Network dimensionality underlies flexible representation of cognitive information

The functional networks in human cortex that most flexibly represent cognitive information are hubs with widespread connectivity throughout the brain. Going beyond simple hub measures, we hypothesized that the dimensionality of each network9s global connectivity pattern (its global dimensionality) underlies its ability to produce highly diverse task activation patterns (its representational flexibility). Supporting our hypothesis, we report that the global dimensionality estimated during resting state correlates with the representational flexibility estimated across a variety of cognitive tasks. Demonstrating the robustness of this relationship, each network9s global connectivity pattern could be used to predict its representational flexibility. Additionally, we found that the frontoparietal cognitive control network had the highest dimensionality and flexibility, and that individuals with higher network dimensionality had higher representational flexibility. Together, these findings suggest that a network9s global dimensionality contributes to its ability to represent diverse cognitive information, implicating dimensionality as a network mechanism underlying flexible cognitive representation.


Introduction
task information flexibly, in part by reducing interference between task-relevant 79 cognitive representations. Providing concrete evidence that links a network's global 80 dimensionality with flexible task representation would suggest a role for intrinsic network 81 organization in providing the space of possible computations (cognitive, or otherwise) 82 performed by the human brain. Given recent evidence suggesting that the FPN acts as 83 a flexible hub network for adaptive task control 8,10,15,16 , we hypothesized that the 84 dimensionality of the FPN's global connectivity patterns estimated during resting-state 85 underlies its ability to flexibly represent a diverse range of tasks. 86 We tested this hypothesis using functional magnetic resonance imaging (fMRI) 87 data collected as part of the Human Connectome Project (HCP). Evidence linking a 88 network's global dimensionality estimated during resting-state fMRI and 89 representational flexibility estimated during task-state fMRI would suggest that such a 90 network can integrate distributed sets of task-relevant information in an organized 91 fashion, reducing pattern overlap/interference and producing highly decodable 92 representations underlying task performance ( hub network are yellow. The high-dimensional connectivity organization allows for information 99 integration from diverse brain systems in a pattern-separated manner. Activity from local 100 networks mapped to hub network regions produces decodable patterns of activation. b) A 101 schematic example of a hub network with low network dimensionality, due to the lack of pattern-102 separated global connections. Every region in the hub network has the same global connectivity 103 pattern, leading to low network dimensionality. Activity from local networks mapped to hub 104 network regions produces a net activity of 0 in each region of the hub network. This is due to the 105 lack of connectivity separation (low-dimensional connections), leading to an interference of 106 information-bearing signals. Note that the regions in the hub network in panels a and b have the 107 same weighted degree centrality.

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Data collection 112 Data were collected as part of the Washington University-Minnesota Consortium 113 of the Human Connectome Project (HCP; Van Essen et al., 2013). The data from the 114 "100 Unrelated Subjects" (n=100) of the greater "500 Subjects" HCP release was used 115 for empirical analyses. Specific details and procedures of subject recruitment and data 116 collection can be found in 45 . 100 human participants (54 female) were recruited from 117 Washington University in St. Louis and the surrounding area. The mean age of the 118 human participants was 29 years of age (range=24 -36 years of age). Whole-brain 119 multiband echo-planar imaging acquisitions were collected on a 32-channel head coil on 120 a modified 3T Siemens Skyra with TR=720 ms, TE=33.1 ms, flip angle=52º, 121 Bandwidth=2,290 Hz/Px, in-plane FOV=208x180 mm, 72 slices, 2.0 mm isotropic 122 voxels, with a multiband acceleration factor of 8. Data for each subject were collected 123 over the span of two days. On the first day, anatomical scans were collected (including 124 T1-weighted and T2-weighted images acquired at 0.7 mm isotropic voxels) followed by 125 two resting-state fMRI scans (each lasting 14.4 minutes), and ending with a task fMRI 126 component. The second day consisted with first collecting a diffusion imaging scan, 127 followed by a second set of two resting-state fMRI scans (each lasting 14.4 minutes), 128 and again ending with a task fMRI session. Each of the seven tasks was collected over 129 two consecutive fMRI runs. Further details on the resting-state fMRI portion can be 130 found in 46 , and additional details on the task fMRI components can be found in 47 . 131 132 Task paradigms 133 The data set was collected as part of the HCP project, which included both 134 resting-state and seven task fMRI scans 45 . The seven collected task scans consisted of 135 an emotion cognition task, a gambling reward task, a language task, a motor task, a 136 relational reasoning task, a social cognition task, and a working memory task. Briefly, 137 the emotion cognition task required making valence judgements on negative (fearful 138 and angry) and neutral faces. The gambling reward task consisted of a card guessing 139 game, where subjects were asked to guess the number on the card to win or lose 140 money. The language processing task consisted of interleaving a language condition, 141 which involved answering questions related to a story presented aurally, and a math 142 condition, which involved basic arithmetic questions presented aurally. The motor task 143 involved asking subjects to either tap their left/right fingers, squeeze their left/right toes, 144 or move their tongue. The reasoning task involved asking subjects to determine whether 145 two sets of objects differ from each other in the same dimension (e.g., shape or texture). 146 The social cognition task was a theory of mind task, where objects (squares, circles, 147 triangles) interacted with each other in a video clip, and subjects were subsequently 148 asked whether the objects interacted in a social manner. Lastly, the working memory 149 task was a variant of the N-back task. A complete description of these task paradigms 150 and scans can be found in 47 . 151 152 fMRI Preprocessing 153 Minimally preprocessed data for both resting-state and task fMRI were obtained 154 from the publicly available HCP data. We performed additional preprocessing steps for 155 resting-state fMRI, which included removing the first five frames of each run and  156  performing nuisance regression on the minimally preprocessed data. Nuisance  157  regression included removing the mean of each run, linear detrending, and regressing  158  out 12 motion parameters (six motion parameter estimates and their derivatives), the  159  mean white matter time series and its derivative, the mean ventricle time series and its  160 derivative, and the mean global signal time series and its derivative. 161 Task data for task activation analyses were additionally preprocessed using a 162 standard general linear model (GLM) for fMRI analysis. The first five frames of each run 163 were removed prior to fitting the GLM. Nuisance regressors included 12 motion 164 parameters, regressors for the mean ventricles, white matter, and global signals and 165 their derivatives. In addition, for each task paradigm, we estimated the task-evoked 166 activations of each task condition by fitting the task timing for each condition convolved 167 with the SPM canonical hemodynamic response function. Two regressors were fit for 168 the emotion cognition task, where coefficients were fit to either the face condition or 169 shape condition. For the gambling reward task, one regressor was fit to trials with the 170 punishment condition, and the other regressor was fit to trials with the reward condition. 171 For the language task, one regressor was fit for the story condition, and the other 172 regressor was fit to the math condition. For the motor task, six regressors were fit to 173 each of the following conditions: (1)  Estimating basic network properties 207 To first test the integrity of the network partition on the HCP data set, we 208 estimated the averaged within-network FC for each subject (Supplementary Figure 1). 209 To ensure that only strong FC values were contributing to our estimate of within-network 210 connectivity, we applied a 2% FC threshold, a previously used threshold for graph 211 analyses 11 . Only 10% of subjects had a non-zero within-network FC for the ORA, and 212 only 1% of subjects had a non-zero within-network FC for the VMM. In other words, for 213 the majority of subjects, these networks had no functional connections that survived a 214 2% FC threshold. 215 To establish whether a network had the basic property of being a hub (i.e., high 216 inter-network connectivity), we used several graph-theoretic techniques. We first used 217 participation coefficient (Supplementary Figure 4) Mathematically, we defined the NPS of a network C as 259 where scorr refers to the Spearman's rank correlation, refers to the connectivity 260 vector for brain region i to all other brain regions k not in network C (i.e., the out-of-261 network connectivity vector), and ܰ refers to the number of regions in network C. NPS 262 was computed for each subject separately using the subject's whole-brain Fisher's z-263 transformed FC matrix estimated with Pearson correlation. No threshold was applied to 264 the matrix prior to computing NPS for each network. We compared the NPS values 265 between pairs of functional networks by performing cross-subject t-tests for every pair of 266 networks. We corrected for multiple comparisons using a False Discovery Rate-267 corrected (FDR) p-value of p<0.05 50 . 268 269 Decoding task information in functional networks using multivariate pattern analysis 270 We performed multivariate pattern analysis 51 to decode task condition 271 information for each of the seven HCP tasks. Whole-brain task condition activations 272 were obtained via task GLM estimates as described above in the fMRI preprocessing 273 subsection. We then segmented the whole-brain activation pattern for each subject into 274 separate activation patterns for each functional network. 275 To estimate how much task information each functional network contained in its 276 activation pattern, we performed a cross-validated n-way classification for each task 277 separately, where n refers to the number of experimental conditions within each task 278 (Supplementary Figure 2; Supplementary Table 1). We employed a leave-one-subject-279 out cross-validation scheme using random splits of the training set, which has been 280 shown to produce more stable and robust decoding accuracies 23 . For each held-out 281 subject, we used 100 random splits of the training data, each time randomly sampling 282 with replacement 49 subjects to train on (approximately half of the training data), and 283 classifying a held-out subject's data. Thus, for each held-out subject, we generated 100 284 x n classification accuracies, from which we calculated a subject's average decoding 285 accuracy. This approach had the advantage of allowing us to perform a random effects 286 cross-subject t-test against chance (given the multiple decoding accuracies from each 287 random split) rather than a fixed effects binomial test to calculate statistical significance. 288 Our decoder was trained using logistic regression. For tasks which had n > 2 289 conditions, we employed a multiclass classification approach with a one versus rest 290 strategy for each class label. Logistic regression was implemented using the scikit-learn 291 package (version 0.18) in Python (version 2.7.9). We then performed a cross-subject t-292 test to test whether the decoder could classify each condition within a task using a 293 functional network's activation pattern significantly greater than chance. Since we ran 294 classifications on all functional networks, we corrected for multiple comparisons using 295 FDR. Statistical significance was assessed using an FDR-corrected p<0.05.

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Estimating the representational flexibility of each functional network 298 The above analysis illustrated that every functional network could decode task 299 condition information significantly above chance. However, to better quantify the degree 300 of decodability for each task, we measured the multivariate pattern distance between 301 the activation patterns for each task condition using Mahalanobis distance 22 . We used 302 Mahalanobis distance as opposed to decoding statistics (e.g., accuracy) given the more 303 intuitive interpretation of distance between activation patterns to infer highly distinct (and 304 therefore decodable) task representations. 305 We used the same cross-validation scheme as the above section for this 306 analysis. To estimate the pattern distinctness of each condition for a subject using the 307 distribution of activation patterns from all other subjects, for each task condition 308 . In 314 other words, we measured the difference between matched conditions and mismatched 315 conditions, for a held-out subject and a set of training subjects determined by the 316 random split. For each subject, we then averaged the pattern distinctness of each 317 condition across all random splits. This provided us with a single measure of how 318 distinct the network's task activation patterns were across task conditions for each 319 subject. 320 We performed this procedure for each task separately. To adjust for differences 321 in distances across tasks (due to the possibility that certain tasks contain more distinct 322 task conditions relative to others), we z-normalized the pattern distinctness (i.e.,

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) 323 across networks. This allowed us to compare the pattern distinctness of each network 324 across tasks, while preserving the relative ‫۾‬ ۲ of each network during a given task. We 325 then computed the representational flexibility of each network by averaging the 326 normalized ‫۾‬ ۲ across tasks (Fig. 3a). The representational flexibility for each network 327 score was calculated within subject. 328 Mahalanobis distance was calculated using SciPy version 1.0.0 (the "cdist" 329 function) with Python version 2.7.9. 330 331 Mapping whole-brain representations to functional networks via information transfer 332 mapping 333 We recently developed a new procedure to characterize the role of resting-state 334 FC in transferring task information 9 . Based on the concept of activity flow -the 335 movement of activity between areas of the brain -via channels described by resting-336 state FC 1 , we constructed a connectivity-based mapping that predicts the activation 337 pattern of a target network using activity from the rest of the brain. Mathematically, we 338 define this mapping between a target network and regions outside that network as 339 is a 1 x n vector corresponding to the predicted activation pattern for a target 340 network (with n regions) for some task condition ݇ , is a 1 x m vector corresponding 341 to the activation pattern for the rest of the brain (with m regions), the m x n matrix representing the region-to-region resting-state FC (estimated using 343 multiple linear regression) between all regions outside the target network and regions 344 inside the target network. Lastly, the operator • refers to the dot product. This 345 formulation allowed us to project activation patterns to a target network using activity 346 from regions outside that network (i.e., a spatial transformation represented as matrix 347 multiplication). 348 We tested whether the connectivity-based mapping could predict the transfer of 349 information from regions outside the target network to the target network (Fig. 4b). This 350 required a two-step process: (1) generating predicted activation patterns for each 351 experimental condition in the target network by estimating the activity flow to the target 352 network from the rest of the brain; (2) training a decoder on the activity flow-predicted 353 activation patterns of that network, and then subsequently classifying the actual (non-354 activity flow-predicted) activation patterns of that network using a held-out subject's 355 data. Note, the training set did not include any data from the to-be-predicted subject's 356 data set, and also were exclusively generated from the activity flow-predicted 357 activations of the target network using the connectivity-based mapping in equation 6. 358 This approach ensured that the analyses were not circular and the predictions were 359 two-fold: (1) predicting a held-out target network's activity; (2) predicting a held-out 360 subject's data. We used the same cross-validation scheme as in the previous section. 361 This involved a leave-one-subject out cross-validation with random splits on the training 362 set using logistic regression. Success of this analysis would suggest that the 363 connectivity-based mapping from out-of-network regions to a target network could 364 accurately predict the target network's actual activation patterns for conditions within a 365 task. This would demonstrate the role of a network's global connectivity organization in 366 transferring information between out-of-network regions and a target network. 367 To assess the statistical significance of the activity flow-predicted activation 368 patterns, we performed a one-sided t-test to assess whether decoding accuracies were 369 greater than chance (where chance is  Predicting representational flexibility using activity flow estimates 377 We wanted to demonstrate a direct relationship between the intrinsic global 378 connectivity organization of functional networks with representational flexibility across a 379 variety of tasks. Thus, we used the activity flow predictions of a target network across all 380 tasks to predict the representational flexibility. In this way, the predicted representational 381 flexibility was exclusively dependent on the combination of the intrinsic global 382 connectivity organization of the target network and out-of-network task activations. 383 To predict the representational flexibility of a network using activity flow estimates 384 from out-of-network regions, we first predicted a target network's activation pattern for 385 each condition within a task as described above. with the set of activity flow-predictions of the 392 target network (Fig. 5a). 393 To quantify the correspondence between the actual and activity flow-predicted 394 representational flexibility across networks, we performed a cross-network rank 395 correlation between the actual and predicted representational flexibility scores for each 396 subject (Fig. 5b)

445
Estimating the dimensionality of a network's global connectivity patterns 446 We first sought to estimate the specific network properties that we hypothesized 447 might contribute to flexible cognitive processing. We hypothesized that high-dimensional 448 hub networks (i.e., networks with high inter-network connectivity containing pattern-449 separated global connections) would demonstrate high involvement during a wide range 450 of tasks. We reasoned that the combination of high inter-network connectivity and 451 pattern-separated global connections would lead to both increased integrative network 452 function while limiting information interference (Fig. 1a). 453 We network, and can potentially be biased by the size of the network. 468 We computed the network dimensionality and NPS for every functional network 469 (Fig. 2d,e). Though network dimensionality and NPS target a distinct theoretical 470 construct relative to region-level measures such as participation coefficient, we ran a 471 control analysis to demonstrate the uniqueness of these measures. We computed the 472 participation coefficient for each network using weighted participation coefficient for 473 each subject at three FC thresholds: all positive weights, 10% FC threshold, and 2% FC 474 threshold (Supplementary Figure 4) Figure 5). This indicates that most networks are 513 hub networks, in the simplistic sense that they have a functional connection to every 514 other network. These findings suggest that simple hub measures alone cannot explain 515 the dimensionality of a network's global connectivity patterns; instead, the global 516 dimensionality of a network collectively emerges as a function of the differences of 517 node-specific global connectivity patterns, a property not captured by existing network 518 statistics. 519 520

540
Estimating the representational flexibility of functional networks using multivariate 541 pattern analysis 542 We next sought to characterize a network's ability to flexibly represent task 543 information (i.e., representational flexibility). To estimate a network's representational 544 flexibility, we rely on the notion that patterns of task-related activity can represent task 545 information 22 . We performed multivariate pattern analysis to decode task conditions 546 within each task using network-level activation patterns. We used a leave-one-subject 547 out cross-validation scheme with random splits on the training set, allowing us to 548 generate an averaged decoding accuracy for each subject across the random splits 23 . 549 We then performed a cross-subject t-test against chance to assess whether we could 550 decode task conditions significantly above chance for each task. We found that across 551 all seven HCP tasks, data from every network could be used to decode task information 552 significantly above chance (Supplementary Figure 2; FDR-corrected p<0.05 for each 553 task). This was unsurprising, since we had many subjects (n=100) and trained each 554 decoding model using distributed regions across large-scale networks. This suggested 555 task-relevant information was widely distributed across many brain regions and 556 functional networks, which is consistent with previous findings 9,24,25 . 557 Since all networks could decode task information with respect to statistical 558 significance, we instead quantified the pattern distinctness of the activation patterns 559 associated with each task condition. Using the same cross-validation scheme, we 560 measured the average representational distance of each task condition (relative to the 561 other task conditions within each task) using Mahalanobis distance 26 . This provided a 562 measure for how distinct each network's task representations were, which allows for 563 greater decodability. We then took the averaged Z-scored pattern distinctness across all 564 tasks to obtain the measure of representational flexibility (Fig. 3a)

590
Relating global dimensionality to representational flexibility 591 We hypothesized that networks with high-dimensional global connectivity 592 patterns would produce flexible representations that are highly decodable. The 593 preceding results identified these two properties of functional networks using 594 independent data: resting-state data was used to identify the global dimensionality of 595 networks, and task data was used to estimate the representational flexibility of 596 networks. We next sought to determine whether these two independent measures are 597 related to one another. 598 We first performed a simple cross-network rank correlation between network 599 dimensionality and representational flexibility, and NPS and representational flexibility. 600 As a comparison, we also correlated representational flexibility and participation 601 coefficient. We computed the cross-network rank correlation of every subject's 602 representational flexibility with each graph-theoretic measure separately (Fig. 3c). We 603 found that network dimensionality significantly explained cross-network variance in 604 representational flexibility (cross-subject mean rho=0.33; t-test versus 0, t 99 =10.77; 605 p<0.0001; Supplementary Table 4). We further demonstrate that network dimensionality 606 significantly explains more cross-network variance of representational flexibility than all 607 other measures (Supplementary Figure 5), including participation coefficient (averaged 608 t 99 across all FC thresholds=9.87; FDR-corrected p<0.05). This suggests that the 609 dimensionality of a network's global connectivity patterns can explain a network's ability 610 to flexibly represent task information more than a previously method used to infer 611 integrative network function (i.e., participation coefficient). 612 While the above analysis describes a simple correlative relationship between 613 task-based representational flexibility and the intrinsic network properties estimated 614 from resting-state fMRI, the analysis does not implicate a network mechanism relating 615 the two properties. Thus, we next wanted to test whether the organization of a network's 616 intrinsic global connectivity patterns could -via a mechanistic model of how connectivity 617 influences task activations 1,9 -predict the representational flexibility of a network. 618 Explicit prediction of a network's representational flexibility using the network's global 619 connectivity organization would more rigorously test the hypothesis that its global 620 connectivity organization is critical to its ability to flexibly integrate a wide variety of task-621 relevant information. 622 Recent work has demonstrated that the intrinsic FC architecture estimated during 623 resting-state fMRI accurately describes the routes of activity flow -the movement of 624 task-evoked activations between regions -during tasks 1 (Fig. 4a). We recently 625 validated a new procedure -information transfer mapping -to infer the transfer of task 626 information between two brain areas by mapping task representations between those 627 regions 9 . Briefly, the procedure involves two steps: (1) mapping estimated activity flow 628 from a source area to a target area using a resting-state connectivity-based mapping, 629 and (2) information decoding of the actual activation pattern by a decoder trained on the 630 activity flow-predicted activation patterns. We sought to build on these findings to 631 demonstrate that the organization of a network's intrinsic global connections can explain 632 a network's ability to integrate diverse sets of task-evoked information for flexible task 633 representation. 634 To map activity to a target network using brain regions outside of that network, 635 we first estimated a connectivity-based mapping by obtaining the resting-state FC 636 patterns between regions in the target network and regions outside the network. We 637 then predicted the task activation pattern in the target network by transforming 638 activations from out-of-network regions into the spatial dimensions of the target network 639 (Fig. 4b). Briefly, this involved calculating the weighted sum of all out-of-network 640 regions' activations weighted by the to-be-predicted region's connections. To see how 641 well these connectivity-based mappings preserved task information in the target 642 network, we trained a decoder using the activity flow-predicted activation patterns, and 643 tested that decoder with the network's actual activation pattern for a held-out subject. By 644 training the decoder using predicted activation patterns and testing on the actual 645 activation patterns, this approach required that the activity flow-predicted activation 646 patterns retained representations that were in the same representational geometry as 647 the original activation pattern. Success with this procedure would suggest that the 648 network's intrinsic global connectivity organization was responsible for its ability to 649 integrate widespread information from the rest of the brain. 650 651 652 performed to produce a predicted activation pattern for the FPN for each task condition. We 664 subsequently trained a decoder using the predicted FPN activation patterns, and then classified 665 the actual FPN activation patterns using a held-out subject's data. This procedure was repeated 666 for each network and every HCP task.

668
We performed the information transfer mapping procedure using activations from 669 out-of-network regions to a target network for every functional network (see Fig. 4c for 670 an example). We then computed a network's representational flexibility based on the 671 predicted activation pattern for that network (Fig. 5a). To see how well the activity flow-672 predicted representational flexibility scores recapitulated the actual representational 673 flexibility scores for each network, we performed a cross-network rank correlation 674 between the actual and predicted representational flexibility scores for each subject 675 (Fig. 5b). We found that the activity flow-predicted   744 which task-evoked activity propagates between brain regions 1,2,9 , providing evidence 791 that estimated intrinsic functional connections reflect the capacity for inter-region 792 communication. Building on these findings, the present results provide evidence that a 793 static property of intrinsic functional networks -global dimensionality -contributes to a 794 network's ability to flexibly represent cognitive task information. 795 The finding that the global dimensionality of networks contributes to their ability to 796 flexibly represent cognitive information has several broader implications. First, it 797 suggests that a network's global dimensionality estimated during resting state reflects 798 the representational capacity of that network during task states. Second, it provides a 799 specific property of network organization that can be leveraged to design future network 800 models and architectures that can maximize representational ability. Lastly, it improves 801 upon the previously described notion that rich club networks (or diverse club networks) 802 underlie integrative network function 38-40 . In contrast to previous studies focusing on rich 803 and diverse club networks, which typically characterized networks by averaging region-804 level connectivity properties such as weighted degree centrality 12,41,39 or participation 805 coefficient 38,40 , we sought to further characterize specific topological features emergent 806 at the network level that might contribute to flexible representations. Global 807 dimensionality takes into account the collective global connections of a network and the 808 degree to which they target distinct sets of regions. Thus, global dimensionality refines 809 the concept of an integrative hub network by taking into account the collective 810 dimensionality of all global connections belonging to a network. 811 Though most studies in cognitive neuroscience are limited to a single 812 experimental paradigm, we leveraged the HCP's multi-task dataset to investigate the 813 brain-behavior relationship underlying flexible cognitive representation. Despite this 814 advantage, our measure of representational flexibility was still constrained by the seven 815 cognitive tasks included in the HCP dataset. As a particularly prominent example of a 816 limitation of this dataset, all but the Language task used only visual stimuli. Thus, while 817 neuroimaging studies with human participants becomes more difficult as the number of 818 tasks increases (largely due to the experimental duration), recent advances in 819 computational modeling has made it tractable to study the computational properties of 820 models able to perform large number of tasks 42 . It will thus be important for future work 821 to find converging evidence from both empirical and computational studies to study the 822 neural and computational basis of flexible task representation. 823 Another limitation of this study is that the information transfer mapping procedure 824 used to link intrinsic FC organization and task activation patterns assumes a linear 825 relationship between sets of regions. While this provides a simple approach to 826 approximate the flow of activity between brain regions with minimal assumptions, neural 827 processing is typically thought to rely on nonlinear information transformation through a 828 sequence of processing pipelines, such as in the ventral visual stream 43 . Further, 829 transformation of information via recurrent network connections is also thought to be 830 crucial for many cognitive tasks 42,44 , as well as for pattern completion in hippocampal 831 networks 17 . Thus, future work elucidating the contribution of nonlinear neural 832 transformations through either feedforward or recurrent network architectures will be 833 important to understand how information is transformed between brain systems. 834 In summary, we used graph-theoretic analysis of resting-state networks and 835 information decoding across a wide range of tasks to show the co-occurrence of a 836 network's global dimensionality and its ability to flexibly represent task information. We 837 then demonstrated that information from the whole brain can be mapped to specific 838 networks by inferring the transfer of information over a network's global connectivity 839 organization. These results demonstrate the close relationship between global 840 dimensionality and representational flexibility at the large-scale network level, 841 implicating a network mechanism underlying flexible representation for adaptive task 842 control. We expect these findings to prompt further research into the relationship 843 between network properties and their ability to produce cognitive representations, 844 providing a deeper insight into the mechanisms underlying flexible cognitive control. 845 846 Author