Example. Equivariance neither guarantees nor precludes recovery [ftip-00BR]
Example. Equivariance neither guarantees nor precludes recovery [ftip-00BR]
The source records controls on both sides of the proposed implication. Its ScaledGD-inspired control is equivariant but equalizes the spectral schedule and does not recover the planted low-rank target at the declared budget. A long-anneal sign update is non-equivariant but eventually reaches a low-recovery-error regime.
The controls are reported in Remark 4.7 and Appendix D.10 of The loss does not see the basis, but Adam does[singh2026lossbasis]. The source reports no tuned reproducibility baseline for the ScaledGD control. The diagram is not a convergence theorem.