Bayes-Optimal Diagonal Regularization in Modal Inverse Problems Follows Closed-Form Power Law

A new machine learning theory paper establishes a 'diagonal saturation principle' for modal inverse problems. When truncation noise is isotropic, the optimal diagonal Tikhonov regularizer takes a closed-form power-law shape whose exponent is fixed entirely by the prior. The authors argue this explains why learned regularization converges on an analytic solution rather than a data-dependent one.