De-floored Principal Component Regression: When Rank Selection Alone Is Insufficient for Prediction

What the math gives to ML

The paper isolates a failure mode of spectral truncation: selecting the correct rank does not remove a nearly isotropic sample-space floor added by high-rank covariance tails. Its transferable asset is the separation between denominator inflation, controlled by first spectral mass, and the prediction cost of subtracting the floor, controlled by squared spectral mass. This suggests a low-rank neural-network preconditioner that estimates an isotropic covariance floor and subtracts it only inside the retained eigenspace, while enforcing a positive denominator margin for stability. The most direct test is on feature covariance in a final layer or blockwise optimizer, where this correction can be compared against ordinary low-rank covariance preconditioning.