The Variance Brain Foundation Models Forgot: Third-Order Statistics Predict Cognition Where Billion-Parameter Models Fail

ArXi:2606.04010v1 Announce Type: cross 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 pre.