EGGROLL, Unrolled: Understanding and Improving Low-Rank Evolution Strategies at Scale
Updated 15 min ago · first seen 11 Sept 2026
paper_01M294FNXNJGMXMH6604MBQD9K
- Published
- 11 Sept 2026
- T1 · 15 min ago
- arXiv
- 2609.10980
- T1 · 15 min ago
- Category
- cs.LG
- T1 · 15 min ago
Abstract
EGGROLL 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 mean EGGROLL update field at finite rank and nonzero perturbation radii, then analyze the error of its finite-population estimator. The population field is obtained by applying an explicit resolvent to the gradient of the objective smoothed by the perturbations. We show that the resolvent can introduce a nonconservative component and can reverse the local stability of an optimum. EGGROLL is nevertheless exact on every quadratic objective at every rank and radius. For smooth objectives, its first local finite-rank correction is $O(\sigma^2/r)$, and nonasymptotic bounds control the resulting field error under smoothness assumptions. Under a local affine model, rank-one perturbations increase the variance of the gradient estimator by only $\frac{2(m+n+1)}{mn+1}$ relative to dense Gaussian ES, or $0.098\%$ for a $4096\times4096$ matrix. We then introduce LOO-ROLL, a leave-one-out estimator that preserves the finite-rank population field while replacing EGGROLL's two antithetic evaluations per direction by one. At equal evaluation cost, LOO-ROLL halves estimator MSE in transformer blocks. At matched wall time across ten post-training settings and models up to 8B parameters, LOO-ROLL improves seven outcomes in individual paired tests, with no significant loss. On the GSM8K test set, accuracy increases from $38.1\%$ to $63.0\%$ at 0.6B and from $65.9\%$ to $80.0\%$ at 8B. Transformer measurements recover the predicted finite-rank variance, while the rank comparisons show no reproducible reward-based advantage for rank eight.
Authors 2
Ege C. Kaya, Abolfazl Hashemi
Specification
- Official page
Source:arXiv (Atom API + RSS)T1observed 15 min agohigh
- Arxiv announce type
- new
Source:arXiv (Atom API + RSS)T1observed 15 min agohigh
- arXiv id
- 2609.10980
Source:arXiv (Atom API + RSS)T1observed 15 min agohigh
- Categories
- cs.LG, cs.AI, math.OC
Source:arXiv (Atom API + RSS)T1observed 15 min agohigh
Source:arXiv (Atom API + RSS)T1observed 15 min agohigh
- Primary category
- cs.LG
Source:arXiv (Atom API + RSS)T1observed 15 min agohigh
- Published
- 11 Sept 2026
Source:arXiv (Atom API + RSS)T1observed 15 min agohigh
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9
Source tiers
T19
Freshest observation
15 min ago
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- Authors
- Ege C. Kaya, Abolfazl Hashemi
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Claim history
Official pageofficial_url1
| Value | Valid from → to | Status | Source | Confidence | Extractor |
|---|---|---|---|---|---|
| https://arxiv.org/abs/2609.10980 | → current | current | arXiv (Atom API + RSS)T1 | high | deterministic |
Abstractabstract1
| Value | Valid from → to | Status | Source | Confidence | Extractor |
|---|---|---|---|---|---|
| EGGROLL 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 mean EGGROLL update field at finite rank and nonzero perturbation radii, then analyze the error of its finite-population estimator. The population field is obtained by applying an explicit resolvent to the gradient of the objective smoothed by the perturbations. We show that the resolvent can introduce a nonconservative component and can reverse the local stability of an optimum. EGGROLL is nevertheless exact on every quadratic objective at every rank and radius. For smooth objectives, its first local finite-rank correction is $O(\sigma^2/r)$, and nonasymptotic bounds control the resulting field error under smoothness assumptions. Under a local affine model, rank-one perturbations increase the variance of the gradient estimator by only $\frac{2(m+n+1)}{mn+1}$ relative to dense Gaussian ES, or $0.098\%$ for a $4096\times4096$ matrix. We then introduce LOO-ROLL, a leave-one-out estimator that preserves the finite-rank population field while replacing EGGROLL's two antithetic evaluations per direction by one. At equal evaluation cost, LOO-ROLL halves estimator MSE in transformer blocks. At matched wall time across ten post-training settings and models up to 8B parameters, LOO-ROLL improves seven outcomes in individual paired tests, with no significant loss. On the GSM8K test set, accuracy increases from $38.1\%$ to $63.0\%$ at 0.6B and from $65.9\%$ to $80.0\%$ at 8B. Transformer measurements recover the predicted finite-rank variance, while the rank comparisons show no reproducible reward-based advantage for rank eight. | → current | current | arXiv (Atom API + RSS)T1 | high | deterministic |
Arxiv announce typearxiv_announce_type1
| Value | Valid from → to | Status | Source | Confidence | Extractor |
|---|---|---|---|---|---|
| new | → current | current | arXiv (Atom API + RSS)T1 | high | deterministic |
arXiv idarxiv_id1
| Value | Valid from → to | Status | Source | Confidence | Extractor |
|---|---|---|---|---|---|
| 2609.10980 | → current | current | arXiv (Atom API + RSS)T1 | high | deterministic |
Categoriescategories1
| Value | Valid from → to | Status | Source | Confidence | Extractor |
|---|---|---|---|---|---|
| cs.LG, cs.AI, math.OC | → current | current | arXiv (Atom API + RSS)T1 | high | deterministic |
PDFpdf_url1
| Value | Valid from → to | Status | Source | Confidence | Extractor |
|---|---|---|---|---|---|
| https://arxiv.org/pdf/2609.10980 | → current | current | arXiv (Atom API + RSS)T1 | high | deterministic |
Primary categoryprimary_category1
| Value | Valid from → to | Status | Source | Confidence | Extractor |
|---|---|---|---|---|---|
| cs.LG | → current | current | arXiv (Atom API + RSS)T1 | high | deterministic |
Publishedpublished_at1
| Value | Valid from → to | Status | Source | Confidence | Extractor |
|---|---|---|---|---|---|
| 11 Sept 2026 | → current | current | arXiv (Atom API + RSS)T1 | high | deterministic |
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New paper: EGGROLL, Unrolled: Understanding and Improving Low-Rank Evolution Strategies at Scale
arxiv
| Source | Document | Type | Tier | Last observed | Snapshots |
|---|---|---|---|---|---|
| arXiv (Atom API + RSS) | rss.arxiv.org/rss/cs.LG | feed | T1· Official | 15 min ago | 1 |
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