Abstract
Noise correlations (that is, trialtotrial covariations in neural activity for a given stimulus) limit the stimulus information encoded by neural populations, leading to the widely held prediction that they impair perceptual discrimination behaviors. However, this prediction neglects the effects of correlations on information readout. We studied how correlations affect both encoding and readout of sensory information. We analyzed calcium imaging data from mouse posterior parietal cortex during two perceptual discrimination tasks. Correlations reduced the encoded stimulus information, but, seemingly paradoxically, were higher when mice made correct rather than incorrect choices. Singletrial behavioral choices depended not only on the stimulus information encoded by the whole population, but unexpectedly also on the consistency of information across neurons and time. Because correlations increased information consistency, they enhanced the conversion of sensory information into behavioral choices, overcoming their detrimental informationlimiting effects. Thus, correlations in association cortex can benefit task performance even if they decrease sensory information.
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Data availability
The sound localization task data that support the findings of the current study can be downloaded at https://gin.gnode.org/MMoroni/PPC_AC_2p_sound_localization/ (ref. ^{44}).
The evidence accumulation task data that support the findings of the current study can be downloaded at https://gin.gnode.org/MMoroni/PPC_2p_evidence_accumulation/ (ref. ^{43}).
Code availability
The code for the biophysical information transmission model (Fig. 6) is available for download at https://github.com/gbondanelli/BiophysicalReadout/.
The code for the encoding and readout model (Figs. 2 and 3) is available for download at https://github.com/moni90/encoding_readout_model/.
The code for data analysis is available from the corresponding authors upon reasonable request.
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Acknowledgements
We thank E. Piasini for early contributions; members of our laboratories for helpful discussions; G. Iurilli, C. Kayser, E. Piasini, C. Becchio and J. Drugowitsch for feedback; and M. Libera for technical support. This work was supported by National Institute of Health grants from the NIMH BRAINS program R01 MH107620 (to C.D.H.), NINDS R01 NS089521 (to C.D.H.), the BRAIN Initiative R01 NS108410 (to C.D.H. and S.P.) and U19 NS107464 (to S.P.) and the Fondation Bertarelli (S.P).
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S.P. and C.D.H. conceived, designed and supervised the study. C.A.R. and A.S.M. acquired the experimental data. M.V., G.P., G.B. and M.M. performed computations. S.P., C.D.H., M.V., G.P., G.B. and M.M. wrote the paper, with feedback from all authors.
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Peer review information Nature Neuroscience thanks Yong Gu, Joel Zylberberg, and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.
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Extended data
Extended Data Fig. 1 Response properties and acrosstime and acrossneuron correlations in PPC during perceptual discrimination tasks for different trials categories.
Panels al refer to PPC data during the sound localization task and acrosstime correlations. ac, Accuracy of a linear decoder of the stimulus applied to the joint population activity at two different time points, for recorded (black) or trialshuffled (gray) population vectors, for ‘easy’ trials with high level of sensory evidence (a, sound locations further from the midline than 45 deg), ‘difficult’ trials with low level of sensory evidence (b, sound locations closer to the midline than 45 deg) and behaviorally correct trials only (c). Errorbars report mean ± SEM across n = 6 sessions and all time point pairs within the specified lag range. For all comparisons, P = 10^{−4}, twosided permutation test. df, Distribution of the signalnoise angle γ (over n = 6 sessions and all time point pairs within a 2 s lag), for ‘easy’ trials (d), ‘difficult’ trials (e) and behaviorally correct trials only (f). Boxplots show the median (line), quartiles (box) and whiskers extend to ±1.5*interquartile range. Red dotted line: theoretical value of the critical angle γ_{C} between the informationlimiting and informationenhancing regime. gh, Pairwise noise correlations in timelagged activity, for correct and error trials, for ‘easy’ (g) and ‘difficult’ (h) trials. Errorbars report mean ± SEM across n = 6 sessions, all time point pairs within the specified lag range and all cell pairs. For all comparisons, P = 10^{−4}, twosided permutation test. ij, Populationwise noise correlations in timelagged activity, for correct and error trials, for ‘easy’ (i) and ‘difficult’ (j) trials. Errorbars report mean ± SEM across n = 6 sessions and all time point pairs within the specified lag. In i, P = 0.0380 for Lag 01 s, n.s. P = 0.1510 for Lag 12 s, twosided permutation test. In j, P = 0.0480 for Lag 01 s, P = 0.001 for Lag 12 s, twosided permutation test. k, Relation between pairwise and populationwise noise correlations. Each dot represents the average across n = 6 session and all time points with a given lag. The black line indicates the linear fit. l, Accuracy of a linear, quadratic and radial basis function SVM decoder of stimulus identity applied to joint population activity at two different time points for real recorded population vectors. Errorbars report mean ± SEM across n = 6 sessions and all time point pairs within the specified lag range. Panels mx refer to PPC data during the evidence accumulation task and acrossneuron correlations. mo, Same as in ac. pr, Same as in df. st, Same as in gh. uv, Same as in ij. For the evidence accumulation task, ‘easy’ and ‘difficult’ trials were defined as trials with net evidence ≥4 or <4 respectively. In panels mv errorbars report mean ± SEM across n = 11 sessions, Early and Late Delay epochs and 100 pairs of neuronal pools. In mo, for all comparisons, P = 10^{−4}. In s, P = 0.0120. In t, P = 9 × 10^{−4}. In u, P = 0.001. In v, P = 0.8641. For all comparisons, twosided permutation test. w, Same as in k. Each dot represents the average across n = 11 sessions for a given delay epoch. x, Same as in l, with errorbars reporting mean ± SEM across all n = 11 sessions, Early and Late Delay epochs, and 100 pairs of randomly split neuronal pools.
Extended Data Fig. 2 Parameter exploration of the twopools encodingreadout model and comparison with PPC data.
a, Populationwise noise correlations ν as a function of the pairwise noise correlations ρ, for different values of the active neurons 2N (N neurons per pool). Here we assumed that all neurons were active (M = 2N). For ρ = 0, the populationwise correlation is equal to ν = 1/(2N) b, Populationwise noise correlations ν as a function of the average over all pairs of pairwise noise correlations ρ (where · denotes the average over neuron pairs), for different fraction of active neurons 2N/M (total number of neurons given by M = 2N + K). By decreasing the fraction of active neurons, the constant of proportionality between ν and ρ increases. c, Blue line: critical signalnoise angle γ_{C} below which correlations are informationlimiting in the model, as a function of the number of neurons per pool N, computed using the experimental value of the PPC acrosstime populationwise correlation for the sound localization task. Red line: critical value γ_{C,BP} for the angle above which the task performance in correlated data is higher than that in shuffled data. The experimental distribution of PPC signalnoise angles is reported for comparison (n = 6 sessions and all time point pairs within a 2 s lag). Horizontal gray line indicates the median. Box edges indicate the first and third quartile. d, Same as c for the evidence accumulation task and acrossneuron PPC correlations.
Extended Data Fig. 3 Extension of the encoding readout model to multiple features, multiple stimuli per category and multiple categories.
a, Left: schematic of the encoding readout models with two neural features, two categories, two stimuli per category. Each axis represents the activity of a single feature. Colored ellipses: 95% confidence intervals for the simulated neural responses to two different stimuli (s=1, s=1). Dashed black line: stimulus axis. Gray shaded areas: regions of the response space in which stimulus information is encoded consistently across pools and the behavioral readout efficacy is enhanced. b, Difference in stimulus classification accuracy between correlated and shuffled responses computed using a linear decoder applied to the joint population activity across the two features, as a function of the signalnoise angle γ. c, Difference in task performance between correlated and shuffled responses predicted by an enhancedbyconsistency readout of simulated neural activity, as a function of the signalnoise angle γ. In panel bc, the red dashed lines delimit the parameter range where correlations are informationlimiting but task performance is enhanced for correlated data. Data are mean ± SEM over n = 10 simulations with 50,000 trials each, with \(d = \sqrt {0.02}\), ρ = 0.8, σ = 0.2, η = = 0.7. df, Same as in ac, but for an encoding model with two neural features, two categories, and multiple (n = 2) stimuli per category. Within each category, stimulusspecific distributions are symmetrically displaced on either side of the betweencategory signal axis. Within each category, the noise axes of the individual distributions are aligned to each other and aligned to the vector of differences of mean activity. Data are mean ± SEM over n = 10 simulations with 50,000 trials each. We set half the distance between the centers of the distributions of the two categories to \(d = \sqrt {0.02}\), and the distance between the centers of the distributions of individual stimuli within each category to d_{2} = 03. In simulations, we set ρ = 0.8, σ = 0.13 (for the distributions of individual stimuli within each category), η = 0.7. gi, Same as in ac, but for an encoding readout model with two pools and multiple (n = 3) stimulus categories. Mean responses to the three stimulus categories are aligned along a unique signal axis, and the noise axes of individual distributions form an angle γ with the stimulus axis. Data are mean ± SEM over n = 10 simulations with 50,000 trials each, with \(d = \sqrt {0.02}\) (distance between the distributions across individual categories), ρ = 0.8, σ = 0.2 (for individual distributions), η = 0.7. jl, Same as in ac, for a model with three onedimensional neural features. Neural activity is considered consistent if the same stimulus is decoded from all three features. Data are mean ± SEM over n = 10 simulations with 50,000 trials each, with \(d = \sqrt {0.02}\), ρ = 0.8, σ = 0.2, η = 0.7.
Extended Data Fig. 4 Exploration of the parameter space of the encoding readout model.
Same as in Fig. 3, for an encoding readout model with N = 10 neurons in each pool. a, Difference in the accuracy of a linear decoder of stimulus applied to correlated and shuffled simulated neural activity for different values of the signalnoise angle (γ) and populationwise correlations (ν). For all panels, black solid line: boundary between a regime with informationlimiting correlations and informationenhancing correlations. b, The difference between correlated and shuffled activity in the fraction of trials in which the two neural features encode consistent stimulus information is higher in the informationlimiting regime and increases with populationwise correlations strength. Panels ce refer to the consistencyindependent readout. cd, Difference in average pairwise correlations (c) and populationwise correlations (d) between trials with correct and incorrect predicted task performance for different combinations of model parameters. e, Difference in task performance predicted by applying the consistencyindependent readout to correlated and shuffled simulated neural activity for different combinations of model parameters. For panels ci, dashed black line: boundary between a regime where task performance is higher for correlated responses and a regime where performance is higher for shuffled responses. The overlap between the continuous and dashed black line indicates that correlations that limits information are also detrimental for behavior. Panel fh refer to the enhancedbyconsistency readout (consistency modulation index η = 0.85). fg, Same as in cd. With the enhancedbyconsistency readout correlations are higher in correct trials. h, Same as in e. The area between the dashed and the continuous black line indicates a regime where correlations are informationlimiting but task performance is higher for correlated responses. Thus, in the parameter range between the two lines, the readout is able overcoming the negative impact of correlations. Dark and light gray dots and ellipses: mean values and range between the 25^{th} and the 75^{th} percentile of the signalnoise angles and populationwise correlations for PPC data from the sound localization task and evidence accumulation task, respectively. i, Difference in task performance predicted by applying the enhancedbyconsistency readout or the consistencyindependent readout with matched readout efficacy for different combinations of model parameters. The enhancedbyconsistency readout yields increased task performance with respect to the consistencyindependent readout. Panels represent the mean over n = 100 simulations with 300,000 trials each.
Extended Data Fig. 5 The effect of neural correlations on the mouse’s single trial choices cannot be explained by higher stimulus information associated to consistent neural representations.
a, Schematic example showing response distributions along two neural features (r_{1}, r_{2}) to two stimuli (s = −1: blue, s = 1: orange). Black dashed line: optimal decoding boundary of a linear decoder trained on the simulated neural responses. The background color represents the linear decoder posterior probability that stimulus s=1 has occurred given the observation of the neural response r = (r_{1}, r_{2}). Intuitively, the farther neural response r is from the decoding boundary, the farther p(s = 1r) is from 0.5, and the more ‘informative’ r is about the stimulus. Note that, in the example shown, consistent trials have on average higher posterior probability than inconsistent trials, which might represent a confounder for the effect of consistency on mouse’s choices. To control for potential confounders due to differences in the levels of stimulus information between trials with consistent and inconsistent stimulus information, we fitted to the data a readout model that predicted choice using the posterior probability of the stimulus and posterior probabilities consistency given the neural responses, rather than just the decoded stimulus identity (b, f). We further repeated the analyses of Fig. 4 on trials partitioned into those with low (\(\left {p\left( {s = 1{\boldsymbol{r}}} \right)  0.5} \right < 0.16\)), medium (\(\left {p\left( {s = 1{\boldsymbol{r}}} \right)  0.5} \right > 0.16 \wedge \left {p\left( {s = 1{\boldsymbol{r}}} \right)  0.5} \right < 0.32\)), or high (\(\left {p\left( {s = 1{\boldsymbol{r}}} \right)  0.5} \right > 0.32\)) ‘stimulus information’ (ce, gi). Panels be refer to PPC data during the sound localization task. b, Performance (fraction of deviance explained) in explaining singletrial choice of models using neural predictors based on posterior probabilities. Full model includes all predictors values, comprising stimulus posterior probability and posterior probability consistency. No Cons model neglects neural consistency by shuffling consistency values across trials. ce, Left (purple dots). Task performance in trials with correctly decoded stimulus is higher when information is encoded consistently than inconsistently. Right (orange dots). The opposite happens for trials with incorrectly decoded stimulus. Thus, stimulus information in neural activity has a larger impact on choices when it is encoded consistently across time, even when subsets of trials having approximately the same posterior are used. For all comparisons in be, P = 10^{−4}, twosided permutation test. Errorbars represent mean ± SEM across n = 6 sessions and all time point pairs within a 1 s lag. Panels fi refer to PPC data during the evidence accumulation task. f, Same as in b. P = 6 × 10^{−4}, twosided permutation test g, Same as in c. h, Same as in d. i, Same as in j. In panels fi, consistency and mouse choices are computed from the activity of two pools of neurons. For all comparisons in gi, P = 10^{−4}, twosided permutation test. In fi, errorbars represent mean ± SEM across n = 11 sessions, Early and Late Delay epochs and 100 pairs of neuronal pools. From bi, the fact that information in neural activity informs choice more effectively when it is consistent cannot be explained by differences in overall stimulus information level. Rather, for a given amount of sensory information, more information can be extracted to guide behavioral choices if it is distributed redundantly across neurons or across time.
Extended Data Fig. 6 The role of neural consistency in the readout of PPC activity is not due to the consistency of measured behavioral parameters.
Panels ae refer to PPC neural activity during the sound localization task. To rule out the concern that the impact of acrosstime consistency of PPC activity on the mouse’s choice does not only reflect the effect of running related parameters (whose temporal consistency may correlate with both the mouse’s choice and the temporal consistency of neural activity), we developed and fit to PPC data a more sophisticated readout model that explicitly includes such contributions in predicting choices. a, The temporal evolution of the decoder posterior probability of left stimulus presentation given the recorded PPC population activity is shown along with the corresponding temporal evolution of a selection of three concurrentlymeasured behavioral parameters (lateral position, lateral velocity, view angle), for an example left (orange) and right (blue) cue trial. Colored dots indicate two example time point pairs with consistent (t_{1} − t_{2}, dark purple) or inconsistent (t_{3}t_{4}, light purple) neural information. Colored dots in the first and third row show that neural consistency is not necessarily associated to behavioral consistency (when considering lateral running speed, t_{1}t_{2} are behaviorally inconsistent while t_{3} − t_{4} are behaviorally consistent). b, Schematic representation of the virtual Tmaze with corresponding xy coordinates labelling and mouse’s view angle (for a mouse oriented along the y axis). ce, Performance (fraction of deviance explained) in explaining (using two population vectors at different points) singletrial mouse choice of models that use both neural and behavioral consistency (c: lateral position, d: lateral velocity, e: view angle). Full model includes all predictors values, comprising neural and behavioral consistency. No Cons model neglects neural consistency by shuffling consistency values across trials. c, P = 10^{−4}. d, P = 2 × 10^{−4}. e, P = 10^{−4}, twosided permutation test. Errorbars report mean ± SEM across n = 6 sessions and all pairs of time point within a 1 s lag. Results in ce show that neural consistency still contributed to predicting choices when we added the consistency of runningrelated variables to the choice regression. This suggests that consistency of the instantaneous PPC population activity across time genuinely influences the behavioral readout of the stimulus information, above and beyond what can be predicted about choice from the consistency of measured behavioral variables.
Extended Data Fig. 7 Acrosstime correlations in AC do not benefit task performance as they do in PPC.
Panels ah refer to PPC neural activity during the sound localization task. ah, Summary of the main results of the analysis of acrosstime correlations in PPC activity (from Fig. 1, Fig. 4 and Fig. 5), useful for the comparison with AC data. Panels ip refer to AC neural activity during the sound localization task. i, Pairwise (left) and populationwise (right) noise correlations in timelagged activity, for correct and error trials. Overall, noise correlations strength is lower in AC than in PPC. j, Distribution of the signalnoise angle γ (over n = 6 sessions and all time point pairs within a 2 s lag). Boxplots show the median (line), quartiles (box) and whiskers extend to ±1.5*interquartile range. Red dotted line: analytically computed bound between the informationlimiting and informationenhancing regime. k, Accuracy of a linear decoder of the stimulus applied to joint population activity at two different time points, for real recorded (black) or trialshuffled (gray) data. The decoder accuracy is higher in AC than in PPC (fraction correct: 0.676 ± 0.003 in AC, 0.602 ± 0.001 in PPC, P = 10^{−4}, twosided permutation test), compatible with the view that AC is involved in the encoding of sound information. Acrosstime correlations limit the encoding of stimulus information also in AC, but with a smaller effect than in PPC (average increase in decoder accuracy by shuffling: 0.018 ± 0.001 in AC, 0.026 ± 0.001 in PPC. P = 10^{−4}, twosided permutation test. Equivalent percentage increase of abovechance (that is above 50%) decoding performance: 10.5% in AC, 25.5% in PPC). l, Fraction of trials in which stimulus information is encoded consistently across time, for real recorded (black) or trialshuffled (gray) data. The increase in consistency due to acrosstime correlations is smaller in AC than in PPC (−0.025 ± 0.001 in AC, −0.064 ± 0.01 in PPC, P < 10^{−4}, twosided permutation test). m, Performance (fraction of deviance explained) in explaining singletrial choices of several readout models (see Methods). Full model uses all predictors (neural and nonneural). ‘No Cons’ model neglects neural consistency. ‘No Neural’ model neglects stimulus decoded from neural activity and neural consistency. A linear SVM is used to decode the stimulus from neural activity. Acrosstime consistency in AC provides negligible improvements in behavioral choice predictions when compared to PPC (increase in fraction of deviance explained when comparing the Full with the ‘No Cons’ model: 0.0045 ± 0.0001 in AC, 0.0083 ± 0.0012 in PPC, P = 10^{−4}, twosided permutation test). n, Bestfit coefficients of the Full readout model. AC neural predictors are characterized by low weights. o, Task performance predicted by applying the bestfit readout model to real recorded (black) or trialshuffled (gray) data. Task performance attributable to recorded neurons is much lower in AC than in PPC (~1% in AC, ~3.5% in PPC). Correlations in AC activity enhance task performance, but the effect is small. p, Task performance predicted by applying to real recorded population vectors the bestfit enhancedbyconsistency (black) and the consistencyindependent readout model (green). Task performance attributable to the recorded AC neural activity would not be substantially different if the behavioral readout was consistencyindependent. In i, k–p, errorbars report mean ± SEM across all cell pairs (only bleft) and all time point pairs within the specified lag range or within a 1 s lag from n = 6 sessions. For i, left, P = 10^{−4} for all comparisons, right, P = 0.0016 for lag 01 s, P = 0.001 for lag 1–2 s. For k, l, P = 10^{−4}. For m, ***P = 10^{−4}, *P = 0.0324. For o, P = 0.0191. For p, P = 0.0690. All comparisons, twosided permutation test.
Extended Data Fig. 8 Exploration of the parameters of the biophysical model for the enhancedbyconsistency readout.
a, Normalized coefficient of variation (CV) computed for different values of the membrane time constant τ_{m} of the readout neuron and EPSP strength w (connection strength from the input to the readout neuron). The mean input rate was set to R_{in} = 6 Hz. The red parameter region corresponds to the region where the standard deviation of the readout firing rate increases less than the readout mean firing rate with the value of spatial correlations. b, Contour lines corresponding to the parameter values (τ_{m}, w) where the normalized CV is equal to 1, for different values of the input firing rate. c, Contour lines for which the normalized CV is equal to unity, in the parameter space defined by the membrane time constant τ_{m} and the mean EPSP input in a window τ_{m} normalized by the voltage gap \({\Delta}V = V_{threshold}  V_r\), that is \(K = wR_{in}\tau _m/{\Delta}V\). Regions of parameters on the left of the contour lines correspond to the parameter values where the standard deviation of the readout neuron increases less than its mean with spatial correlations. d–f, Same as ac for temporal correlations.
Extended Data Fig. 9 Encoding model internally generating correlated activity through recurrent dynamics.
a, Schematic illustrating the basic setup of the encoding recurrent model. Two neurons receive stimulusdependent feedforward input (which determines the signal correlations) and input noise, and are connected through recurrent synapses with strength w. b, Noise correlations are generated through recurrent connectivity, and depend on the sign of w (for w = 0 responses are uncorrelated). Top: for positive signal correlations, positive (resp. negative) values of the connectivity generate informationlimiting (resp. informationenhancing) noise correlations. Bottom: for negative signal correlations, positive (resp. negative) values of the connectivity generate informationenhancing (resp. informationlimiting) noise correlations. cf, Average pairwise noise correlation (over n = 10000 random pairs of neurons) (c), decoding accuracy for correlated and shuffled responses (d), difference in decoding accuracy between correlated and shuffled responses for different values of shared noise (e) and average consistency (f) as a function of connectivity strength w. In c,d,f the external input noise is uncorrelated across the two neurons. g, Schematic illustrating the 2Ndimensional encoding recurrent model. Two Ndimensional neuronal groups with opposite stimulus selectivity receive stimulusdependent feedforward input and input noise. The connectivity strength is excitatory, sparse and takes the value w > 0 between neurons belonging to the same group, and η > 0 between neurons belonging to different groups. h, Example of a connectivity matrix adopted in these analyses. All matrix entries are positive (excitatory synapses) and sparse with connection probability p. il Same quantities computed in cf as a function of the difference between the withingroup connectivity and betweengroups connectivity strength, w − η. We set N = 50, p = 0.5, η = 0.5. In cf, il data are presented as mean ± SEM over n = 50 simulations.
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Valente, M., Pica, G., Bondanelli, G. et al. Correlations enhance the behavioral readout of neural population activity in association cortex. Nat Neurosci 24, 975–986 (2021). https://doi.org/10.1038/s41593021008451
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DOI: https://doi.org/10.1038/s41593021008451
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