Fig. 4. Exploitable nonlinearity is apparent in different open datasets but not in functional brain images.

To complement our classification of ten age/sex-stratified groups (Figs. 2 and 3), we decoupled the stratified prediction goal by separately examining continuous age regression and categorical sex classification using linear (red tones), kernel (green tones), and deep (blue tones) models. In the superconductivity benchmark dataset (a), critical temperature was predicted based on 82 physical properties like thermal conductivity, atomic radius, and atomic mass⁵³. Here, kernel and deep models clearly outperform linear models as measured by out-of-sample explained variance (R², coefficient of determination). In contrast, in age prediction based on functional brain scans (b), the best performing linear model (Ridge regression) has scaling behavior virtually identical to kernel and deep models. This age prediction using fMRI scans is conceptually similar to previous analyses on brain maturity that reported 55% explained variance on 238 subjects aged 7–30 years⁷⁰. These investigators noted “asymptotic maturation toward a predicted population mean maximum brain age of ~22 years […] The fitted models mainly differed in their predictions for younger ages.” In our much older UKBiobank subjects (62.00 ± 7.50 years), we reach ~40% explained variance, whereas the learning curves suggest further performance gains as more brain data become available. We identify a similar discrepancy between machine learning and brain-imaging datasets in the binary classification setting. In even (0, 2, 4,…) vs. odd (1, 3, 5,…) digit classification on MNIST (c), kernel and deep models diverge from linear models in classification accuracy as the sample size increases. However, the kernel and deep models are not superior in sex classification based on fMRI data (d), where all examined models showed virtually identical prediction performance. The number of input variables in a modeling scenario is denoted by p. IDP = image-derived phenotype. Error bars = mean ± SD across 20 cross-validation iterations (all panels).