General extensive-rank matrix denoising

Characterize inference for an unknown deterministic symmetric matrix with extensive rank in the Gaussian Orthogonal Ensemble observation model, beyond the previously studied rotationally invariant priors.

Background

The paper observes that extensive-rank matrix denoising can be formulated as a single-token, single-index attention-indexed model. The observation is Y = S* + Z, where S* is an unknown deterministic symmetric matrix whose operator norm is negligible relative to its Frobenius norm, and Z is GOE noise.

The authors note that existing work has extensively studied rotationally invariant priors, whereas the general extensive-rank setting is not resolved. Establishing a theory for this broader class would extend the applicability of the attention-indexed framework to matrix inference problems with non-rotationally-invariant extensive-rank signals.

References

While prior work has extensively studied rotationally invariant priors , the general extensive-rank setting remains largely open .

— High-Dimensional Learning Dynamics of Attention-Indexed Models  (2609.03858 - Xu et al., 3 Sep 2026) in Appendix, Section “Examples of attention-indexed models,” Example 5: Extensive-rank matrix denoising