A Scaling Study for fMRI Foundation Models

Clinical risk prediction using longitudinal medical data supports individualized care. Self-supervised foundation models have emerged as a promising approach for leveraging large-scale unlabeled healthcare records. In natural language processing, scaling laws suggest that larger models achieve predictably lower pretraining losses, supporting the foundation model paradigm. However, for structured medical data, characterized by a limited vocabulary and sparse observations, whether increasing model size consistently improves downstream predictions is unclear, as most studies evaluate only a single model scale. In this study, we evaluated the relationship between model scale and downstream task performance for structured medical foundation models. Using a random sample (2.3 million patients, 32 hospitals) from a nationwide 519-hospital Japanese claims database, we pretrained encoder-only Transformers at five scales (2.2M-101M parameters) for disease incidence and medication prediction. Downstream performance saturated at task-dependent thresholds: disease prediction benefited from larger models (32M-101M), whereas medication prediction saturated at 11M, reducing pretraining time by 178 h. Across all tasks, the best-performing model consistently outperformed a Light Gradient Boosting Machine baseline in the area under the precision-recall curve. These findings indicate that, unlike the monotonically decreasing pretraining loss, the optimal model size varied depending on task characteristics. This task-dependent saturation provides practical guidance for balancing predictive performance and computational cost in structured medical foundation models.

fMRI foundation models increasingly aggregate heterogeneous data across brain states, cohorts, and acquisition settings, yet pretraining domains are commonly treated as a flat mixture and downstream tasks are adapted independently. We study whether measured learning relations can organize both stages without modifying the backbone. During pretraining, a lightweight Brain-DiT proxy estimates difficulty and directed facilitation across ten fMRI domains, yielding a priority-guided cumulative domain curriculum combined with high-to-low-noise timestep scheduling and joint consolidation. During adaptation, controlled first- and higher-order transfer across fifteen tasks constructs a directed taskonomy, from which budgeted integer programming (BIP) selects directly supervised source tasks and target-specific routes. The joint priority-domain and high-to-low-timestep curriculum reduces v-NMSE, PSD-NMSE, and FC-MSE by 6.5%, 16.3%, and 10.5%, respectively, relative to uniform sampling over both dimensions, and shows strong downstream performance across six in- and out-of-domain tasks. The taskonomy reveals asymmetric, target-dependent transfer, while exploratory sealed-test evaluation shows larger descriptive gains for BIP policies when higher-order route spaces are available than for matched random controls. Together, these findings support organizing fMRI pretraining and adaptation by measured learning relations rather than treating domains and tasks as independent flat sets.

Brain foundation models (BFMs) are self-supervised Transformers pretrained on fMRI data. We posit that these models should capture each subject's cognitive performance from their fMRI signal. Yet across three state-of-the-art BFMs and every readout we test, they predict cognition worse than a linear regression from the $\sim$80K parameters of the functional connectivity matrix (FC). The gap widens with scale: BrainLM's 650M model predicts cognition worse than its 111M. We attribute this to a \textbf{variance allocation problem}: BFM pretraining captures the variance components that dominate fMRI but not the higher-order structure that predicts cognition. Our per-cumulant analysis of the reconstructed signal shows that the second-order covariance is partially preserved, while the third-order co-skewness tensor is largely destroyed. To recover what BFMs lose, we design a linear pipeline that projects the fMRI signal into the subspace that best preserves its co-skewness and computes FC there. This \textbf{exceeds raw FC and every pretrained BFM} on every dataset and parcellation we test, outperforming prior state-of-the-art under controlled evaluation \textbf{with no pretraining and no GPU}. We \textbf{recover the raw-FC ceiling on BrainLM's forward pass} by finetuning with a loss targeted at this same subspace. This shows that the bottleneck is the pretraining objective, not the architecture or the model size.