Evolution With Purpose: Hierarchy-Informed Optimization of Whole-Brain Models

TL;DR

This work addresses overfitting and limited cross-subject transfer in large-scale brain models by embedding biological structure into evolutionary optimization. By comparing a homogeneous parameterization with a heterogeneous, RSN-specific parameterization across five curricula, the authors show that a cortex-wide, hierarchy-informed curriculum (HICO) yields superior generalization and robust, behaviorally informative solutions. The key contributions include demonstrating that curriculum-guided, biologically grounded search improves cross-subject stability, enables reliable prediction of cognitive and psychopathology-related behaviors, and reveals distinct geometry of the learned parameter space. The findings suggest that domain-informed inductive biases are essential for scalable, interpretable, and translational whole-brain modeling, with potential applications to large datasets and clinical interventions.

Abstract

Evolutionary search is well suited for large-scale biophysical brain modeling, where many parameters with nonlinear interactions and no tractable gradients need to be optimized. Standard evolutionary approaches achieve an excellent fit to MRI data; however, among many possible such solutions, it finds ones that overfit to individual subjects and provide limited predictive power. This paper investigates whether guiding evolution with biological knowledge can help. Focusing on whole-brain Dynamic Mean Field (DMF) models, a baseline where 20 parameters were shared across the brain was compared against a heterogeneous formulation where different sets of 20 parameters were used for the seven canonical brain regions. The heterogeneous model was optimized using four strategies: optimizing all parameters at once, a curricular approach following the hierarchy of brain networks (HICO), a reversed curricular approach, and a randomly shuffled curricular approach. While all heterogeneous strategies fit the data well, only curricular approaches generalized to new subjects. Most importantly, only HICO made it possible to use the parameter sets to predict the subjects' behavioral abilities as well. Thus, by guiding evolution with biological knowledge about the hierarchy of brain regions, HICO demonstrated how domain knowledge can be harnessed to serve the purpose of optimization in real-world domains.

Figures (6)

• Figure 1: Large-scale cortical organization used to define RSN-specific parameter blocks. (a) Surface renderings of a 400-region cortical parcellation mapped to the seven canonical RSNs of Yeo2011, shown for lateral and medial views of both hemispheres. Colors denote Visual, Somatomotor, Dorsal Attention, Ventral Attention, Limbic, Frontoparietal Control, and Default Mode RSNs. (b) Distribution of parcels along the principal macroscale gradient of cortical organization (Gradient 1), ordered from unimodal sensory–motor systems to transmodal association cortex. This gradient defines the hierarchical ordering used to construct curriculum phases in the proposed optimization framework.
• Figure 2: Distribution of fitness scores across optimization strategies when models were optimized separately for each individual subject. The points represent subjects and the boxes show the interquartile range (IQR) with median (solid line) and mean (dashed line). Unpaired statistical tests against the homogeneous baseline indicate that the heterogeneous, HICO, and reverse curricula achieve significantly higher fitness, demonstrating the advantage of increased model dimensionality. In contrast, the shuffled curriculum fails to realize this benefit, suggesting that the curriculum needs to be systematic to take advantage of such dimensionality.
• Figure 3: Leave-one-out (LOO) fitness distributions across optimization strategies. Violin plots show the distribution of LOO fitness scores across subjects, with embedded boxplots indicating median and interquartile range; triangles denote means. Homogeneous and flat heterogeneous strategies collapse to zero LOO fitness across the board, reflecting dynamical instability LOO fitness calculation. In contrast, curriculum-based strategies—particularly HICO and reverse-phased curricula—maintain robust, non-degenerate LOO performance, indicating improved cross-subject generalization.
• Figure 4: UMAP embedding of subject-level parameter vectors (averaged by parameter type). Each point is a subject, colored according to the approach used. Curriculum-based methods (HICO, Reverse, Shuffled) occupy a large overlapping region of parameter space, whereas homogeneous and heterogeneous approaches form distinct, focused clusters shifted away from this region. As seen in Fig. \ref{['fig:loo_boxplot']}, the generalization properties are very different in these two areas.
• Figure 5: Predicting behavior based on solutions obtained by the different optimization strategies. Each subplot reports ridge regression $R^{2}$ values (across RSNs) for a different behavioral target: (A) fluid reasoning ability (PMAT24_A_CR), (B) inwardly directed affective and somatic symptoms (ASR_Intn_Raw), and (C) outwardly directed behavioral tendencies (ASR_Extn_Raw). For each optimization strategy, colored points show the $R^{2}$ values obtained for the seven individual RSNs, and error bars indicate the mean $\pm$ standard deviation across RSNs. Reported $p$-values and $q$-values correspond to permutation-based significance testing with False Detection Rate (FDR) correction. Across all targets, only HICO produced solutions that encode behaviorally relevant information.