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


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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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.

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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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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.

Author information

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.

Competing interests

The authors declare no competing interests.

Correspondence to Danielle S. Bassett.

Integrated supplementary information

  1. 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.

  2. 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.

  3. 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.

  4. 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.

  5. 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).

  6. 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.

  7. 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).

Supplementary information

  1. Supplementary Figs. 1–7 and Supplementary Table 1

  2. Reporting Summary

  3. Supplementary Software 1

  4. Supplementary Software 2

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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.
Supplementary Fig. 1: Increasing correlations between an individual’s behavioral accuracy and their separability dimension each day from day 1 to day 4.
Supplementary Fig. 2: Emerging relationship between the dimension of neural responses and behavioral accuracy.
Supplementary Fig. 3: Changes in stimulus separability dimension across 4 d.
Supplementary Fig. 4: Replication of results using the whole-brain Power parcellation.
Supplementary Fig. 5: Quick learners have an increasing dimension of representation across the experiment.
Supplementary Fig. 6: Use of a graded learning curve for behavioral metric confirms findings.
Supplementary Fig. 7: The choice of data partition does not affect the cross-validation results.