AI RESEARCH
Discrete Double-Bracket Flows for Isotropic-Noise Invariant Eigendecomposition
arXiv CS.LG
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ArXi:2602.13759v2 Announce Type: replace We study eigendecomposition on $SO(n)$ under streaming observations $C_k = C_{\mathrm{sig}} + \sigma_k^2 I + E_k$, where the isotropic background $\sigma_k^2 I$ may be time-varying and arbitrarily large. Standard algorithms couple their stability to $\lVert C_k \rVert_2 \approx \sigma^2$, forcing step sizes, contraction rates, and iteration counts to degrade with the noise floor. We observe that $\sigma^2 I$ lies in the center of the matrix algebra and therefore *should never enter* the eigenspace dynamics.