EGGROLL, Unrolled: Understanding and Improving Low-Rank Evolution Strategies at Scale
EGGROLL (Sarkar et al., 2026) makes evolution strategies (ES) practical for LLMs by replacing dense Gaussian weight perturbations with low-rank Gaussian products, often of rank one. This choice is computationally attractive but geometrically severe: Each rank-one perturbation lies in a zero-volume subset of the ambient matrix space, despite having identity covariance. We characterize the EGGROLL update mean field at finite rank and nonzero perturbation radius as a resolvent applied to the gradient of the perturbation-smoothed objective. This transformation can make the mean field nonconservative and reverse the local stability of an optimum. EGGROLL nevertheless recovers the gradient exac...
| Authors | Ege C. Kaya, Abolfazl Hashemi |
|---|---|
| Primary category | cs.LG |
| Published | 10 September 2026 |
| Last updated at source | 25 September 2026 |
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