Stimulus-Driven Population Activity Patterns in Macaque Primary Visual Cortex
[['Dimensionality reduction has been applied to neural population activity to study decision making [1 , 2] , motor control [3–5] , olfaction [6] , working memory [7 , 8] , visual attention [9] , audition [10] , rule learning [11] , speech [12] , and more ( for a review , see [13] ) .', 'In many cases , dimensionality reduction is applied in brain areas for which the relationship between neural activity and external variables , such as the sensory stimulus or behavior , is not well characterized .', 'This is indeed the setting in which dimensionality reduction may be most beneficial because it allows one to relate the activity of a neuron to the activity of other recorded neurons , without needing to assume a moment-by-moment relationship with external variables .', 'However , it is also the setting in which the outputs of dimensionality reduction can be the most difficult to interpret .', 'To aid in interpreting the outputs of dimensionality reduction in such settings , it is important to vary the inputs to a brain area and ask whether the outputs of dimensionality reduction change in a sensible way .', 'This is most readily done for a brain area close to the sensory periphery , such as the primary visual cortex ( V1 ) .', 'Here , we apply dimensionality reduction to V1 and ask two fundamental , population-level questions .', 'First , how is neural complexity related to stimulus or task complexity ?', 'Previous studies have used dimensionality reduction to analyze population activity in a reduced space ( e . g . , [1–13] ) .', 'Implicit in these studies is the appropriate dimensionality of the reduced space , which is a measure of neural complexity .', 'It is currently unknown how neural complexity scales with stimulus or task complexity for a given population of neurons [14] .', 'Second , how does a neural circuit flexibly encode ( or “multiplex” ) the representation of the vast number of stimuli encountered in the natural world ?', 'Recent studies suggest that it may be possible to take advantage of the multi-dimensional properties of the population activity space [2 , 7 , 15–17] .', 'In particular , the population activity representing different stimuli might occupy similar dimensions of the population activity space [10] .', 'It is currently unknown how the similarity of the dimensions being occupied by the population activity changes with the similarity of the stimuli .', 'The concept of dimensionality is illustrated in Fig 1 . Consider a high-dimensional space ( termed the population firing rate space ) in which each axis represents the firing rate of a recorded neuron ( Fig 1A ) .', 'The goal of dimensionality reduction is to identify', 'i ) how many dimensions are occupied by the neural population activity , i . e . , the dimensionality of the population activity , and', 'ii ) how these dimensions are oriented within the population firing rate space .', 'In this three-neuron example , the population activity is two-dimensional , where the dimensions are defined by the orthogonal basis patterns ( Fig 1A , basis patterns 1 and 2 ) .', 'Equivalently , we can think of dimensionality reduction in terms of decomposing the population activity into a weighted sum of basis patterns and a mean offset ( Fig 1B ) .', 'A basis pattern describes a characteristic way in which activity of the neurons covaries .', 'Each basis pattern is fixed and is weighted by a time-varying latent variable , which represents the contribution of the basis pattern at each point in time .', 'We can compare the outputs of dimensionality reduction for two different stimuli ( Fig 1B and 1C ) .', 'The population activity for stimulus 1 is two-dimensional because it can be described by two basis patterns ( Fig 1B ) , whereas that for stimulus 2 is three-dimensional ( Fig 1C ) .', 'Thus , the population response to stimulus 2 would be deemed more complex than the population response to stimulus 1 . In addition , we can ask whether the population responses to different stimuli occupy similar dimensions within the population firing rate space .', 'This is assessed by comparing the basis patterns across stimuli .', 'In this example , there is one basis pattern that is shared by both stimuli ( red ) , one basis pattern that is similar between stimuli ( green ) , and one basis pattern ( black ) that is employed only by stimulus 2 . In this work , we characterize how neural complexity varies with stimulus complexity in macaque V1 by applying principal components analysis ( PCA ) to the trial-averaged neural responses to different classes of visual stimuli , including sinusoidal gratings , a natural movie , and white noise .', 'In addition , we develop a new method ( termed the pattern aggregation method ) to measure how the basis patterns extracted from the population responses to each stimulus relate to each other .', 'This method allows one to characterize how the similarity of the dimensions being occupied by the population activity changes with the similarity of the stimuli .', 'A key advantage of studying these questions in V1 is that there are well-established receptive field ( RF ) models .', 'By applying the same dimensionality reduction methods to the outputs of an RF model , we can more deeply understand the relationship between the outputs of dimensionality reduction and known properties of V1 neurons .', 'The results described in this work show that the outputs of dimensionality reduction , when applied to V1 population activity , are sensible , and thus may be fruitfully applied to other brain areas .'], ['We first investigated how changing the complexity of the visual stimulus changes the dimensionality of trial-averaged population responses using drifting sinusoidal gratings .', 'To change the stimulus complexity , we included different numbers of consecutive grating orientations in the analysis ( ranging from 1 to 12 orientations ) .', 'For example , the least complex stimulus included a single orientation , and more complex stimuli included two or five consecutive orientations ( Fig 2A ) .', 'We asked how quickly the dimensionality of the population activity grows as the number of orientations increases .', 'At one extreme , it may be that the population response to each orientation uses an entirely different set of basis patterns ( i . e . , dimensions ) .', 'In this case , the dimensionality for two orientations would be two times the dimensionality for one orientation .', 'At the other extreme , it may be that the population response to each orientation resides in the same set of dimensions .', 'In other words , the population response is formed using the same basis patterns , but linearly combined using different weights for different orientations .', 'In this case , the dimensionality for two orientations would be the same as the dimensionality for one orientation .', 'We first computed the basis patterns of each orientation individually by applying PCA to the trial-averaged population response ( taken in 20 ms bins ) , and identifying the patterns explaining the greatest variance in the population response ( up to a chosen cumulative variance threshold , e . g . , 90% ) .', 'To assess the dimensionality of the population response to multiple orientations , we developed the pattern aggregation method ( see Methods ) , which first aggregates the basis patterns for different orientations as column vectors in a matrix , and then computes the number of linearly independent columns of the aggregated matrix ( i . e . , the effective rank ) .', 'This value is the dimensionality for multiple orientations .', 'Using a 90% variance threshold , we found that the dimensionality for two orientations was 1 . 62 times the dimensionality for one orientation ( Fig 2B , ‘90%’ curve ) , and significantly smaller than what would be expected had the basis patterns been randomly chosen ( Fig 2B , ‘chance 90%’ curve , p < 10−5 ) .', 'In other words , for consecutive orientations separated by 30° , the population responses share about half of their basis patterns .', 'As more orientations were included , the dimensionality of population responses remained lower than expected by chance ( Fig 2B ) , indicating that population responses to oriented gratings separated by angles larger than 30° also tend to use similar basis patterns .', 'Similar trends were found using different variance thresholds ( Fig 2B , ‘70%’ , ‘80%’ curves ) , so we use a 90% threshold in the rest of this work .', 'The pattern aggregation method requires a choice for the rank threshold t to determine how different basis patterns need to be before they define separate dimensions .', 'We repeated the above analysis for different choices of t and a fixed variance threshold of 90% ( Fig 2C ) .', 'We found that the dimensionality trends are similar for rank thresholds t near 0 . 5 , so we use t = 0 . 5 in the rest of this work .', 'Because the absolute dimensionality depends on the variance and rank thresholds , we make no claims about absolute dimensionality .', 'Rather , we focus on relative comparisons of dimensionality for fixed variance and rank thresholds .', 'We observed a change in the rate of increase of dimensionality after six orientations ( Fig 2B , black curve ) .', 'Because consecutive orientations were separated by 30° , the first and seventh orientations were 180° apart and differed only in their drift direction .', 'Thus , the seventh to twelfth orientations were identical to the first to sixth orientations respectively , but drifted in opposite directions .', 'A small proportion of V1 neurons are direction selective [18 , 19] , so the change in slope of the dimensionality curve might be due to the population activity using similar basis patterns for opposite drift directions .', 'To test this possibility , we performed two analyses .', 'First , we assessed the direction selectivity of each neuron ( direction index = 1 − null response / preferred response ) , and found that 16 of 183 neurons had a direction index greater than 0 . 5 , consistent with [19] .', 'If none of the neurons encoded direction selectivity , we would expect the dimensionality curve to be flat beyond 6 orientations in Fig 2B .', 'The increase in dimensionality after 6 orientations is consistent with the finding that at least some neurons show direction selectivity .', 'A potential concern is that the increase in dimensionality beyond 6 orientations arises from the fact that a larger number of patterns are being aggregated for a larger number of orientations .', 'To address this , we performed a control analysis which equalized the number of patterns being aggregated across different numbers of conditions by including patterns from many subsamples of the data .', 'We found that the dimensionalities for 7 or more orientations were significantly greater than the dimensionality for 6 orientations ( p < 0 . 001 ) , following the same trend shown in Fig 2B .', 'Second , we assessed how the dimensionality of the population activity for two orientations varies with the angular offset between the orientations ( Fig 2D ) .', 'This indicates how the similarity of the dimensions being occupied by the population activity changes with the similarity of the stimuli .', 'We found that the dimensionality increases with angular offset up to 90° , indicating that the population activity differs the most for two orientations with 90° offset .', 'Then , the dimensionality decreases as the angular offset increases , reaching a minimum at a 180° offset , where gratings drift in opposite directions .', 'Thus , the population activity uses more similar basis patterns for gratings drifting in opposite directions ( 180° offset ) than to gratings of different orientations ( angular offsets other than 180° ) .', 'The dimensionality for 180° offset was higher than that for 0° offset ( p < 10−5 ) , indicating that the population activity does not use identical basis patterns for opposite drift directions .', 'Because these dimensionalities were computed differently ( the pattern aggregation method for 180° offset and a variance threshold for 0° offset ) , we aggregated an equal number of patterns ( identified over many subsampled runs ) for 0° offset as that for 180° offset , and still found a higher dimensionality for 180° offset than for 0° offset ( p < 10−5 ) .', 'This result , combined with the change in slope of the dimensionality curve ( Fig 2B ) , indicates that the population activity tends to use similar ( but not identical ) basis patterns for opposite drift directions .', 'Taken together , the analyses in Fig 2B and 2D characterize how the outputs of dimensionality reduction vary with the sensory input ( in this case , drifting sinusoidal gratings ) to V1 .', 'We also visualized the basis patterns describing the largest percentage of variance for three different orientations ( Fig 2E ) .', 'These basis patterns extracted from the trial-averaged population activity are akin to the hypothetical basis patterns shown in Fig 1 ( red , green , black ) .', 'For a given basis pattern , the absolute height of each bar indicates the degree to which each neuron contributes to that basis pattern .', 'The following are two salient properties of the identified basis patterns .', 'First , most of the neurons in the recorded population contribute to each basis pattern to some extent .', 'Thus , the basis patterns capture changes in firing rates that are shared broadly across the population , rather than reflecting the activity of only a small number of neurons .', 'Second , the basis patterns capture both positive and negative signal correlations between neurons , where the signal is the phase of the grating at different time points .', 'A basis pattern describes positive signal correlation between a pair of neurons if the neurons have coefficients of the same sign .', 'Conversely , a basis pattern describes negative signal correlation for coefficients of opposite sign .', 'We can relate these basis patterns to the results shown in Fig 2B–2D by asking how similar are the linear combinations of each set of basis patterns across different stimulus orientations .', 'This is difficult to assess by eye , and so we rely on the quantifications shown in Fig 2B–2D to determine how similar are the basis patterns across stimulus orientations .', 'We next sought to determine how the dimensionality of the trial-averaged population activity varies with the complexity of the visual stimulus for a wider range of stimuli .', 'We presented three movie stimuli ( Fig 3A ) : a sequence of sinusoidal gratings ( ‘gratings movie’ ) , contiguous natural scenes ( ‘natural movie’ ) , and white noise ( ‘noise movie’ ) .', 'In contrast to Fig 2A where the order of stimulus complexity is clear ( i . e . , a larger number of orientations is more complex ) , here we needed first to assess the relative complexity of the three movie stimuli .', 'By applying PCA to the pixel intensities , we found that 40 dimensions could explain nearly 100% of the variance of the pixel intensities for the gratings movie ( Fig 3B ) .', 'For the natural movie , the top few dimensions explained a large percentage of the variance due to global luminance changes caused by zooming and panning the camera , and a large number of additional dimensions were needed to explain the remaining variance .', 'For the noise movie , each dimension explained only a small percentage of the total variance .', 'We summarized these cumulative percent variance curves by finding the number of dimensions ( gratings movie: 24 , natural movie: 64 , noise movie: 459 ) needed to explain 90% of the variance ( Fig 3B , dashed line ) .', 'Based on these values , the gratings movie was least complex , followed by the natural movie , then the noise movie .', 'Similar results were obtained when first transforming the pixel intensities using a V1 receptive field model , then applying PCA ( see “Comparing to a V1 receptive field model” ) .', 'We further asked how much the pixel intensities varied for each movie stimulus , and found that the noise movie had a smaller variance than the other two movie stimuli ( Fig 3B , inset ) .', 'Together , this indicates that the distribution of pixel intensities for the gratings movie and natural movie is akin to an elongated ellipsoid ( low dimensionality , high variance ) , whereas that for the noise movie is akin to a small ball ( high dimensionality , low variance ) .', 'Having measured the relative complexity of the movie stimuli , we then asked how the dimensionality of the population responses to the movie stimuli varies with stimulus complexity .', 'We found that for a 90% variance threshold , the dimensionality of the trial-averaged population responses ( 20 ms bins ) was ordered in the same way as the stimulus complexity ( Fig 3C ) ; namely , the population responses to the gratings movie had the lowest dimensionality , followed by the natural movie , then the noise movie .', 'This ordering did not simply follow from the ordering of the mean population firing rates for the different movies ( monkey 1: 4 . 2 , 6 . 4 , 5 . 4 spikes/sec , monkey 2: 6 . 6 , 8 . 2 , 6 . 7 spikes/sec for gratings , natural , and noise movies , respectively ) , and was consistent for a wide range of neuron counts for both monkeys ( S1 Fig ) .', 'We also assessed how much the firing rates varied in response to each movie stimulus—that is , we measured how much the mean firing rate ( averaged across experimental trials ) varies over time .', 'As with pixel intensities , we found that the population response to the noise movie had the smallest variance , followed by the gratings movie , then the natural movie ( Fig 3C , inset ) .', 'Overall , the dimensionality and variance ordering in the visual stimuli and the population responses were similar , indicating that the population activity in V1 retains the complexity of the ordering of the visual stimuli themselves .', 'Having compared the dimensionality of the population activity across stimuli , we next asked how the basis patterns of the population activity ( corresponding to the dimensions being occupied by the population activity ) compare across stimuli .', 'Previous studies have found that the ability of a RF model to predict a neuron’s response can depend on the stimulus class on which the model was trained [20–22] , suggesting that the population activity might use somewhat distinct basis patterns for different stimulus classes .', 'On the other hand , if basis patterns are influenced by the shared underlying network structure [4 , 10] , then we would expect them to be shared across responses to different stimuli .', 'We first asked whether there are qualitative differences in the coefficients of the basis patterns for population responses to the stimulus movies ( Fig 4A ) .', 'As in Fig 2E , we found that most of the basis patterns represented activity across a large number of neurons and described both positive and negative signal correlations .', 'However , there were two notable exceptions .', 'First , the basis pattern describing the most variance for the population response to the gratings and noise movies involved primarily two neurons ( Fig 4A , right and left panels , pattern 1 , neuron indices 26 and 27 ) .', 'For these movies , the two neurons had the highest firing rate modulation ( maximum—minimum firing rate ) across the recorded population .', 'The weights for the gratings movie appeared to be sparser than those for individual gratings ( Fig 2E ) , likely because the gratings movie contained different orientations that strongly co-modulated these similarly-tuned neurons , whereas individual gratings with a single orientation co-modulated many neurons together with phase .', 'Second , the basis pattern describing the most variance for the population response to the natural movie had coefficients of the same sign ( Fig 4A , middle panel , pattern 1 ) .', 'This is due to the entire population increasing or decreasing its firing rates together in response to global luminance changes prevalent in natural movies .', 'Other than the similarity of the top basis pattern for the gratings and noise movies , it was difficult to determine by eye whether the basis patterns were being shared across stimuli .', 'Thus , we used the pattern aggregation method to quantitatively assess the similarity of the identified basis patterns .', 'As a baseline , we assessed the extent to which the visual stimuli themselves reside in the same dimensions in pixel space .', 'We compared the dimensionalities of the individual movies ( Fig 4B , teal dots , consistent with Fig 3B ) to those of combinations of movies ( Fig 4B , orange and purple dots ) .', 'If the stimuli reside in overlapping dimensions , then the resulting dimensionality would be the maximum of the dimensionalities for the individual movies .', 'However , if the stimuli reside in completely non-overlapping ( i . e . , orthogonal ) dimensions , then the resulting dimensionality would be the sum of the dimensionalities for the individual movies .', 'To measure the extent of overlap , we computed a similarity index s , for which s > 0 indicates that the patterns are more similar ( i . e . , more overlapping ) than expected by chance and s < 0 indicates that the patterns are less similar ( i . e . , closer to orthogonal ) than expected by chance ( see Methods ) .', 'There are two main observations .', 'First , the dimensions occupied by the gratings movie overlap with those for the natural movie .', 'To see this , note that the dimensionality for the gratings and natural movies together ( 80 dimensions ) was less than the sum of the individual dimensionalities for the two movies ( Fig 4B , gray , 88 dimensions ) .', 'To ensure that the overlap in patterns was meaningful , we confirmed that the aggregated dimensionality of 80 was less than the dimensionality ( 88 dimensions ) that would be expected by combining randomly-chosen dimensions ( s = 0 . 33 , p < 10−5 ) .', 'Second , the dimensions occupied by the noise movie include many of the dimensions for the other two stimuli .', 'This is indicated by the fact that the dimensionality corresponding to any combination of stimuli that included the noise movie ( gratings + noise: 472 , natural + noise: 495 , and gratings + natural + noise: 500 dimensions ) was less than the dimensionality that would be expected by chance ( s > 0 . 4 , p < 10−5 for all cases ) .', 'Note that , in all cases , the chance dimensionality was near the maximum dimensionality ( indicating orthogonality between the two sets of randomly-chosen patterns ) because the dimensionality of the pixel space ( 1 , 600 dimensions ) was much larger than the dimensionalities of the individual movies .', 'We used the same approach to analyze the population responses as we did the visual stimuli .', 'We compared the dimensionality of the population responses to individual movies ( Fig 4C , teal dots , consistent with Fig 3C ) to that of population responses to combinations of movies ( Fig 4C , orange and purple dots ) .', 'We found that the relationship of the basis patterns employed by the population activity across stimuli ( Fig 4C ) was similar to the relationship between the stimuli themselves ( Fig 4B ) .', 'First , the dimensions occupied by the population responses to the gratings movie are overlapping with those for the natural movie .', 'This is indicated by the fact that the aggregated dimensionality for the population responses to the gratings and natural movies ( monkey 1: 25 , monkey 2: 38 ) was less than the dimensionality if the patterns were orthogonal ( top of the black brackets ) and the dimensionality expected by chance ( s > 0 . 39 , p < 10−5 ) .', 'Second , the dimensions occupied by the population response to the noise movie include most of the dimensions for the other two stimuli .', 'This is indicated by the fact that the dimensionality corresponding to any combination of stimuli that included the noise movie was less than the dimensionality expected by chance ( s > 0 . 32 , p < 10−5 in all cases ) , and close to entirely overlapping .', 'The chance dimensionality in Fig 4C is computed by assuming that any population activity pattern within the N-dimensional population firing rate space can be achieved ( where N = 61 for monkey 1 and N = 81 for monkey 2 ) .', 'Previous studies indicate that the population activity may only be able to occupy a subset of dimensions due to underlying network constraints [4 , 10] .', 'Although we had no way of identifying exactly how many dimensions could have been occupied by the population of recorded neurons , we computed a lower bound by determining M , the largest value of dimensionality observed in response to any combination of stimuli ( Fig 4C , M = 39 for monkey 1 and M = 52 for monkey 2 ) .', 'If the chance level is computed instead by drawing random patterns from this M-dimensional space , we still find that the population activity tends to occupy more similar dimensions than expected by chance for all pairs of movies ( p < 0 . 05 ) .', 'This is a conservative assessment because larger values of M would only make the comparison more statistically significant .', 'We note that even if the population responses to different stimuli occupy similar dimensions , this does not imply that the responses occupy the same regions of the subspace defined by those dimensions .', 'In other words , the activity may covary along the same dimensions but be centered at different locations in the population activity space .', 'We found that the population responses to the three movies indeed were centered in different locations of the population activity space ( S2 Fig ) .', 'Our analysis of the similarity of basis patterns for the population activity is summarized by the schematic in Fig 4D , where the size of each ellipse represents the dimensionality ( i . e . , number of basis patterns ) of the population response to the corresponding stimulus and the overlap between ellipses represents the extent to which the population responses share basis patterns .', 'We found that the basis patterns for the gratings movie were overlapping with those of the natural movie , and that the basis patterns for the noise movie largely contain the basis patterns for the other two stimuli .', 'However , there were a small number of basis patterns that were unique to each stimulus , shown by the small areas of non-overlap among the ellipses .', 'Overall , this suggests that a neural circuit is capable of expressing a limited repertoire of basis patterns , and that a subset of those basis patterns is employed for any given stimulus .', 'In the preceding sections , the analyses of the movie stimuli and the corresponding neural activity used the entire 30-second movie ( i . e . , 750 time points ) together .', 'Here , we consider time-resolved measurements of dimensionality using one second windows , each comprising 25 time points .', 'This allows us to assess how dimensionality changes over time , and compare the basis patterns employed by the trial-averaged population activity during different parts of the 30-second movies .', 'For the visual stimuli ( Fig 5A , left panel ) and the population responses ( Fig 5A , center and right panels ) , we found that the dimensionality corresponding to the noise movie was higher than the dimensionality corresponding to the gratings and natural movies in each one-second window , consistent with the results of analyzing each 30-second movie in its entirety ( Fig 3 ) .', 'However , the dimensionality of the natural movie was not greater than that of the gratings movie ( cf . colored triangles in Fig 5A , which indicate average dimensionality over time ) , in contrast to Fig 3 .', 'We hypothesized that this was due to temporal correlations in the natural movie , in which frames within a one-second window tend to be self-similar .', 'In contrast , for the gratings and noise movies , there are at least three different grating orientations and 25 different frames of white noise within each one-second window .', 'To reconcile the results for short and long time windows , we performed three analyses .', 'First , we tested the hypothesis that temporal correlations in the natural movie result in lower dimensionalities ( relative to the other movies ) for short time windows .', 'To break the temporal correlations , we shuffled the time points ( 20 ms resolution ) across each 30 second period and performed the same analysis as in Fig 5A .', 'We found that , in a one-second window , the mean dimensionality corresponding to the natural movie was higher than that corresponding to the gratings movie for the shuffled data .', 'This was true for the visual stimuli ( p < 0 . 01 ) and for the population responses ( monkey 1: p < 10−3 , monkey 2: p < 0 . 05 ) .', 'This indicates that the range of basis patterns expressed by the population responses to the natural movie within a short time window is limited by the temporal correlations in the natural movie itself .', 'Second , we asked how the dimensionality grows when increasing the window size progressively from one second to 30 seconds , where each window starts at the beginning of the movie ( Fig 5B ) .', 'If the dimensionality increases with window size , this would indicate that new patterns ( of pixels or of population activity ) are being used throughout the duration of the movie .', 'However , if the dimensionality plateaus , then the patterns are being reused and no new patterns are being expressed .', 'The leftmost points on these curves ( one-second window ) correspond to the leftmost points on the corresponding curves in Fig 5A .', 'The rightmost points on these curves ( 30-second window ) correspond to the dimensionalities shown in Fig 3 .', 'Although the dimensionality corresponding to the natural movie ( green ) is lower than that corresponding to the gratings movie ( blue ) for short time windows , the dimensionality corresponding to the natural movie grows more quickly and surpasses the dimensionality corresponding to the gratings movie for longer time windows .', 'We found this to be true for both the visual stimuli ( Fig 5B , left panel ) and the population responses ( Fig 5B , center and right panels ) .', 'This indicates that the patterns for the natural movie tend to be self-similar within a short time window , and new patterns are expressed over longer time windows .', 'In contrast , the dimensionality corresponding to the gratings movie does not grow as quickly with window size .', 'This is because once a few different grating orientations are included , patterns corresponding to additional grating orientations can be represented approximately as linear combinations of patterns corresponding to existing grating orientations ( both for the visual stimuli and the population responses ) , and therefore do not increase the dimensionality appreciably .', 'Third , we directly measured the similarity of the patterns between different one-second windows using the pattern aggregation method .', 'Fig 5C shows the matrix of similarity indices for the population responses to each of the three movies ( monkey 1 ) .', 'By averaging the values of the off-diagonal similarity indices across the matrix , we found that the patterns corresponding to the gratings movie tended to be more similar across time than those for the natural and noise movies ( Fig 5D ) .', 'This was true for the visual stimuli ( left panel ) , as well as for the population responses ( middle and right panels ) .', 'This result indicates that new patterns tend to be expressed ( for both the visual stimuli and the population responses ) as the movies play out over time more for the natural and noise movies than for the gratings movie .', 'This result also supports the finding in Fig 5B that the dimensionality corresponding to the natural movie grows more quickly than that corresponding to the gratings movie .', 'Taken together , these results indicate that the noise movie drives a large number of basis patterns in the population activity in a short time window , relative to the gratings and natural movies .', 'As the movies play out over time , the noise and natural movies tend to drive new basis patterns , whereas the grating movie tends to recruit the same patterns .', 'We also asked whether the second-by-second fluctuations of the dimensionality of the visual stimulus during the 30-second movie ( Fig 5A , left panel ) were related to that of the population responses ( Fig 5A , middle and right panels ) and found weak correlations ( mean across mo
['Introduction', 'Results', 'Discussion', 'Materials and Methods']
['Dimensionality reduction has been applied in various brain areas to study the activity of populations of neurons .', 'To interpret the outputs of dimensionality reduction , it is important to first understand its outputs for brain areas for which the relationship between the stimulus and neural response is well characterized .', 'Here , we applied principal component analysis ( PCA ) to trial-averaged neural responses in macaque primary visual cortex ( V1 ) to study two fundamental , population-level questions .', 'First , we characterized how neural complexity relates to stimulus complexity , where complexity is measured using relative comparisons of dimensionality .', 'Second , we assessed the extent to which responses to different stimuli occupy similar dimensions of the population activity space using a novel statistical method .', 'For comparison , we performed the same dimensionality reduction analyses on the activity of a recently-proposed V1 receptive field model and a deep convolutional neural network .', 'Our results show that the dimensionality of the population response changes systematically with alterations in the properties and complexity of the visual stimulus .']
['A central goal in systems neuroscience is to understand how large populations of neurons work together to enable us to sense , to reason , and to act .', 'To go beyond single-neuron and pairwise analyses , recent studies have applied dimensionality reduction methods to neural population activity to reveal tantalizing evidence of neural mechanisms underlying a wide range of brain functions .', 'To aid in interpreting the outputs of dimensionality reduction , it is important to vary the inputs to a brain area and ask whether the outputs of dimensionality reduction change in a sensible manner , which has not yet been shown .', 'In this study , we recorded the activity of tens of neurons in the primary visual cortex ( V1 ) of macaque monkeys while presenting different visual stimuli .', 'We found that the dimensionality of the population activity grows with stimulus complexity , and that the population responses to different stimuli occupy similar dimensions of the population firing rate space , in accordance with the visual stimuli themselves .', 'For comparison , we applied the same analysis methods to the activity of a recently-proposed V1 receptive field model and a deep convolutional neural network .', 'Overall , we found dimensionality reduction to yield interpretable results , providing encouragement for the use of dimensionality reduction in other brain areas .']
['neural networks', 'engineering and technology', 'signal processing', 'vertebrates', 'social sciences', 'neuroscience', 'animals', 'mammals', 'primates', 'multivariate analysis', 'mathematics', 'statistics (mathematics)', 'white noise', 'computational neuroscience', 'vision', 'old world monkeys', 'research and analysis methods', 'computer and information sciences', 'monkeys', 'animal cells', 'mathematical and statistical techniques', 'principal component analysis', 'macaque', 'cellular neuroscience', 'psychology', 'cell biology', 'single neuron function', 'neurons', 'biology and life sciences', 'cellular types', 'sensory perception', 'computational biology', 'physical sciences', 'amniotes', 'statistical methods', 'organisms']