate maps are close together, and cells with dissimilar activity rates are further apart, b, Three-dimensional embedding given by UMAP colored by different experimentally relevant variables. Top Left: Cells/points are colored by the morph value for which their activity is the highest (color bar right). Top Right: Cells/points are colored by their position of peak activity (color bar right). Bottom Left: Cells/points are colored by whether they came from the rare morph condition (orange) or frequent morph condition (blue). Bottom Right: Density based clustering was performed to separate the two main manifolds. K-means clustering was performed on each of the manifolds (10 clusters per manifold, 20 total clusters [numbered on plot], colors correspond to different clusters). c, Decoding performance (logistic regression) for classifying cells as coming from the rare morph or frequent morph condition for each cluster from the S = 0 manifold (magenta, Top) or from the S = 1manifold (cyan, Bottom). Classification accuracy is plotted as a function of the spatial preference of that cluster. Grey shaded region indicates the range of chance performance by permutation test (n = 1,000 permutations). Red shaded regions highlight reward locations d, Average remapping patterns for rare and frequent morph cells within an example cluster (b, lower right). For each cluster, we give the rare vs. frequent classification accuracy. For each example cluster, we plot the cell averaged morph-binned activity rate map for rare morph (first column, top) and frequent morph (second column, top) cells as well as the associated cosine similarity matrix (bottom). Third column shows the difference between the first and second column (Rare-Freq.). Black arrows indicate S = 0.25–.5 region where magnitude of difference is expected to be the largest.

Extended Data Fig. 6 ∣. Nonnegative matrix factorization on population of single cell trial by trial similarity matrices confirms discrete (rare morph) versus continuous remapping (frequent morph).

a, Schematic for how Nonnegative Matrix Factorization (NMF) was performed. For each cell within an imaging session, we flattened the upper triangle of its trial by trial similarity matrix (as seen in Fig. 1g,i) to form a vector. These vectors were then stacked to form a Neurons × (Trials * (Trials – 1)/2) matrix, X. NMF was then performed on this matrix yielding a factors matrix, H^T, and a loadings matrix, W. The rows of H^T can be reshaped into ‘prototypical similarity matrices’. b, NMF factors for rank three models for example rare morph sessions from each rare morph mouse. Color coding indicates maximum (yellow) and minimum (blue) values. c, Same as (b) for example sessions from each frequent morph mouse.

Extended Data Fig. 7 ∣. Population similarity analyses from every rare morph session and mouse.

The animal from which data is derived is shown in large bold text above (for example R1). For each animal, each row of plots indicates data from a single session sorted by increasing session number. Session 3 data is included for all animals except R6. Left: Trial by trial population similarity matrices are shown, sorted by morph value (lower plot), as in Fig. 3a. Right: Q estimates (estimates of $P(f_h\mid {\widehat{f}}_h)$) for given session. ΔD_KL value is given for each session.

Extended Data Fig. 8 ∣. Population similarity analyses from every frequent morph session and mouse.

The animal from which data is derived is shown in large bold text above (for example F1). For each animal, each row of plots indicates data from a single session sorted by increasing session number. Session 3 data is included for all animals. Left: Trial by trial population similarity matrices are shown, sorted by morph value (lower plot), as in Fig. 3a. Right: Q estimates (estimates of $P(f_h\mid {\widehat{f}}_h)$) for given session. ΔD_KL value is given for each session.

Extended Data Fig. 9 ∣. Session 3 remapping patterns are consistent with later session remapping in the majority of animals, and results are poorly fit by null posterior distributions.

a, Left Column: Trial by trial similarity matrices for session 3 from two rare morph mice (R3-1,973, 90 trials; R4-922 cells, 60 trials). Trials sorted by increasing morph value. Right column: Q estimates for example sessions. b, Same as (a) for example frequent morph sessions (F6, 3,657 neurons, 100 trials; F3, 295 cells, 120 trials). c, ΔD_KL for each rare morph mouse plotted as a function of session number. Session 3 data unavailable for R6. d, Same as (c) for frequent morph animals. e, Q estimate for accumulated session 3 data across rare morph mice, f, Same as (e) for frequent morph mice, g-h, Reconstructed prior distributions for rare (g) and frequent (h) morph mice using session 3 data alone. Average rare (maroon) and frequent (blue) morph prior are shown. i, Relative distance of reconstructed priors to ideal priors, ΔD_KL, for each mouse (rare mice-left; frequent mice-right). j, Top: Prior distributions for additional models tested for comparison with Q estimates. Bottom: Associated posterior distributions for each prior. We additionally compared Q estimates to a uniform posterior ($P\left(f_h\mid \widehat{S}\right)=c$, where c is a constant). k, Left: Kullback-Leibler divergence (D_KL) between each posterior in (j) and the Q estimate. Points are colored by mouse ID. Thick maroon line indicates the across session average. (***) indicate significant differences in D_KL with the rare morph D_KL values (Wilcoxon signed-rank test, n = 24 sessions; frequent, p = 2.3 × 10⁻⁴; uniform, p = 4.7 × 10⁻⁴; Gaussian, p = 1.8 × 10⁻⁵; multimodal, p = 1.8 × 10⁻⁵; uniform posterior, p = 1.82 × 10⁻⁵). Right: D_KL between reconstructed prior and different priors shown in (j). I, Same as (k) for frequent morph sessions. Left: Thick blue line indicates across session average. Wilcoxon signed rank tests compare D_KL for the frequent morph condition to D_KL for all other posteriors in (j) (Wilcoxon signed-rank test, n = 21 sessions; rare, p = 6.0 × 10⁻⁵; uniform, p = 0.019; Gaussian, p = 6.0 × 10⁻⁵; multimodal, p = 6.0 × 10⁻⁵; uniform posterior, p = 6.0 × 10⁻⁵).

Extended Data Fig. 10 ∣. Requiring frequent morph animals to behaviorally categorize morph values does not change neural context discrimination.

a, Stimulus design, as in Fig. 1b, for frequent morph trained animals that had to behaviorally categorize morph values (frequent morph with decision, n = 4 animals, FD1-FD4). A side view of a subset of VR tracks with different morph values (S) are shown. Vertical location indicates approximate morph value for the track shown (color bar to the right of tracks). For trials where S ≤ 0.5, animals had to lick within a 65 cm region surrounding the third tower (polka dot tower, magenta highlighted region). For trials where S > 0.5, animals had to lick within a 65 cm region surrounding the fourth tower (hatched pattern tower, cyan highlighted region). For one animal (FD1), we added punishments for licking in the incorrect reward zone after session 3. If the animal licked in the incorrect reward zone, it was instantly teleported to a dark hallway for 10 seconds before being able to begin the next trial. b, Left: Lick rate as a function of position for each trial as in Extended Data Fig. 1c,d for an example session (FD1, session 13, n = 120 trials). Red dots indicate error. Color indicates morph value of the trial. Shaded regions indicate reward zones as in (a). Right: Trials are sorted by increasing morph value c, For mice that did not receive timeouts for incorrect licks (n = 3, FD2-4), we plot the across mouse average normalized lick rate (normalization as in Extended Data Fig. 1) as a function of position (across mouse mean ± SEM) for binned morph values ($\tilde{S}=0$, 0.25, 0.5, 0.75, 1). d. Far Left: Trial by trial cosine similarity matrix sorted by increasing morph value for an example session from the mouse that experienced timeouts (FD1, session 13; 120 trials, 1451 cells). Middle Left: Projection of single trials onto the principal two eigenvectors of the similarity matrix. Color indicates morph value. Middle Right: Similarity Fraction, SF, as a function of position as in Fig. 3f. Color indicates morph value. Far Right: Q estimates. e, Same as (d) for an example session from an animal that did not receive timeouts for incorrect licks (FD4, session 12; 100 trials, 924 cells). f, Q estimate using pooled data across all FD mice. g, Background heatmap is the ideal frequent morph posterior distribution. Blue scatterplot points are the MAP estimate from this ideal posterior. Remaining overlaid scatterplot is the linearly transformed SF(f_h) values for every trial and every mouse (N = 2,460 trials). Colors indicate mouse ID. h, Reconstructed prior distributions for each FD mouse. Maroon thick plot indicates ideal rare morph prior, blue thick plot indicates ideal frequent morph prior, thinner lines indicate individual mouse reconstructions. Colors indicate mouse ID as in (g).

Fig. 1 ∣. VR setup for imaging CA1 neurons and the construction of priors for rare morph versus frequent morph conditions.

a, Top view (left) and side view (right) of the VR setup, b, Example FOV from an imaging session (mouse F2, session 12; λ = 920 nm) with identified CA1 neurons highlighted (n = 2,006 cells). Inset shows coronal histology for the same animal (green, GCaMP; blue, DAPI (4,6-diamidino-2-phenylindole)). c, The stimulus desig,n with example linear tracks for different morph (S) values (the color bar on the far right indicates S value). Left: side view of VR tracks; the red bar indicates a random reward zone (250–400 cm). Right: view from the perspective of the mouse. d, Illustration of the training protocol for the rare morph (top; n = 6 mice, R1–R6) and the frequent morph (bottom; n = 6 mice, F1–F6) conditions. Imaging was performed on sessions 1, 3 and 8–N (Extended Data Fig. 2f,g). For the rare morph condition, only extreme morph values were shown during trials before imaging begins (pre-) and after imaging ends (post-). For the frequent morph condition, intermediate morph values were shown on each session. Note that for a given trial, morph values were randomly interleaved according to the training condition, e, Left: the empirical prior distribution over the morph values, P(S), at the beginning of session 8 for mice in the rare morph group (top; R1–R6) and the frequent morph group (bottom; F1–F6). Colors indicate mouse ID. Right: same as the left, but after converting morph values to horizontal wall frequency f_h (cycles per 500 cm). f, Heatmap of the probability mass function of the posterior probability for each value of $\widehat{S}$ (left) and ${\widehat{f}}_{\mathrm{h}}$ (right). MAP estimates are plotted as maroon (rare; top) or blue (frequent; bottom) points. Note that if CA1 population activity approximates this form of probabilistic inference, the population activity in the rare morph condition will change abruptly when S is between 0.25 and 0.5 (as indicated by the red arrow). Rare morph and frequent morph activity could appear largely similar outside this range of stimuli.

Fig. 2 ∣. Prior experience of stimulus frequency determines CA1 place cell remapping.

a, Top row: co-recorded place cells from an example rare morph session (mouse R2, session 8). Columns show heatmaps from different cells, with each row indicating the activity of that cell on a single trial as a function of the position of the mouse on the VR track (n = 120 trials). Rows are sorted by increasing morph value. The color indicates the deconvolved activity rate normalized by the overall mean activity rate for the cell (Norm. activity rate). Bottom row: trial-by-trial cosine similarity (Cos. sim.) matrices for the corresponding cell above, color coded for maximum (yellow) and minimum (blue) values. b, First row: for all rare morph sessions 8–N, place cells (PCs) were identified in the $\tilde{S}=0$ morph trials and sorted by their location of peak activity on odd-numbered trials. The average activity on even-numbered trials is then plotted (left-most panel). Each row indicates the activity rate of a single cell as a function of position, averaged over even-numbered $\tilde{S}=0$ morph trials. The color indicates the activity rate normalized by the peak rate from the odd-numbered $\tilde{S}=0$ average activity rate map for that cell. The trial-averaged activity rate map for these cells is then plotted for the other binned morph values using the same sorting and normalization process (remaining panels to the right). Second to fifth rows: same as the top row for the same rare morph sessions, but for place cells identified in the $\tilde{S}=0.25$ (second row), $\tilde{S}=0.50$ (third row), $\tilde{S}=0.75$ (fourth row) and $\tilde{S}=1.0$ (fifth row) morph trials. For each row, cells are sorted and normalized across all panels according to the place cells identified in the respective morph trial, c, Same as in a, but for an example frequent morph session (mouse F4, session 8, n = 75 trials). d, Same as in b, but for all frequent morph sessions 8–N. e, Average cosine similarity matrix for the union of all rare morph place cells in b. f, Average cosine similarity matrix for the union of all frequent morph cells in d. g, Rare morph cosine similarity matrix, from e, minus the frequent morph cosine similarity matrix from f (asterisks indicate significance based on a permutation test of mice across conditions, P < 0.05, two-sided). h, Same as g, but the cosine similarity matrix for each cell is z-scored before group comparisons (asterisks indicate significance based on a permutation test of mice across conditions, P < 0.0011, two-sided).

Fig. 3 ∣. Population similarity analyses reveal distinct remapping patterns visible at the level of single trials.

a, Data for an example session from each mouse in the rare morph condition. The left panels show population trial-by-trial cosine similarity matrices for example rare morph sessions, color coded for maximum (black) and minimum (white) values. The number of cells imaged in the example sessions is denoted on the right. The color and the height on the vertical axis of the scatterplots below indicate the morph value, with trials sorted in ascending morph value as indicated by the color bar. Note that this is not the order in which trials were presented. The right panels show projections of the activity of each trial onto the principal two eigenvectors (Eig vec 1 and 2) of the similarity matrix. Each dot indicates one trial, colored by morph value. b, Same as in a, but for an example session from each mouse in the frequent morph condition. All individual sessions from all mice are shown in Extended Data Figs. 7 and 8. c, Population similarity matrices were binned across morph values (diagonal entries of the original matrix excluded) and averaged across sessions within animals and then across animals for all rare morph sessions 8–N (R1–R6 mice, n = 24 sessions). d, Same as c, but for all frequent morph sessions 8–N (F1–F6 mice, n = 21 sessions). e, The difference between the average rare morph and frequent morph (c) trial-by-trial similarity matrices. f, Same as e, but after the binned trial-by-trial similarity matrix for each session is z-scored (asterisks indicate significant differences, P < 0.05, mouse permutation test, two-sided).

Fig. 4 ∣. CA1 representations show stable discrimination of morph values along the length of the track.

a, Schematic of how the SF is calculated. Each dimension indicates the activity of a single neuron at a single position bin. For the left panels in b and c, only one position bin is included in the calculation at a time. The $\tilde{S}=0$ centroid is calculated by averaging the population vector for all $\tilde{S}=0$ trials (magenta dot). Likewise, the $\tilde{S}=1$ centroid is calculated by averaging the vector for all $\tilde{S}=1$ trials (cyan dot). b, Data for an example session from all mice in the rare morph condition. Left panels show the SF plotted as a function of the position of the animal on the track for each trial in an example rare morph session (for example, mouse R3, session 9; 976 cells, 120 trials). Each line represents a single trial, and the color code indicates the morph value (color bar in a). Right panels show the SF(f_h) plotted (black dots, left vertical axis) as a function of f_h for the same example session shown on the left. Each dot represents a single trial, c, Same as b, but for an example session from all mice in the frequent morph condition. All individual sessions from all are mice shown in Extended Data Figs. 7 and 8. d, Average SF by position plot across rare morph sessions (8–N) and animals (R1–R6). Shaded regions represent across-animal means for binned morph values ($\tilde{S}=0$, 0.25, 0.50, 0.75 and 1.0) ± s.e.m. across mice. Note that the data for morph values 0.75 and 1.0 are nearly overlapping, e, Same as d, but for all frequent morph sessions (8–N, F1–F6 mice, n = 19 sessions). Note that the data for morph values 0.5, 0.75 and 1.0 are partially overlapping.

Fig. 5 ∣. CA1 hippocampal remapping approximates the optimal estimation of the stimulus.

a, Schematic for calculating $P\left(f_{\mathrm{h}}\mid {\widehat{f}}_{\mathrm{h}}\right)\approx P(\alpha \text{SF}(f_{\mathrm{h}})+\beta =f_{\mathrm{h}})=Q$ estimates. Left: ideal posterior distribution for the rare morph prior as in Fig. 1f. Middle: SF(f_h) plotted (black dots, left vertical axis) for an example rare morph session (top; R3, session 11; 932 cells, 120 trials). The MAP estimates as a function of f_h are plotted for the rare morph (maroon dots, right vertical axis) and frequent morph (blue dots, right vertical axis) conditions. The red circled regions indicate the $\tilde{S}=0$ and $\tilde{S}=1.0$ trials used to estimate the affine transform for forming Q estimates. Right: example from the middle column after affine transform. To perform the affine transform, we stretched and shifted the range of SF(f_h) values (black dots) in the direction of the red arrows (middle panel) to match the range of the MAP estimates as a function f_h (maroon dots for the rare morph condition or blue dots for the frequent morph condition). Q estimates were then formed by kernel density estimation. b, Same as a, but for the ideal posterior distribution for the frequent morph prior (left) and an example frequent morph session (F2, session 11; 2,006 cells, 85 trials). c, Q estimates for an example session from each mouse in the rare morph condition. d, Same as c, but for an example session from each mouse in the frequent morph condition. All individual sessions from all mice are shown in Extended Data Figs. 7 and 8.

Fig. 6 ∣. Individual animal prior distributions can be recovered solely from remapping patterns.

a, Relative distances of the Q estimates for each session to the ideal rare morph and frequent morph posteriors, ΔD_KL. Each dot represents an individual session. The mouse ID is on the horizontal axis. Jitters were added to the horizontal location for visibility. b, Left: Q estimate achieved by averaging and re-normalizing the across-session Q estimate for each mouse. Middle left: the background heatmap is the ideal rare morph posterior distribution. The maroon scatterplot points are the MAP estimate from this ideal posterior. The remaining points are the linearly transformed SF(f_h) values (as in Fig. 5a, rightmost panel) for every trial and every mouse (n = 2,610 trials). Colors indicate the mouse ID. Middle right: same transformed SF data as in the middle left, but plotted with the ideal frequent morph posterior (heatmap) and MAP estimates (blue scatterplot). The black arrow indicates a mismatch between the transformed SF(f_h) values and the ideal posterior. Right: ideal rare morph prior distribution (maroon), ideal frequent morph prior distribution (blue) and the reconstructed prior for each rare morph mouse (colors indicate mouse the ID). Note that this is the unsupervised recovery of the priors. c, Same as b, but for accumulated data from all mice in the frequent morph group (n = 1,986 trials). d, Relative distances of reconstructed priors (left: rare morph mice; right: frequent morph mice) to either ideal prior, ΔD_KL.

Fig. 7 ∣. Neural context discrimination is well explained by associative-learning models.

a, Schematic of the computational model. The input layer contains neurons that form a basis for representing the stimulus using radial basis functions. Activations are linearly combined via the matrix W, and thresholding is applied to the output layer via a KWTA mechanism to achieve the output activation. W is updated after each stimulus presentation using Hebbian learning. Model training is performed by drawing trials randomly from either the rare morph prior or the frequent morph prior. b, Left: trial-by-trial similarity matrix, as in Fig. 3a, for an example model trained under the rare morph condition. Right: same as the left, but for an example model trained under the frequent morph condition. c, Average trial-by-trial similarity matrices across model instantiations (n = 50) for rare morph (left) and frequent morph (right) trained models. d, Left: the average rare morph similarity matrix minus the average frequent morph similarity matrix. Right: same as the left, but the similarity matrix for each model is z-scored before averaging. e, Q estimates for accumulated rare morph trained models (left) and frequent morph models (right). f, Smoothed histogram of ΔD_KL values for rare morph (maroon) and frequent morph (blue) trained models. Red line indicates zero. g, Reconstructed priors for rare morph (top, black, mean ±s.e.m.) and frequent morph (bottom, black, mean ±s.e.m.) trained models. Note that this is the unsupervised recovery of the priors. Ideal rare morph (maroon) and frequent morph (blue) priors are shown for reference. ΔD_KL is for the averaged reconstructed prior.