Exact low-rank EDLAE solution under the zero-diagonal constraint

Derive an exact closed-form solution for the low-rank Enhanced Denoising Linear Autoencoder (EDLAE) optimization problem with its zero-diagonal constraint, rather than relying on ADMM or approximate low-rank constructions.

Background

EDLAE combines a weighted Frobenius-norm regularizer with the zero-diagonal constraint used by EASE. The full-rank problem has a closed-form solution, whereas existing low-rank approaches use the ADMM algorithm. The paper introduces approximate low-rank closed-form methods that relax the zero-diagonal constraint, but it does not provide an exact closed-form solution for the constrained low-rank EDLAE problem. Thus, the exact constrained formulation remains unresolved in the stated discussion.

References

Even though both the Nuclear norm based regularization as well as the full rank DLAE and EDLAE solutions all have closed-form solutions, such solution is unknown for the low-rank DLAE and EDLAE, whose existing solution is based on ADMM\citet{DBLP:conf/nips/Steck20}.

— On the Regularization Landscape for the Linear Recommendation Models  (2609.11876 - Li et al., 10 Sep 2026) in Section 4, subsection “Approximate Low rank DLAE and EDLAE.”