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Effective learning is accompanied by high-dimensional and efficient representations of neural activity

Nature Neuroscience volume 22, pages 1000–1009 (2019)Cite this article

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Abstract

A fundamental cognitive process is to map value and identity onto the objects we learn about. However, what space best embeds this mapping is not completely understood. Here we develop tools to quantify the space and organization of such a mapping in neural responses as reflected in functional MRI, to show that quick learners have a higher dimensional representation than slow learners, and hence more easily distinguishable whole-brain responses to objects of different value. Furthermore, we find that quick learners display more compact embedding of their neural responses, and hence have higher ratios of their stimuli dimension to their embedding dimension, which is consistent with greater efficiency of cognitive coding. Lastly, we investigate the neurophysiological drivers at smaller scales and study the complementary distinguishability of whole-brain responses. Our results demonstrate a spatial organization of neural responses characteristic of learning and offer geometric measures applicable to identifying efficient coding in higher-order cognitive processes.

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Fig. 1: Neural responses from the fMRI data: separability dimension and assortativity.
Fig. 2: Experimental protocol and behavioral results.
Fig. 3: Quick learners show higher dimensional and more efficient representations.
Fig. 4: Regional drivers of the relationship between representation and behavior.
Fig. 5: Quick learners show a larger stimulus dimension of responses in certain task-relevant regions at the voxel level.
Fig. 6: Dimension and assortativity provide a geometric depiction of neural data.
Fig. 7: Dimension of neural data from the size judgment session.

Data availability

The datasets generated and analyzed during the current study are available from the corresponding author upon reasonable request. The code used for the statistical analysis and modeling has been provided as Supplementary Software.

References

  1. Freedman, D. J., Riesenhuber, M., Poggio, T. & Miller, E. K. Categorical representation of visual stimuli in the primate prefrontal cortex. Science 291, 312–316 (2001).

    Article  CAS  Google Scholar 

  2. Barlow, H. in Sensory Communication (ed. Rosenblith, W. A.) Ch. 13 (MIT Press, 1961).

  3. Olshausen, B. A. & Field, D. J. Sparse coding with an overcomplete basis set: a strategy employed by V1? Vision Res. 37, 3311–3325 (1997).

    Article  CAS  Google Scholar 

  4. Poldrack, R. A. Is efficiency a useful concept in cognitive neuroscience? Dev. Cogn. Neurosci. 11, 12–17 (2015).

    Article  Google Scholar 

  5. Buzsáki, G. & Watson, B. O. Brain rhythms and neural syntax: implications for efficient coding of cognitive content and neuropsychiatric disease. Dialogues Clin. Neurosci. 14, 345–367 (2012).

    PubMed  PubMed Central  Google Scholar 

  6. Gold, B. T., Kim, C., Johnson, N. F., Kryscio, R. J. & Smith, C. D. Lifelong bilingualism maintains neural efficiency for cognitive control in aging. J. Neurosci. 33, 387–396 (2013).

    Article  CAS  Google Scholar 

  7. Heinzel, S. et al. Working memory load-dependent brain response predicts behavioral training gains in older adults. J. Neurosci. 34, 1224–1233 (2014).

    Article  CAS  Google Scholar 

  8. Rigotti, M. et al. The importance of mixed selectivity in complex cognitive tasks. Nature 497, 585–590 (2013).

    Article  CAS  Google Scholar 

  9. Diedrichsen, J., Wiestler, T. & Ejaz, N. A multivariate method to determine the dimensionality of neural representation from population activity. Neuroimage 76, 225–235 (2013).

    Article  Google Scholar 

  10. Ganguli, S. et al. One-dimensional dynamics of attention and decision making in LIP. Neuron 58, 15–25 (2008).

    Article  CAS  Google Scholar 

  11. Fitzgerald, J. K. et al. Biased associative representations in parietal cortex. Neuron 77, 180–191 (2013).

    Article  CAS  Google Scholar 

  12. Grill-Spector, K. & Malach, R. The human visual cortex. Annu. Rev. Neurosci. 27, 649–677 (2004).

    Article  CAS  Google Scholar 

  13. Waskom, M. L., Kumaran, D., Gordon, A. M., Rissman, J. & Wagner, A. D. Frontoparietal representations of task context support the flexible control of goal-directed cognition. J. Neurosci. 34, 10743–10755 (2014).

    Article  CAS  Google Scholar 

  14. Bzdok, D. et al. Characterization of the temporo-parietal junction by combining data-driven parcellation, complementary connectivity analyses, and functional decoding. Neuroimage 81, 381–392 (2013).

    Article  Google Scholar 

  15. Chang, L. J., Yarkoni, T., Khaw, M. W. & Sanfey, A. G. Decoding the role of the insula in human cognition: functional parcellation and large-scale reverse inference. Cereb. Cortex 23, 739–749 (2013).

    Article  Google Scholar 

  16. Mattar, M. G., Thompson-Schill, S. L. & Bassett, D. S. The network architecture of value learning. Netw. Neurosci. 2, 128–149 (2018).

    Article  Google Scholar 

  17. Squire, L. R. Memory and the hippocampus: a synthesis from findings with rats, monkeys, and humans. Psychol. Rev. 99, 195–231 (1992).

    Article  CAS  Google Scholar 

  18. Peelen, M. V. & Caramazza, A. Conceptual object representations in human anterior temporal cortex. J. Neurosci. 32, 15728–15736 (2012).

    Article  CAS  Google Scholar 

  19. Bush, G. et al. Dorsal anterior cingulate cortex: a role in reward-based decision making. Proc. Natl Acad. Sci. USA 99, 523–528 (2002).

    Article  CAS  Google Scholar 

  20. Grill-Spector, K. The neural basis of object perception. Curr. Opin. Neurobiol. 13, 159–166 (2003).

    Article  CAS  Google Scholar 

  21. Cunningham, J. P. & Yu, B. M. Dimensionality reduction for large-scale neural recordings. Nat. Neurosci. 17, 1500–1509 (2014).

    Article  CAS  Google Scholar 

  22. Gao, P. et al. A theory of multineuronal dimensionality, dynamics and measurement. Preprint at bioRxiv https://www.biorxiv.org/content/10.1101/214262v2 (2017).

  23. Fusi, S., Miller, E. K. & Rigotti, M. Why neurons mix: high dimensionality for higher cognition. Curr. Opin. Neurobiol. 37, 66–74 (2016).

    Article  CAS  Google Scholar 

  24. Sadtler, P. T. et al. Neural constraints on learning. Nature 512, 423–426 (2014).

    Article  CAS  Google Scholar 

  25. Barak, O., Rigotti, M. & Fusi, S. The sparseness of mixed selectivity neurons controls the generalization–discrimination trade-off. J. Neurosci. 33, 3844–3856 (2013).

    Article  CAS  Google Scholar 

  26. Chung, S., Lee, D. D. & Sompolinsky, H. Classification and geometry of general perceptual manifolds. Phys. Rev. X 8, 031003 (2018).

    CAS  Google Scholar 

  27. Zimmer, H. D., Popp, C., Reith, W. & Krick, C. Gains of item-specific training in visual working memory and their neural correlates. Brain Res. 1466, 44–55 (2012).

    Article  CAS  Google Scholar 

  28. Bullmore, E. & Sporns, O. The economy of brain network organization. Nat. Rev. Neurosci. 13, 336–349 (2012).

    Article  CAS  Google Scholar 

  29. Bassett, D. S. et al. Efficient physical embedding of topologically complex information processing networks in brains and computer circuits. PLoS Comput. Biol. 6, e1000748 (2010).

    Article  Google Scholar 

  30. Simon, H. A. A behavioral model of rational choice. Q. J. Econ. 69, 99–118 (1955).

    Article  Google Scholar 

  31. Bassett, D. S. et al. Dynamic reconfiguration of human brain networks during learning. Proc. Natl Acad. Sci. USA 108, 7641–7646 (2011).

    Article  CAS  Google Scholar 

  32. Shine, J. et al. The dynamics of functional brain networks: integrated network states during cognitive task performance. Neuron 92, 544–554 (2016).

    Article  CAS  Google Scholar 

  33. Braun, U. et al. Dynamic reconfiguration of frontal brain networks during executive cognition in humans. Proc. Natl Acad. Sci. USA 112, 11678–11683 (2015).

    Article  CAS  Google Scholar 

  34. Gariepy, J.-L. in Developmental Science, 3rd edn, Vol. 4 (eds Cairns, R. B. et al.) Ch. 8 (Cambridge University Press, 1996).

  35. Tishby, N. & Zaslavsky, N. Deep learning and the information bottleneck principle. In Proc. 2015 IEEE Information Theory Workshop (ed. Xing, C.) 1–5 (ITW, 2015).

  36. Goldt, S. & Seifert, U. Thermodynamic efficiency of learning a rule in neural networks. New J. Phys. 19, 113001 (2017).

    Article  Google Scholar 

  37. Ruitenberg, M. F. L. et al. Neural correlates of multi-day learning and savings in sensorimotor adaptation. Sci. Rep. 8, 14286 (2018).

    Article  CAS  Google Scholar 

  38. Gorbet, D. J. & Sergio, L. E. Move faster, think later: women who play action video games have quicker visually-guided responses with later onset visuomotorrelated brain activity. PLoS One 13, e0189110 (2018).

    Article  Google Scholar 

  39. Haier, R. J. et al. Regional glucose metabolic changes after learning a complex visuospatial/motor task: a positron emission tomographic study. Brain Res. 570, 134–143 (1992).

    Article  CAS  Google Scholar 

  40. Momi, D. et al. Acute and long-lasting cortical thickness changes following intensive first-person action videogame practice. Behav. Brain Res. 353, 62–73 (2018).

    Article  Google Scholar 

  41. Tompary, A. & Davachi, L. Consolidation promotes the emergence of representational overlap in the hippocampus and medial prefrontal cortex. Neuron 96, 228–241.e5 (2017).

    Article  CAS  Google Scholar 

  42. Mason, R. A. & Just, M. A. Physics instruction induces changes in neural knowledge representation during successive stages of learning. Neuroimage 111, 36–48 (2015).

    Article  Google Scholar 

  43. Karlsson Wirebring, L. et al. Lesser neural pattern similarity across repeated tests is associated with better long-term memory retention. J. Neurosci. 35, 9595–9602 (2015).

    Article  Google Scholar 

  44. Milivojevic, B., Vicente-Grabovetsky, A. & Doeller, C. F. Insight reconfigures hippocampal-prefrontal memories. Curr. Biol. 25, 821–830 (2015).

    Article  CAS  Google Scholar 

  45. Dunsmoor, J. E., Kragel, P. A., Martin, A. & LaBar, K. S. Aversive learning modulates cortical representations of object categories. Cereb. Cortex 24, 2859–2872 (2014).

    Article  Google Scholar 

  46. Vuilleumier, P., Henson, R. N., Driver, J. & Dolan, R. J. Multiple levels of visual object constancy revealed by event-related fMRI of repetition priming. Nat. Neurosci. 5, 491–499 (2002).

    Article  CAS  Google Scholar 

  47. Koutstaal, W. et al. Perceptual specificity in visual object priming: functional magnetic resonance imaging evidence for a laterality difference in fusiform cortex. Neuropsychologia 39, 184–199 (2001).

    Article  CAS  Google Scholar 

  48. Simons, J. S., Koutstaal, W., Prince, S., Wagner, A. D. & Schacter, D. L. Neural mechanisms of visual object priming: evidence for perceptual and semantic distinctions in fusiform cortex. Neuroimage 19, 613–626 (2003).

    Article  Google Scholar 

  49. Giusti, C., Pastalkova, E., Curto, C. & Itskov, V. Clique topology reveals intrinsic geometric structure in neural correlations. Proc. Natl Acad. Sci. USA 112, 13455–13460 (2015).

    Article  CAS  Google Scholar 

  50. Saggar, M. et al. Towards a new approach to reveal dynamical organization of the brain using topological data analysis. Nat. Commun. 9, 1399 (2018).

    Article  Google Scholar 

  51. Ward, G. J. The radiance lighting simulation and rendering system. In Proc. 21st Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 1994 (eds. Schweitzer, D. Glassner, A. & Keeler, M.) 459–472 (ACM, 1994).

  52. Dale, A. M., Fischl, B. & Sereno, M. I. Cortical surface-based analysis. I. segmentation and surface reconstruction. Neuroimage 9, 179–194 (1999).

    Article  CAS  Google Scholar 

  53. Greve, D. N. & Fischl, B. Accurate and robust brain image alignment using boundary-based registration. Neuroimage 48, 63–72 (2009).

    Article  Google Scholar 

  54. Jenkinson, M. Improving the registration of b0-distorted EPI images using calculated cost function weights. In Proc. Tenth International Conference on Functional Mapping of the Human Brain 459–472 (2004).

  55. Jenkinson, M., Bannister, P., Brady, M. & Smith, S. Improved optimization for the robust and accurate linear registration and motion correction of brain images. Neuroimage 17, 825–841 (2002).

    Article  Google Scholar 

  56. Smith, S. M. Fast robust automated brain extraction. Hum. Brain Mapp. 17, 143–155 (2002).

    Article  Google Scholar 

  57. Friston, K. J., Williams, S., Howard, R., Frackowiak, R. S. & Turner, R. Movement-related effects in fMRI time-series. Magn. Reson. Med. 35, 346–355 (1996).

    Article  CAS  Google Scholar 

  58. Behzadi, Y., Restom, K., Liau, J. & Liu, T. T. A component based noise correction method (CompCor) for bold and perfusion based fMRI. Neuroimage 37, 90–101 (2007).

    Article  Google Scholar 

  59. Jo, H. J., Saad, Z. S., Simmons, W. K., Milbury, L. A. & Cox, R. W. Mapping sources of correlation in resting state fMRI, with artifact detection and removal. Neuroimage 52, 571–582 (2010).

    Article  Google Scholar 

  60. Murphy, K., Birn, R. M., Handwerker, D. A., Jones, T. B. & Bandettini, P. A. The impact of global signal regression on resting state correlations: are anti-correlated networks introduced? Neuroimage 44, 893–905 (2009).

    Article  Google Scholar 

  61. Saad, Z. S. et al. Trouble at rest: how correlation patterns and group differences become distorted after global signal regression. Brain Connect. 2, 25–32 (2012).

    Article  Google Scholar 

  62. Chai, X. J., Castañón, A. N., Öngür, D. & Whitfield-Gabrieli, S. Anticorrelations in resting state networks without global signal regression. Neuroimage 59, 1420–1428 (2012).

    Article  Google Scholar 

  63. Power, J. D., Schlaggar, B. L. & Petersen, S. E. Recent progress and outstanding issues in motion correction in resting state fMRI. Neuroimage 105, 536–551 (2015).

    Article  Google Scholar 

  64. Murphy, K. & Fox, M. D. Towards a consensus regarding global signal regression for resting state functional connectivity MRI. Neuroimage 154, 169–173 (2017).

    Article  Google Scholar 

  65. Daducci, A. et al. The connectome mapper: an open-source processing pipeline to map connectomes with MRI. PLoS One 7, e48121 (2012).

    Article  CAS  Google Scholar 

  66. Julian, J. B., Fedorenko, E., Webster, J. & Kanwisher, N. An algorithmic method for functionally defining regions of interest in the ventral visual pathway. Neuroimage 60, 2357–2364 (2012).

    Article  CAS  Google Scholar 

  67. Glasser, M. F. et al. A multi-modal parcellation of human cerebral cortex. Nature 536, 171–178 (2016).

    Article  CAS  Google Scholar 

  68. Honey, C. J., Kötter, R., Breakspear, M. & Sporns, O. Network structure of cerebral cortex shapes functional connectivity on multiple time scales. Proc. Natl Acad. Sci. USA 104, 10240–10245 (2007).

    Article  CAS  Google Scholar 

  69. van den Heuvel, M. P. & Sporns, O. Network hubs in the human brain. Trends Cogn. Sci. 17, 683–696 (2013).

    Article  Google Scholar 

  70. Hagmann, P. et al. Mapping the structural core of human cerebral cortex. PLoS Biol. 6, e159 (2008).

    Article  Google Scholar 

  71. Curran, P. J. & Bauer, D. J. The disaggregation of within-person and between-person effects in longitudinal models of change. Annu. Rev. Psychol. 62, 583–619 (2011).

    Article  Google Scholar 

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Acknowledgements

We thank B. Falk for helpful discussions and S. Solomon for helpful comments on an earlier version of this paper. This work was supported by the J.D. and C.T. MacArthur, A.P. Sloan, ISI and Paul G. Allen Family Foundations, the US Army Research Laboratory (grant no. W911NF-10-20022), the Army Research Office (grant nos. Bassett-W911NF-141-0679, Grafton-W911NF-16-1-0474 and DCIST-W911NF17-2-0181), the Office of Naval Research, the National Institute of Mental Health (grant nos. 2-R01-DC-009209-11, R01MH112847, R01-MH107235 and R21-M MH-106799), the Eunice Kennedy Shriver National Institute of Child Health and Human Development (grant no. 1R01HD086888-01), the National Institute of Neurological Disorders and Stroke (grant no. R01 NS099348) and the National Science Foundation (grant nos. BCS-1441502, BCS-1430087, NSF PHY-1554488 and BCS-1631550). The content is solely the responsibility of the authors and does not necessarily represent the official views of any of the funding agencies.

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Authors and Affiliations

  1. Department of Bioengineering, School of Engineering & Applied Science, University of Pennsylvania, Philadelphia, PA, USA

    Evelyn Tang, Chad Giusti, David M. Lydon-Staley & Danielle S. Bassett

  2. Department of Living Matter Physics, Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany

    Evelyn Tang

  3. Department of Psychology, College of Arts and Sciences, University of Pennsylvania, Philadelphia, PA, USA

    Marcelo G. Mattar & Sharon L. Thompson-Schill

  4. Department of Mathematical Sciences, College of Arts and Sciences, University of Delaware, Newark, DE, USA

    Chad Giusti

  5. Department of Electrical & Systems Engineering, School of Engineering & Applied Science, University of Pennsylvania, Philadelphia, PA, USA

    Danielle S. Bassett

  6. Department of Physics & Astronomy, College of Arts & Sciences, University of Pennsylvania, Philadelphia, PA, USA

    Danielle S. Bassett

  7. Department of Neurology, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA, USA

    Danielle S. Bassett

  8. Department of Psychiatry, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA, USA

    Danielle S. Bassett

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  1. Evelyn Tang
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Contributions

E.T. developed the theory, performed the computational modeling and wrote the manuscript. E.T., M.G.M. and D.S.B. designed the study. D.S.B. M.G.M. and D.L.S. revised the manuscript. C.G. contributed intellectually to theory development through discussions. D.L.S. performed the statistical analyses and contributed to data interpretation. M.G.M. developed the experiment in collaboration with S.T.-S. and D.S.B. M.G.M. also collected and preprocessed the data. S.T.-S. acquired funding to support data collection and contributed to data interpretation. D.S.B. acquired funding to support theory development and data analysis, and contributed to theory and data interpretation.

Corresponding author

Correspondence to Danielle S. Bassett.

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Journal peer review information: Nature Neuroscience thanks Stefano Fusi and other anonymous reviewer(s) for their contribution to the peer review of this work.

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Integrated supplementary information

Supplementary Fig. 1 Increasing correlations between an individual’s behavioral accuracy and their separability dimension each day from day 1 to day 4.

The neural data on the first day does not display a significant amount of variability between fast and slow learners. We collapse across behavioral accuracy scores to understand whether they better predict a subject’s separability dimension earlier in the experiment versus later in the experiment. Visually, we find evidence for a linear increase as we move from Day 1 to Day 4. The box-plot center line is the median; box limits, upper and lower quartiles; whiskers, 1.5x interquartile range; and we use a 1000 bootstrap replications of the data available at each day from 19 subjects. An analysis of covariance with separability as the independent variable, behavioral accuracy as the dependent variable, and day as the categorical factor gives a significant main effect of day (F(df = 3) = 28.27, p < 0.001). Collectively, these results suggest that the neural representations on Day 4 most strongly reflect the effects of learning in this experiment.

Supplementary Fig. 2 Emerging relationship between the dimension of neural responses and behavioral accuracy.

We also investigate how the learning of value emerges throughout the first day. We examine how performance accuracy changes across the three learning sessions and value judgement session on the first day of training where the greatest individual differences were observed, and its correlation with stimuli separability dimension on the final day of training. We see that this correlation increases from r = 0.38 in the first learning session (top left) to r = 0.56 by the end of the first day in the value judgement session (bottom right). These data suggest that this relationship between the dimension of neural data and the response accuracy of participants emerges across sessions on the first day of training. Note that in contrast to the non-parametric permutation test used to yield p < 0.001 for the bottom right data in the main text, here we simply provide the parametric p-values from the one-sided Pearson’s correlation (df = 17, n = 19) which are much less computationally intensive to estimate.

Supplementary Fig. 3 Changes in stimulus separability dimension across 4 d.

We study the correlation of the separability dimension of neural data from the value judgment sessions at the end of each day, with the response accuracy of participants on the first day. We find that quick learners do not have a particularly large dimension of neural response patterns on the first day, r = −0.05, df = 17, p = 0.85, as compared to the fourth day, r = 0.56, df = 17, p = 0.01, suggesting that this larger dimension for quick learners takes time to emerge. Pearson’s correlations and parametric p-values reported here; n = 19 in a one-sided test.

Supplementary Fig. 4 Replication of results using the whole-brain Power parcellation.

We repeat our analyses on data obtained from a different whole-brain parcellation – a functional-based parcellation that subdivides the brain into 264 regions [Power, J.D. et al., Neuron 2011]. Left: Stimuli separability dimension of a subject’s representation on the fourth day is strongly correlated with the behavioral accuracy of n = 19 subjects from the first day, with Pearson’s r = 0.66 (one-sided) and non-parametric p < 0.001 obtained from comparison with the null model. Right: Label assortativity (retaining all twelve original labels) of the same data displays a positive trend with the response accuracy of n = 19 subjects from the first day, with Pearson’s r = 0.41 (one-sided) and non-parametric p < 0.036 obtained from comparison with the null model. As in the main text, we used a permutation test (one-sided) with n = 1000 bootstrapped samples. These results are consistent with our results obtained using the 83-region Lausanne parcellation. Note that because not all subjects had data in 3 out of the 264 regions, we retain only the 261 brain regions with data for all 19 participants.

Supplementary Fig. 5 Quick learners have an increasing dimension of representation across the experiment.

As our interests generally lie in understanding the process of learning, we are most interested in considering changes that occur during the full time course of the experiment. These changes are neatly and parsimoniously reflected by the outcomes of the learning process in terms of the neural representations on the final day. Thus, we focus the majority of our analyses on the neuroimaging data collected on this fourth and final day of training. An alternative approach is to consider changes in the neural data from the first day to the fourth day. Taking the changes in dimension of the geometric representation of each individual’s neural data, we find that these changes are positively correlated with their learning accuracy (Pearson’s r = 0.40, one-sided, n = 19 subjects). To verify that this correlation is statistically significant, we permute the differences among the 19 individuals to recalculate this correlation in n = 1000 bootstrapped samples, which yields p < 0.047, confirming our findings from the main analysis. The consistency between the results of the two analyses is likely due to the fact that the neural data on the first day does not display a significant amount of variability between fast and slow learners (see Fig. 1 in this Supplemental document).

Supplementary Fig. 6 Use of a graded learning curve for behavioral metric confirms findings.

As an alternative measure of the learning rate for each subject, we use the slope of response accuracy across all three sessions of the learning phase in Day 1. We observe that this learning rate has a positive correlation with the dimension of representation across subjects, with a non-parametric permutation test yielding p < 0.006 (n = 1000 bootstrapped samples, n = 19 subjects). Specifically, we consider the slope of response accuracy across all three sessions of the learning phase on Day 1; this metric provides an estimate of the rate at which individuals learned to associate the assigned values to the presented shapes. To unpack this metric a bit further, we note that as each session consisted of 132 trials, where responses to each trial were binary (right or wrong), we examine the number of correct responses within a given window to give an average accuracy for that window. Windows of 22 trials were chosen in order to create 6 equally sized windows for each session. Hence, the three learning sessions on Day 1 yield 18 windows, and we calculate the slope of response accuracy across those windows for each individual. Next, we calculate the correlation between this slope (or learning rate) and the dimension of the stimuli representation from day 4. We found that the two variables were positively correlated with one another (Pearson’s r = 0.34, one-sided, n = 19 subjects), confirming the findings that we report in the main text.

Supplementary Fig. 7 The choice of data partition does not affect the cross-validation results.

The analysis in this manuscript relies on cross-validation using a standard k-fold partition, where the data from each trial is randomly assigned to k-folds, such that each fold has a similar number of data points. Here, we repeat our cross-validation using a block-wise partition, where now each fold consists of data from the same temporal block. In all cases, we retain a standard k = 5 folds and divide the data such that each fold has a similar number of data points. This procedure is chosen so as to verify that our results do not depend on the standard choice of randomly assigned partitions, where neighboring trials that are temporally overlapping could be entered into training and test sets, and thereby potentially violate independence. We find that there still remains a positive correlation of Pearson’s r = 0.40 (one-sided, n = 19 subjects) between the response accuracy of the participants and their separability dimension (left), and that this result is significant with p < 0.004 when compared to the null data (right; n = 1000).

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Tang, E., Mattar, M.G., Giusti, C. et al. Effective learning is accompanied by high-dimensional and efficient representations of neural activity. Nat Neurosci 22, 1000–1009 (2019). https://doi.org/10.1038/s41593-019-0400-9

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