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Logo of nihpaAbout Author manuscriptsSubmit a manuscriptHHS Public Access; Author Manuscript; Accepted for publication in peer reviewed journal;
Neuron. Author manuscript; available in PMC 2012 August 25.
Published in final edited form as:
PMCID: PMC3163063

Perceptual learning reduces interneuronal correlations in macaque visual cortex


Responses of neurons in early visual cortex change little with training, and appear insufficient to account for perceptual learning. Behavioral performance, however, relies on population activity, and the accuracy of a population code is constrained by correlated noise among neurons. We tested whether training changes interneuronal correlations in the dorsal medial superior temporal area, which is involved in multisensory heading perception. Pairs of single units were recorded simultaneously in two groups of subjects: animals trained extensively in a heading discrimination task, and “naïve” animals that performed a passive fixation task. Correlated noise was significantly weaker in trained versus naïve animals, which might be expected to improve coding efficiency. However, we show that the observed uniform reduction in noise correlations leads to little change in population coding efficiency when all neurons are decoded. Thus, global changes in correlated noise among sensory neurons may be insufficient to account for perceptual learning.


Perceptual learning enhances sensory perception and leads to improved behavioral performance (Goldstone, 1998), but the neural basis of this phenomenon remains incompletely understood. One hypothesis is that responses of sensory neurons are altered by learning to increase the information that is encoded. In this case, one would expect to observe neural correlates of increased sensitivity in early sensory areas. However, previous studies have found little or no change in the tuning properties of single neurons in early visual cortex, and it remains unclear whether these changes could account for perceptual learning (Chowdhury and DeAngelis, 2008; Crist et al., 2001; Ghose et al., 2002; Law and Gold, 2008; Raiguel et al., 2006; Schoups et al., 2001; Yang and Maunsell, 2004; Zohary et al., 1994a). Alternatively, perceptual learning may arise from changes in how sensory information is decoded and interpreted by higher brain areas (Dosher and Lu, 1999; Law and Gold, 2008; Li et al., 2004).

Most neurophysiological studies of perceptual learning focused on the activity of individual neurons; however, behavior arises from population activity. By pooling information from many cells, the noise inherent in responses of single neurons could be reduced, thus improving coding efficiency. Theorists have shown that the information capacity of a population code depends on the correlated noise among neurons (Abbott and Dayan, 1999; Averbeck et al., 2006; Oram et al., 1998; Sompolinsky et al., 2001; Wilke and Eurich, 2002). In general, correlated noise could either decrease or increase the information transmitted by a population of neurons, depending on how correlated noise varies with the similarity of tuning between neurons (‘signal correlations’; Averbeck et al., 2006; Oram et al., 1998; Wilke and Eurich, 2002). The impact of correlations could be strong when the relevant neuronal population is large (Bair et al., 2001; Shadlen et al., 1996; Smith and Kohn, 2008; Zohary et al., 1994b).

Whether perceptual learning improves population coding efficiency through changes in the correlated variability among sensory neurons remains unknown. Modest noise correlations have been measured in a number of cortical areas (V1: Bach and Kruger, 1986; Gutnisky and Dragoi, 2008; Poort and Roelfsema, 2009; Reich et al., 2001; Smith and Kohn, 2008) (but see Ecker et al., 2010) (V4: Cohen and Maunsell, 2009; Mitchell et al., 2009) (IT: Gawne et al., 1996; Gawne and Richmond, 1993) (MT: Cohen and Newsome, 2008; Huang and Lisberger, 2009; Zohary et al., 1994b), but how these correlations differ between untrained and trained animals has not, to our knowledge, been tested.

To examine the effect of training on correlated noise, we simultaneously recorded pairs of single neurons in the dorsal medial superior temporal area (MSTd), a multisensory area thought to be involved in heading perception based on optic flow and vestibular signals (Angelaki et al., 2009; Britten, 2008). Correlated noise among pairs of neurons was examined in two groups of animals: one group (‘naïve’) was only trained to fixate; the other group (‘trained’) also learned to perform a fine heading discrimination task. Noise correlations were significantly weaker in trained than naive animals, whereas tuning curves, response variability, and discrimination thresholds of individual neurons were similar. Importantly, training reduced noise correlations uniformly, regardless of tuning similarity between pairs of neurons. As a result, if all neurons contribute equally to perception, this change in correlated noise is unlikely to account for improvements in perceptual sensitivity with training.


Noise correlations in area MSTd

Monkeys were presented with two types of heading stimuli while maintaining fixation on a head-fixed target: inertial motion delivered by a motion platform in the absence of optic flow (vestibular condition) and optic flow stimuli presented while the animal was stationary (visual condition, see Methods for details). Consistent with previous findings (Gu et al., 2006; Takahashi et al., 2007), many MSTd neurons were tuned to heading direction, and their responses mainly followed the Gaussian velocity profile of the stimulus (Fig. 1A). We analyzed responses obtained during the middle 1 second of the stimulus period, during which neuronal activity was robust. Tuning curves of two simultaneously recorded cells are shown in Fig. 1B, C. The similarity of heading tuning between pairs of neurons was quantified as the Pearson correlation coefficient of mean responses across all stimulus directions (‘signal correlation’, rsignal). For this example pair of neurons, rsignal = 0.83 and 0.79 for the visual and vestibular conditions, respectively.

Figure 1
Measuring noise correlation (rnoise) between pairs of single neurons in area MSTd. (A) Response time courses for populations of neurons with significant tuning (p<0.05, ANOVA) in the visual (solid curve, n=231) and vestibular (dashed curve, n=118) ...

As in other cortical areas, the spike counts of MSTd neurons in response to an identical stimulus vary from trial to trial, as illustrated in Fig. 1D (visual condition) and Fig. 1E (vestibular condition). Each datum in these plots represents the spike counts of the two neurons from a single trial. Because heading direction varied across trials, spike counts from individual trials have been z-scored to remove the stimulus effect and allow pooling of data across directions (see Methods). ‘Noise correlation’ is then computed as the Pearson correlation coefficient of the normalized trial-by-trial spike counts, and reflects the degree of correlated variability across trials. For this example pair of cells, there was a weak positive correlation, such that when one neuron fired more spikes, the other neuron did as well (visual condition: rnoise = 0.29, p=0.04, Fig. 1D; vestibular condition: R=0.14, p=0.3, Fig. 1E).

We first examined whether correlated noise in MSTd depends on stimulus modality (Fig. 1F). Noise correlations computed from visual and vestibular responses were significantly correlated across 179 pairs of neurons (R=0.38, p[double less-than sign]0.001, Spearman rank correlation), and their means were not significantly different (vestibular: 0.035±0.014 s.e.m, visual: 0.039±0.015, p>0.8, paired t-test). Thus, to gain statistical power, we recomputed rnoise by pooling z-scored responses across stimulus conditions, thereby obtaining a single value of rnoise for each pair of neurons.

As observed in other visual areas (Huang and Lisberger, 2009; Smith and Kohn, 2008), noise correlations depended on the distance between two simultaneously recorded MSTd neurons, as illustrated in Suppl. Fig. 1, which shows distributions of rnoise for three distance groups: <0.05mm, 0.05 – 1mm and >1mm. Average noise correlations were significantly greater than zero for the first two groups (<0.05mm: 0.042±0.021 s,e,m., p=0.049, t-test; 0.05–1mm: 0.062±0.024, p=0.011), but not for the group of distant pairs (>1mm: 0±0.15, p=0.9). Thus, the following analyses were focused on 127 neuronal pairs separated by <1mm (results were similar for the whole dataset).

Comparison of noise correlations in trained and naïve animals

Our main goal was to examine whether training modifies interneuronal correlations. Five animals were previously trained to perform a heading discrimination task, in which they reported whether their heading was leftward or rightward relative to straight ahead (Gu et al., 2008a; Gu et al., 2007). These monkeys’ heading discrimination thresholds (corresponding to 84% correct) were high (>10°) at early stages of training, and gradually decreased to a plateau of only a few degrees (1~3°), as illustrated in Fig. 2A (Fetsch et al., 2009; Gu et al., 2008a; Gu et al., 2007). We measured noise correlations after these ‘trained’ animals had reached asymptotic performance, and we compared them to correlations measured in three ‘naïve’ animals that had never been trained to perform any task other than visual fixation.

Figure 2
Training effects on behavior and interneuronal correlations. (A) Vestibular psychophysical thresholds from 5 monkeys (denoted by different symbol shapes) decreased gradually during training on a heading discrimination task. Solid curves: best fitting ...

Our most conspicuous finding was a difference in mean rnoise between ‘trained’ and ‘naïve’ animals (Fig. 2B). Correlations in trained animals were shifted toward zero, as compared to those in naïve animals. The mean noise correlation in the trained group (0.023±0.017 s.e.m, n=89) was significantly smaller than that for ‘naïve’ animals(0.116±0.031, n=38, p=0.006, t-test). Note that, for both groups of animals, rnoise was measured during an identical passive fixation task (see Methods).

Because the stimulus was dynamic (Fig. 1A, gray curve), we examined the time course of noise correlation in trained and naïve animals by computing rnoise in 500ms sliding windows (with 50ms steps). As illustrated in Fig. 2C, rnoise was significantly greater in naïve than trained animals throughout the time course of the neural response (p=0.002, permutation test, see Methods). The difference in rnoise between naïve and trained animals was largest at the beginning of the trial and gradually decreased with time (R = −0.9, p[double less-than sign]0.001, Spearman rank correlation, Suppl. Fig. 2A). Importantly, these observations held true when correlations were examined for individual animals (Suppl. Fig. 2B). Thus, the overall reduction in correlated noise among MSTd neurons was a robust finding in trained animals.

Effects of training on tuning curves, variability, and sensitivity of single neurons

It is possible that the difference in correlated noise between naïve and trained animals could be an indirect effect of training on the response properties of individual neurons. Moreover, training-related changes in correlated noise might emerge in parallel with changes in the heading sensitivity of single neurons. To address these issues, we examined the effect of training on the time courses of firing rates and response variability. As illustrated in Fig. 3A, C, the time course of the population-average response to the preferred heading was indistinguishable between trained and naive animals (p=0.8, permutation test, see Methods). There was also no significant effect (p=0.5, permutation test) of training on the time course of the Fano factor, which measures the ratio of response variance to mean response (Fig. 3B, D, see also Methods and Suppl. Fig. 3). This finding contrasts with a previous report that Fano factor in area V4 was significantly reduced after animals were trained to discriminate orientation (Raiguel et al., 2006). In MSTd, the difference in noise correlation between naïve and trained animals does not appear to be linked to changes in firing rates or Fano factors.

Figure 3
Training does not affect the time courses of mean responses and response variability during visual (top) and vestibular (bottom) stimulation. (A, C) Time course of the average response to stimuli presented at each cell’s preferred heading in ‘trained’(red, ...

We further explored whether training shaped the tuning properties of individual MSTd neurons. For this analysis, we only included neurons with significant heading tuning in the horizontal plane (p<0.05, one-way ANOVA). To gain statistical power, we exploited a much larger database of single-unit responses from naïve and trained animals, recorded with a single electrode (Vestibular: n=556; Visual: n=992). As shown in Fig. 4A, E, distributions of tuning width (full width at half-height) were very similar for naïve and trained animals. There was no significant difference in median tuning width for the visual condition (naïve: 124.5° vs. trained: 126°, p=0.21, Wilcoxon rank-sum test). The difference in median tuning width was significant for the vestibular condition (naïve: 121° vs. trained: 131°, p=0.045). However, this effect was weak and, notably, training slightly increased tuning width in the vestibular condition, an effect opposite to that expected if training increases discriminability (e.g. Yang and Maunsell, 2004). Similarly, as shown in Fig. 4B, F, training did not have any significant effect on the distribution of tuning curve amplitudes in either the visual condition (naïve: 35.4° vs. trained: 31.8°, p=0.24, Wilcoxon rank-sum test) or the vestibular condition (naïve: 17.4° vs. trained: 17.2°, p=0.36). Thus, training animals to perform a fine heading discrimination task did not significantly shape the heading tuning of individual MSTd neurons.

Figure 4
Effects of training on heading tuning in MSTd during visual (top) and vestibular (bottom) stimulation. (A, E) Distributions of tuning width (full width at half-maximum response) for naïve (blue) and trained (red) animals. (B, F) Distributions ...

However, it remains possible that training only shaped the tuning of a subset of neurons that were most informative for heading discrimination around the straightforward reference used in training (e.g. Raiguel et al., 2006; Schoups et al., 2001). If so, then effects might only be seen for neurons most sensitive to heading variations around straight forward, and may have been missed in the above analysis. To examine this further, we interpolated tuning curves and used Fisher information analysis (Gu et al., 2010, see Methods) to compute the sensitivity of each neuron for discriminating heading around straight forward. As shown in Fig. 4C, G, the most sensitive neurons (lowest thresholds) are generally those that prefer lateral headings, such that their tuning curves have a steep slope around straight-ahead. For quantitative analysis, neurons were divided into two groups by heading preference: ’fore-aft’ neurons with heading preferences within 45° of forward (0°) or backward (±180°) motion, and ‘lateral’ neurons with heading preferences within 45° of leftward (−90°) or rightward (90°) movements. Consistent with previous findings (Gu et al., 2008a; Gu et al., 2010), lateral neurons were significantly more sensitive than fore-aft neurons for heading discrimination around straight ahead (p[double less-than sign]0.001, Factorial ANOVA, Figure 4D, H). However, neuronal sensitivity was not significantly different between naïve and trained animals (p>0.5, Factorial ANOVA) for either group of neurons, with no significant interaction effect (p>0.3). In summary, whereas heading discrimination training clearly reduced correlated noise among MSTd neurons, we find no clear evidence that training altered the basic tuning properties or sensitivity of individual neurons, including those neurons that are most informative for performing the task. This result also generalizes to neuronal discrimination of heading about any arbitrary reference (Supplementary Fig. 4).

Training effects on the noise-signal correlation structure

It is well established that rnoise is related to rsignal (Cohen and Maunsell, 2009; Cohen and Newsome, 2008; Gutnisky and Dragoi, 2008; Huang and Lisberger, 2009; Kohn and Smith, 2005; Smith and Kohn, 2008; Zohary et al., 1994b), so it is important to evaluate whether training alters this relationship. Fig. 5A,B shows the relationship between rnoise and rsignal, with each datum corresponding to a pair of MSTd neurons. This relationship was quantified using general linear models (analysis of covariance, ANCOVA), with rsignal in each stimulus condition (visual or vestibular) as a continuous variable and training group (trained or naïve) as a categorical factor. There was a significant positive correlation between rnoise and rsignal in both stimulus conditions (vestibular: p=0.0001; visual: p=0.0004, ANCOVA), reflecting the fact that noise correlations tended to be positive for pairs of neurons with similar tuning (rsignal >0) and near zero or negative for pairs with opposite tuning (rsignal <0).

Figure 5
Relationship between noise correlation (rnoise) and signal correlation (rsignal) in MSTd. (A, B) Noise correlations depend significantly on rsignal computed from visual (A) or vestibular (B) tuning curves. Lines represent regression fits (ANCOVA). Red: ...

Importantly, the slope of the relationship between rnoise and rsignal (Fig. 5A,B )was not significantly affected by training (vestibular: p=0.9; visual: p=0.9, ANCOVA interaction effect), as also indicated by overlap of the 95% confidence intervals around the regression slopes (Fig. 5C, nearly identical slopes were obtained by Type II regression). In contrast, training had a significant main effect on rnoise (vestibular: p=0.02; visual; p=0.008 ANCOVA), and the 95% confidence intervals around the regression intercepts were non-overlapping for naïve and trained animals (Fig. 5D). Thus, training reduced noise correlations uniformly across all signal correlations, such that the dependency of rnoise on rsignal remained unchanged.

Multisensory MSTd neurons can have matched visual and vestibular heading preferences (‘congruent’ cells) or mismatched preferences (‘opposite’ cells) (Gu et al., 2008a; Gu et al., 2006). Thus, we also tested whether rnoise depends on congruency. Specifically, the two units in each pair could be (1) both congruent, (2) both opposite or (3) a mixture of congruent and opposite cells. As illustrated in Suppl. Fig. 5, rnoise was not substantially affected by congruency. Next, we incorporate these results into an information analysis to investigate how the fidelity of population activity changes between naïve and trained animals.

Computation of covariance matrix

Although neurons were recorded pair-wise, our goal is to determine whether population activity in MSTd can account for the effect of training on behavioral sensitivity. For this purpose, we need to estimate the covariance matrix that characterizes correlations among the MSTd population in naïve and trained animals. This was done by assigning each value of the covariance matrix according to the measured noise and signal correlation structures in our data set. Because rnoise depended on rsignal in both the vestibular and visual conditions (Fig. 5A, B), both relationships were taken into account when constructing the covariance matrices. For simplicity, all neurons in the simulations discussed below were assumed to have congruent visual and vestibular heading preferences. Results were similar when variable congruency was introduced into the simulation, consistent with the observation that noise correlations were not strongly influenced by congruency (Suppl. Fig. 5).

We constructed covariance matrices with two different correlation structures (see Methods): (1) rnoise depended on rsignal with regression slopes and intercept specified according to data from naïve animals: rnoise=0.12×rsignal, vestibular+0.091×rsignal, visual+0.072, and (2) rnoise depended on rsignal with slopes and intercept derived from trained animals: rnoise=0.12×rsignal, vestibular+0.091×rsignal, visual+0.005. Note that the slopes were common across the two correlation structures, since no significant difference in slopes was found (Fig. 5C). We then used these covariance matrices to compute the precision with which a population of MSTd neurons in naïve or trained animals could discriminate heading, as described below. Importantly, noise correlations did not depend on whether trained monkeys performed a passive fixation task or the heading discrimination task (p=0.3, t-test), as shown in Suppl. Fig. 6 for a subset of neuronal pairs recorded in both tasks. Thus, we are justified in predicting heading discrimination performance from population activity measured during the fixation task for both trained and naïve animals.

Effect of training on population coding efficiency

We computed population discrimination thresholds from the inverse of Fisher information (If), an upper bound on information capacity that can be extracted by any unbiased estimator (Abbott and Dayan, 1999; Seung and Sompolinsky, 1993). Predicted thresholds from If define the performance that an ideal observer could achieve, based on MSTd population activity, in a fine heading discrimination task. For a simulated population of neurons with independent noise, predicted thresholds decreased steadily with population size (Fig. 6A, dashed black curve). As expected from previous findings (Bair et al., 2001; Cohen and Maunsell, 2009; Shadlen et al., 1996; Smith and Kohn, 2008; Zohary et al., 1994b), correlated noise similar to that seen in our naïve animals degraded population coding efficiency (Fig. 6A, blue curve). For a simulated population of 2000 neurons, the predicted heading discrimination threshold was ~5-fold larger compared to the case of independent noise. Surprisingly, the uniform reduction in rnoise that we observed in trained animals (Fig. 5) had little effect on predicted discrimination thresholds, as compared to naïve animals (Fig. 6A, red curve).

Figure 6
Impact of noise correlations on population coding efficiency. (A) Population heading discrimination thresholds as a function of population size. Each simulated population contained neurons with wrapped-Gaussian tuning curves (bandwidth=135°) and ...

Why doesn’t the reduction in mean noise correlation seen in trained animals improve the sensitivity of the population code? We simulated performance of a population of neurons using many covariance matrices that were constructed by systematically varying both the slope and intercept of the relationship between rnoise and rsignal. As shown in Fig. 6B, predicted thresholds were very sensitive to changes in the slope of the relationship between rnoise and rsignal. In contrast, changes in the intercept of the rnoise vs. rsignal relationship had weak effects on predicted thresholds. Counterintuitively, a uniform increase in rnoise (across all values of rsignal) produced a mild decrease in population thresholds, improving performance slightly (barely visible in Fig. 6A, see also Abbott and Dayan, 1999; Wilke and Eurich, 2002). These simulations suggest that a uniform reduction of noise correlations in trained animals is expected to have little impact on discrimination performance.

This conclusion is based on the assumption that all neurons contribute to discrimination performance. We can infer from the simulations of Fig. 6B that a change in noise correlation produces different effects for neurons with positive and negative signal correlations. To illustrate this, consider a population consisting of a single pair of neurons, having rsignal that could range from −1 (opposite heading preferences) to +1 (matched preferences). As illustrated in Fig. 7A, reducing the noise correlation between this pair of neurons results in a lower population threshold (red curve below blue curve) when the pair of neurons has positive rsignal. In contrast, reducing noise correlation increases the predicted threshold for negative rsignal (see also Supplementary Fig. 7A). This simple prediction was confirmed when decoding responses of pairs of MSTd neurons. For each pair of neurons, we compute a discrimination threshold under the assumption of correlated noise, as well as the assumption of independent noise. As shown in Fig. 7B, pairs of neurons with positive rsignal yield discrimination thresholds that increase with rnoise, whereas pairs with negative rsignal have discrimination thresholds that decrease with rnoise (R=0.49, p[double less-than sign]0.001, Spearman rank correlation). Thus, in a population of neurons with an even mixture of positive and negative signal correlations, the opposite effects of correlated noise will counteract each other.

Figure 7
Reduced noise correlations improve coding efficiency for neurons with similar tuning and reduce coding efficiency for neurons with dissimilar tuning. (A) Heading discrimination thresholds a pair of neurons with various signal correlations. One neuron ...

With this intuition in hand, we consider larger pool sizes (e.g., n=256 in Fig. 7C). If the direction preferences of neurons in the population are broadly distributed, roughly equal numbers of cell pairs will have positive and negative rsignal (Fig. 7C, left inset) and population thresholds for naïve and trained animals will be similar. If we narrow the distribution of direction preferences to generate more cell pairs with positive rsignal, the weaker noise correlations in trained animals substantially enhance coding efficiency (Fig. 7C, middle and right insets, see also Supplementary Fig. 7B). The more similar the heading tuning among neurons in the population, the greater the benefit of reducing noise correlations. At best, however, the predicted population discrimination threshold for trained animals is ~8% lower than for naïve animals (Fig. 7C, right inset, see also Supplementary Fig. 7B). Clearly, the effect of interneuronal correlations on population coding depends critically on the structure of the correlations, which involves both the relationship between rnoise and rsignal and the distribution of tuning similarity among neurons.

Possible rsignal distributions in area MSTd

Might heading be decoded from a subpopulation of MSTd neurons with similar tuning properties (positive rsignal), such that the uniform reduction of rnoise in trained animals might improve discrimination performance? Although we cannot firmly exclude this possibility, two observations suggest that it is unlikely. First, electrical microstimulation of multi-unit clusters with either leftward or rightward heading preferences can bias choices during a heading discrimination task (Britten and van Wezel, 1998, 2002; Gu et al., 2008b). Second, significant choice probabilities, which may reflect the contribution of single cortical neurons to behavior (Britten et al., 1996; Gu et al., 2007; Purushothaman and Bradley, 2005) (but also see Nienborg and Cumming, 2010), were reported for MSTd neurons preferring both rightward and leftward headings (Gu et al., 2008a; Gu et al., 2007). Thus, we further examined the dependence of choice probability and noise correlation on heading preference.

Compared to neurons with lateral heading preferences, neurons with a preference for fore-aft movement show significantly smaller choice probabilities (p=0.019, t-test, Fig. 8A, B). This result is consistent with the notion that neurons with direction preferences deviated away from straight ahead are more sensitive to small heading variations and thus contribute more to perception (Gu et al., 2007; Purushothaman and Bradley, 2005). Importantly, there was no significant difference in average choice probability between neurons preferring leftward and rightward headings (p=0.11, t-test), suggesting that the population of neurons that contributes to heading perception includes cells with both positive and negative signal correlations (inset to Fig. 8A).

Figure 8
Relationships between choice probability, noise correlation, and heading preferences in MSTd. (A) Choice probability tends to be more deviated away from the chance level of 0.5 for neurons with lateral heading preferences. Filled symbols denote choice ...

Interestingly, a similar dependence on heading preference was not observed for noise correlations in trained animals. As shown in Fig. 8C, D, there was no significant dependence of noise correlation on the heading preferences of MSTd neurons (p=0.2, t-test). Indeed, the average noise correlation for lateral neurons is a bit smaller than that for the fore-aft neurons. This finding suggests that the variation in choice probability with heading preference (Fig. 8A, B) is not driven just by correlated noise, but also depends on other factors such as how the signals are read out by decision circuitry.


By recording simultaneously from pairs of neurons in macaque area MSTd, we have shown that interneuronal correlations are weaker, on average, in animals trained to perform a fine heading discrimination task as compared to animals experienced only in visual fixation tasks. Although we did not record from the same animals before and after training, the difference in correlated noise between naïve and trained subjects was highly significant and consistent across animals within each group.

Our findings suggest that changes in the average strength of noise correlations are not sufficient to account for the effect of training on discrimination performance. The difference in rnoise between naïve and trained animals was uniform and independent of tuning similarity. If all neurons are decoded uniformly, the increased information capacity of neuronal pools with similar tuning is counteracted by the decreased information capacity of neuronal pools with dissimilar tuning curves. Thus, the effect of correlated noise on discrimination performance is conditional on both the relationship between rnoise and rsignal and on the demands of the task which may recruit different neuronal pools into play.

Properties of noise correlations in MSTd

Compared to noise correlations observed in area MT (Bair et al., 2001; Cohen and Newsome, 2008; Huang and Lisberger, 2009; Zohary et al., 1994b), the average noise correlation in our MSTd sample (distance <1mm) was substantially weaker (trained animals: 0.023; naïve animals: 0.116). The average correlation values we have seen in trained animals are similar to those reported in a recent study of macaque primary visual cortex (Ecker et al., 2010).

We found that noise correlations in MSTd are independent of the sensory stimulus modality (visual or vestibular), but depend on distance such that nearby neurons tend to have stronger correlations than more distant pairs (Huang and Lisberger, 2009; Lee et al., 1998; Smith and Kohn, 2008). Correlations in MSTd also depend strongly on tuning similarity, such that neurons with similar tuning curves tend to have greater correlated noise. In addition, we observed that noise correlations decrease in the presence of a stimulus as compared to pre-stimulus baseline activity. This result is consistent with previous studies showing that noise correlations decreased following stimulus onset (Smith and Kohn, 2008) and increased with stimulus intensity (e.g., contrast) (Huang and Lisberger, 2009; Kohn and Smith, 2005).

Possible explanations for the effect of training on correlated noise

Before accepting the conclusion that correlated noise in MSTd was reduced as a consequence of perceptual learning, we consider some alternatives. One possibility is that naive monkeys undergo larger fluctuations in behavioral state (e.g., arousal, attention) than trained animals, and this might cause slow fluctuations in neuronal responses that can inflate noise correlations (Bair et al., 2001; Ecker et al., 2010; Lampl et al., 1999). To address this issue, we removed slow fluctuations in neural responses by renormalizing the data before computing noise correlations (see Methods, Zohary et al., 1994b). This operation had little effect on our measurements, for both naïve and trained animals (Supplementary Fig. 8). This suggests that slow fluctuations in response driven by variations in behavioral state do not account for the greater noise correlations seen in naive animals.

Another possibility is that naive animals fixate the visual target less reliably and make more frequent microsaccades that could induce correlations among neural responses (e.g., Bair and O’Keefe, 1998). However, we found that naïve animals fixate as accurately as trained animals (Supplementary Fig. 8A). Indeed, naïve monkeys as a group made significantly fewer microsaccades than trained animals (Supplementary Fig. 8B). Hence, the reduction of correlated noise in trained animals is unlikely to be explained by differences in eye movements between the two groups of animals.

Two recent studies have indicated that attention directed toward the receptive field could reduce correlated noise among pairs of neurons in area V4 (Cohen and Maunsell, 2009; Mitchell et al., 2009). Although both naïve and trained monkeys only performed a passive fixation task in our study, trained animals might have paid more attention to the heading stimuli due to their relevance in the discrimination task. We cannot exclude this possibility, but three aspects of our results are inconsistent with an explanation based on attention. First, attention typically increases neuronal activity (Desimone and Duncan, 1995; Kastner and Ungerleider, 2000; Reynolds and Chelazzi, 2004; Reynolds and Heeger, 2009; Treue and Maunsell, 1999), but our analysis shows that mean responses were not significantly different between naïve and trained animals (Fig. 3). Second, the reduction in noise correlation with increased attention was also accompanied by decreased neuronal variability (Fano factor, Cohen and Maunsell, 2009; Mitchell et al., 2009). However, we did not find a significant difference in Fano factor between naïve and trained animals. Finally, there was no difference in noise correlation between the fixation and discrimination tasks for a subset of pairs of neurons that were recorded during both tasks (Suppl. Fig. 6). This result is consistent with an earlier study in which noise correlations in area MT were found to be similar during a motion discrimination task and a visual fixation task (Zohary et al., 1994b).

Any fluctuation in common inputs could cause correlated variability among target neurons. It is thus possible that training decreases the shared, common input to area MSTd, likely on a long time scale during learning (Chowdhury and DeAngelis, 2008). The effect of training on neural circuitry may have occurred at two levels. First, training may have altered the feedforward sensory input to MSTd from other cortical and subcortical areas, without changing the average tuning properties of single neurons (Jenkins et al., 1990; Recanzone et al., 1993; Weinberger, 1993). Second, training may have altered feedback connections to MSTd, including feedback from decision circuitry. Our results are consistent with recent findings that perceptual learning does not substantially alter sensory cortical representations, but rather sculpts the decoding of sensory signals by decision circuitry (Dosher and Lu, 1999; Law and Gold, 2008). If training alters the read out of heading signals from MSTd, this in turn may modify the shared feedback to MSTd neurons from downstream circuitry. It is currently not possible to discern which of these training-related changes contributes most to the reduction in correlated noise that we have observed.

Although our data suggest that learning does not alter the sensory representation of heading in a manner that could account for the improvement in behavioral sensitivity with training, it is important to note that we cannot rule out the possibility that training altered the heading tuning and sensitivity of neurons in other brain areas that may also be involved in heading perception, such as area VIP (Zhang and Britten, 2011). In addition, although we assume that noise correlations in MSTd were altered by perceptual learning, we cannot exclude the possibility that some other aspect of training, such as learning the operational rules of the task, may have driven the changes in correlated noise that we have observed. Finally, it is unclear whether the effect of training on correlated noise is specific to tasks for which area MSTd is thought to provide critical input. If we had trained animals to perform a task that was irrelevant to self-motion perception, such as a somatosensory or auditory discrimination task, we presumably would not expect to see changes in correlated noise in MSTd. However, this possibility remains to be tested.

Consequences for population coding efficiency

Despite a robust effect of training on the average noise correlation in MSTd, our simulations show that an optimal, unbiased decoding of all neurons does not predict a substantial change in performance due to learning. Indeed, theorists have shown that correlated noise may or may not harm population coding (Abbott and Dayan, 1999; Averbeck et al., 2006; Wilke and Eurich, 2002). In general, positively correlated noise between neurons with similar tuning (or more generally, any situation in which both neurons fire more strongly under one stimulus/task condition than another) harms the signal to noise ratio of the population code because it cannot be removed by pooling across neurons (Bair et al., 2001; Shadlen et al., 1996; Zohary et al., 1994b). Reducing shared noise among neurons in such cases is thus expected to improve population sensitivity.

Indeed, the effect of attention on the fidelity of population codes appears to follow this logic (Cohen and Maunsell, 2009). In a typical spatial attention task, most neurons with receptive fields at the attended location will increase their response. Because attention has a consistent polarity of effect on the responses of nearby neurons, stronger attention will tend to increase the responses of both neurons in a pair. Hence, most pairs of nearby neurons will have positive signal correlations with respect to the effect of attention. As a result, a reduction in correlated noise due to attention can improve the signal-to-noise ratio of the population code. However, in other contexts for which signals are decoded from populations that include neurons with dissimilar tuning properties, increasing correlated noise can improve the signal-to-noise ratio of a population code (Fig. 7A), as differences in tuning effectively cancel more of the noise in a population response (Abbott and Dayan, 1999; Averbeck et al., 2006; Poort and Roelfsema, 2009; Wilke and Eurich, 2002). Reducing correlated noise in the latter case can harm the coding efficiency of the population. In our heading discrimination task, it is likely that responses are decoded from neurons with a broad range of heading preferences (Gu et al., 2008b; Gu et al., 2010); in this context, reducing correlated noise uniformly across neurons with all signal correlations (Fig. 5A& B) does not improve the fidelity of the neural code (Fig. 6A). Thus, the impact of correlated noise on population coding depends on: (1) the structure of noise correlations and their dependence on signal correlation, and (2) the composition of neuronal pools upon which decoding is based.

We conclude that the effects of training on heading discrimination are not likely to be driven by the reduction in correlated noise that we have observed in area MSTd. Combined with previous observations that perceptual learning has little or no effect on basic tuning properties of single neurons in visual cortex (Chowdhury and DeAngelis, 2008; Crist et al., 2001; Ghose et al., 2002; Law and Gold, 2008; Raiguel et al., 2006; Schoups et al., 2001; Yang and Maunsell, 2004; Zohary et al., 1994a), our results suggest that changes in sensory representations are not necessarily involved in accounting for the improvements in behavioral sensitivity that accompany perceptual learning (at least for some sensory systems and tasks). Rather, our findings support the idea that perceptual learning may primarily alter the routing and/or weighting of sensory inputs to decision circuitry, an idea that has recently received experimental support (Chowdhury and DeAngelis, 2008; Law and Gold, 2008, 2009).



Physiological experiments were performed in 8 male rhesus monkeys (Macaca mulatta) weighing 4–8 kg. Animals were chronically implanted with a plastic head-restraint ring that was firmly anchored to the apparatus to minimize head movement. All monkeys were implanted with scleral coils for measuring eye movements in a magnetic field (Robinson, 1963). Animals were trained using standard operant conditioning to fixate visual targets for fluid reward. All animal surgeries and experimental procedures were approved by the Institutional Animal Care and Use Committee at Washington University and were in accordance with NIH guidelines.

Motion stimuli

Neurons were tested with two types of motion stimuli using a custom-built virtual reality system (Gu et al., 2007, 2008b; Gu et al., 2006). In the ‘vestibular’ stimulus condition, monkeys were passively translated by a motion platform (MOOG 6DOF2000E; East Aurora, NY) along a smooth trajectory (Gaussian velocity profile with peak-acceleration of ~1 m/s2 and duration of 2s, Fig. 1A). In the ‘visual’ stimulus condition, optic flow was provided by rear-projecting images onto a tangent screen in front of the monkey using a 3-chip DLP projector (Christie Digital Mirage 2000) that was mounted on the motion platform. Visual stimuli (90×90°) depicted movement through a 3D cloud of stars that occupied a virtual space 100 cm wide, 100 cm tall, and 50 cm deep. The stimulus contained multiple depth cues, including horizontal disparity, motion parallax and size information.

Experimental protocol and task

Animals were trained to maintain visual fixation on a head-fixed target at the center of the screen. Eye position was required to stay within a 2×2° electronic window throughout each trial in order to receive a water/juice reward. The majority of the data presented here were recorded while passively-fixating animals experienced a range of different heading directions that spanned the horizontal and/or vertical plane (Gu et al., 2006; Takahashi et al., 2007). Specifically, headings relative to straight ahead were: 0, ±22.5, ±45, ±90, and ±135º. Different heading directions and stimulus types (visual or vestibular) were interleaved randomly within a single block of trials. Each distinct stimulus was typically repeated 5 times (minimum of 3 repetitions for inclusion).

In each trial, a fixation point first appeared at the center of the screen. After fixation was established for 100–200 ms, the motion stimulus began and lasted for 2 seconds. In the vestibular condition, the motion platform always began its movement from a common central position. The animal was rewarded if they maintained visual fixation throughout the duration of the stimulus. At the end of the trial (or when fixation was broken), the fixation point disappeared and the motion platform moved back to the original central position during a 2 second intertrial interval. In the visual condition, the random-dot field appeared on the display after fixation was established, and again moved for 2 seconds. The dots then disappeared and the animal was rewarded for maintaining fixation, followed again by a 2 sec intertribal interval.

Three animals were trained only to perform the passive fixation task, whereas 5 animals had been extensively trained to perform a heading discrimination task (Fetsch et al., 2009; Gu et al., 2008a; Gu et al., 2007), in which they were asked to report whether their perceived heading was leftward or rightward relative to straight ahead by making a saccade to one of two choice targets. For a subpopulation of neurons in these ‘trained’ animals, responses were obtained while the animals performed both the fixation task and the heading discrimination task

Electrophysiological recordings

We conducted extracellular recordings of action potentials from single neurons in area MSTd. For most recordings, 2 to 4 tungsten electrodes (Frederick Haer, Bowdoinham, ME; tip diameter 3 μm, impedance 1–2 MΩ at 1 kHz) were used to record multiple single neurons simultaneously. In some cases (57 pairs), 2–4 electrodes were placed inside multiple guide tubes separated by 0.8 to 25 mm (different hemispheres). In other cases (55 pairs), multiple electrodes were placed inside a single guide tube. The distance between two simultaneously recorded neurons was estimated from both the horizontal and vertical (depth) coordinates (shank diameter = 75 microns).

Data from another 67 cell pairs were obtained from previous recordings with a single electrode (Fetsch et al., 2007; Gu et al., 2007; Gu et al., 2006; Takahashi et al., 2007), for which a second cell was isolated off-line using spike sorting software (Spike2, Cambridge Electronics Design). Only pairs of neurons from a single electrode that showed clearly separate clusters in the first three principle components of the spike waveform were included in the sample. Since the exact distance between neurons recorded from a single electrode was unknown, we arbitrarily assigned it to be 50 microns. Although noise correlations were slightly greater for pairs of neurons recorded from a single electrode (0.042±0.02) than for pairs recorded from different electrodes (0.033±0.015), this difference was modest and not significant (p>0.7, t-test). Thus, data collected with single and multiple electrodes were pooled for analysis, yielding 179 cell pairs from a total of 270 neurons (maximum of 5 pairs in an experiment).

Area MSTd was located ~15 mm lateral to the midline and ~2–6 mm posterior to the interaural plane, and was identified using both MRI scans and neurophysiological response properties (see Gu et al., 2006 for details). MSTd neurons had large receptive fields that typically occupied a quadrant or a hemi-field on the display screen and were often centered in the contralateral visual field but could extend well into the ipsilateral field. Once the electrodes were targeted to MSTd, we recorded from any neuron that was spontaneously active or could be activated by patches of flickering dots.

Data analysis

Noise and signal correlations

Noise correlation (rnoise) was computed as the Pearson correlation coefficient (ranging between −1 and 1) of the trial-by-trial responses from a pair of neurons driven by the same stimulus (Bair et al., 2001; Zohary et al., 1994b). The response in each trial was taken as the number of spikes during the middle 1s of the stimulus period (Gu et al., 2006). For each heading direction, responses were z-scored by subtracting the mean response and dividing by the standard deviation. This operation removed the effect of heading on the responses, such that the measured noise correlation reflected trial-to-trial variability. To avoid artificial correlations caused by outliers, we removed data points with z-scores larger than 3 (Zohary et al., 1994b). We then pooled data across headings to compute rnoise; the corresponding p-value was used to assess the significance of correlation for each pair of neurons.

Because there was no significant difference in rnoise between visual and vestibular stimulus conditions (Fig. 1F), we pooled responses across conditions to gain statistical power. To remove slow fluctuations in responsiveness that could result from changes in cognitive state over time (e.g., arousal), we re-normalized the z-scored responses in blocks of 20 trials, as described by Zohary et al (1994b). This additional normalization had no significant effect on rnoise (p>0.3, paired t test; R=0.9, p[double less-than sign]0.001, Spearman rank correlation, n=127, Supplementary Fig. 8). More importantly, the effect of re-normalization on noise correlations was similar in naïve and trained animals (p=0.7, interaction effect, p=0.9, group effect, ANCOVA, Supplementary Fig. 8). This suggests that the greater noise correlations in naïve animals were not the result of larger slow fluctuations in neural response (Ecker et al., 2010), such as might arise if naïve animals experienced greater fluctuations in arousal during the session.

Signal correlation (rsignal) was computed as the Pearson correlation coefficient (ranging between −1 and 1) between the tuning curves from two simultaneously recorded neurons. Tuning curves for each stimulus condition were constructed by computing the mean response (average firing rate during the middle 1s of the stimulus duration) across trials for each heading direction.

Permutation test

Permutation tests were applied to test for significant differences between trained and naïve animals with respect to: the difference in time courses of noise correlation (Fig. 2C), mean response (Fig. 3A,C), and Fano factor (Fig. 3B, D). We first computed the sum of squared differences between two time courses:

equation M1

using a 500ms sliding window moved in 50ms steps, for a total of 31 data points. We then created permuted ‘naïve’ and ‘trained’ groups by randomly drawing data from the original groups, pooled together. Within each cell, all of the responses were preserved (no shuffling across trials). We computed a new x2 value for each permutation (x2permuted), and this process was repeated 10000 times. A p-value was computed as the proportion of x2permuted > x2. A difference between the two groups of animals was considered significant if p < 0.05.

Fano factor

Fano factor, or the variance/mean ratio, was computed from log-log scatter plots of the variance of the spike count against the mean spike count, and this was done for each 500ms time window used to compute time courses. The data were fit by minimizing the orthogonal distance to the fitted line (type II regression). The slope was generally close to 1 and was thus forced to be 1 for convenience, such that variance scaled linearly with mean spike count. The Fano factor was then computed as 10^intercept (see Suppl. Fig. 3).

Population coding

Fisher information (IF) provides an upper limit on the precision with which an unbiased estimator can discriminate between small variations in a variable (x) around a reference value (xref) (Pouget et al., 1998; Seung and Sompolinsky, 1993). We computed the smallest deviation in heading around straight ahead (threshold, Δx) that could be reliably discriminated (at 84% correct) by an ideal observer:

equation M2

where IF was computed according to (Abbott and Dayan, 1999):

equation M3

Here, f’ denotes the derivative of a matrix of tuning curves; superscript T denotes the matrix transpose, Tr represents the trace operation, and superscript −1 indicates the matrix inverse. The reference heading was straight ahead in our simulations (xref=0°). Q represents the covariance matrix of neural responses, which was given by

equation M4

where ri,j denotes the noise correlation between the ith and jth neurons. When i=j, ri,j was set to 1. When i≠j, ri,j was assigned according to a linear relationship between noise and signal correlation:

equation M5

We minimized the orthogonal distance between the fit plane and the raw data using type II regression.

Supplementary Material



This work was supported by grants from NIH (EY019087 to DEA, and EY016178 to GCD).


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