Beyond-LIR non-diagonal estimators and learned heat regularizers

Determine whether non-diagonal estimators beyond Learned Iterative Ridge can escape the diagonal regularization ceiling, and whether learned methods can outperform the analytic heat-diffusion regularizer Γ_k∝λ_k^s e^{2κtλ_k}.

Background

The paper finds that learned architectures restricted to diagonal per-mode penalties do not robustly improve on the analytic acoustic regularizer Γ_k=λ_k^{|s|}. Learned Iterative Ridge improves performance by exploiting cross-mode coupling, demonstrating that gains are possible outside the diagonal family.

Two questions remain unresolved: whether other non-diagonal estimator constructions can improve beyond Learned Iterative Ridge, and whether learning can beat the theory-derived exponential-power regularizer for heat diffusion. The paper explicitly identifies both as open directions rather than resolving them experimentally or theoretically.