Quantifying the compressibility of the human brain

TL;DR

The study addresses how many and which inter-regional brain correlations are needed to predict cortex-wide neural activity. It proposes a minimax entropy framework on Gaussian graphical models, solved by a greedy edge-addition algorithm to minimize the network entropy $S_G$ and yield a compression curve $\\tilde{S}(f)$. Applying this to cortex-wide fMRI from 99 subjects and 100 parcels reveals extreme brain compressibility: a small fraction of correlations suffices to explain most structure, and the most informative connections are not merely the strongest but tend to span across cognitive systems. These findings imply a sparse backbone of influential interactions and provide a scalable method to quantify brain compressibility across individuals, tasks, and modalities, with broad implications for understanding neural constraints and disease.

Abstract

In the human brain, the allowed patterns of activity are constrained by the correlations between brain regions. Yet it remains unclear which correlations -- and how many -- are needed to predict large-scale neural activity. Here, we present an information-theoretic framework to identify the most important correlations, which provide the most accurate predictions of neural states. Applying our framework to cortical activity in humans, we discover that the vast majority of variance in activity is explained by a small number of correlations. This means that the brain is highly compressible: only a sparse network of correlations is needed to predict large-scale activity. We find that this compressibility is strikingly consistent across different individuals and cognitive tasks, and that, counterintuitively, the most important correlations are not necessarily the strongest. Together, these results suggest that nearly all correlations are not needed to predict neural activity, and we provide the tools to uncover the key correlations that are.

Figures (9)

• Figure 1: Fig. \ref{['fig:intro']}$|$ Quantifying uncertainty given a network of correlations.a-b, Covariance matrix (a) and network representation (b) for a minimal system of four regions with z-scored activity (Methods). c-d, Networks of correlations $G$ (c) and the covariances predicted by the corresponding maximum entropy models $P_G$ (d). The network formed by the three strongest covariances produces accurate predictions for all covariances (middle). e, Illustration of the normalized entropy $\tilde{S}$ versus the fraction of correlations (or the density of the network $G$) for neural activity that is either more compressible (blue) or less compressible (red). In a more compressible system, one can achieve lower uncertainty for a given number of correlations (vertical line), and one can find a sparser network (with fewer correlations) to achieve a given level of uncertainty (horizontal line).
• Figure 1: Fig. S\ref{['fig:entropy_predictions']}$|$ Information gained from adding a constraint can be predicted accurately.a, Predicted and true information gains from adding each possible next constraint to the optimal network with 100 correlations fit, for the combined fMRI data, versus the error on the prediction of the corresponding covariance before it is fit. For each of true and predicted, each point represents one of the 4850 possible correlations that could be added to become the 101st edge in the network. b, Predicted information gain from adding each possible next constraint to the optimal network with 100 correlations fit, for the combined fMRI data, versus the true information gain. Each point represents one of the 4850 possible correlations that could be constrained. The diagonal line represents a slope of one.
• Figure 2: Fig. \ref{['fig:results1']}$|$ Human neural activity is highly compressible.a, Normalized entropy $\tilde{S}_G$ as a function of the fraction of correlations in $G$ for the optimal networks (blue), strongest correlations $|\Sigma_{ij}|$ (orange), and random networks (red). b, Covariances between brain regions measured in activity concatenated across all subjects and tasks. c-d, Predicted covariances based on the optimal networks (c) and random networks (d) with different fractions of the correlations. e-f, Predicted covariances versus their true values for models constructed from optimal networks (e) and random networks (f). Lines and shaded regions indicate means and standard deviations across all covariances that are not included in each model.
• Figure 2: Fig. S\ref{['fig:heuristics']}$|$ Model entropy for heuristic methods.a, Normalized model entropy of models of the combined fMRI data for various heuristics for selecting correlations to add to the model, compared to optimal and random methods. Here $\rho$ stands for partial correlation, $\Sigma$ is the data covariance, $\Sigma^{-1}$ is the data precision matrix, and MI stands for mutual information. b, Same as a but with log scale y-axis and for fraction of correlations between 0 and 0.2
• Figure 3: Fig. \ref{['fig:results3']}$|$ Quantifying compressibility across subjects and cognitive tasks.a, Optimal normalized entropy $\tilde{S}(f)$ versus the fraction of correlations $f$ for data combined across all tasks and subjects. Compressibility is the shaded area above the compression curve. Inset displays compressibility values for optimal, maximum correlation, and random networks. b-c, Normalized entropy versus fraction of correlations in optimal (blue), maximum correlation (orange), and random (red) networks for data within specific tasks (b) and within specific subjects (c). Insets display compressibility values averaged across tasks (b) and across subjects (c) with one-standard-deviation error bars. d, Average overlap (fraction of shared correlations) between optimal networks for pairs of tasks (blue) and pairs of subjects (yellow) versus the fraction of correlations. Red line illustrates the overlap between random networks.