Sarkar et al. (2025) — ARXIV-2511.16652
Key takeaways
The bottleneck it removes is arithmetic intensity, not memory alone. Naïve
ES at scale is slow on GPUs because batched matrix multiplications against
unstructured random perturbations have nothing for the hardware to exploit.
EGGROLL structures each worker’s perturbation as a rank-r product of two
small Gaussian matrices in place of the full-rank E. Auxiliary storage per
layer falls from O(mn) to O(r(m+n)) and the forward pass gets cheaper by
the same argument — but the update is an average over N workers, so it
stays high-rank. The saving is per-worker; the expressiveness is in the
population.
The headline number is throughput, and it is large. A hundredfold increase in training speed for billion-parameter models at large population sizes, reaching up to 91% of the throughput of pure batch inference — which is the right ceiling to quote, because it says the optimizer has stopped being the bottleneck at all.
There is a convergence result, not just an engineering claim. The paper
analyses Gaussian ES for high-dimensional objectives, reports a linearising
effect in high dimensions, and proves consistency between the low-rank and
full-rank updates as parameter dimension grows, at an O(1/r) rate. That is
what licenses reading r = 1 as an approximation rather than a different
algorithm.
Three experimental claims, and they are about different things. It pre-trains nonlinear recurrent language models operating purely in integer datatypes — a thing backpropagation cannot do, and the strongest argument in the paper for gradient-free optimization existing at all. It is competitive with GRPO for post-training LLMs on reasoning. And it does not cost performance against full-rank ES in tabula rasa RL despite being much faster.
Its criticism of the prior ES-at-scale work is about population size. It names Qiu et al.’s approach, and Korotyshova et al.’s, as using “relatively small population sizes, on the order of a hundred unique perturbations per update”, collecting hundreds of rollouts per perturbation to keep GPUs busy. EGGROLL instead lets every generation use a different perturbation, so the population per update is orders of magnitude larger — bounded by the inference batch size rather than by the cost of drawing noise.
What the evidence does not cover
The LLM reasoning results are on RWKV-7, not on transformers. Countdown with an RWKV-7 1.5B (35% against GRPO’s 23% at equal hardware and wall clock) and GSM8K with an RWKV-7 7B. The paper is upfront that the recurrent architecture is especially suited to this, because memory not spent on a KV cache can be spent on population members. That is a real advantage of the pairing and it is also a reason the transformer case is not established here. Both arms were hyperparameter-swept, which is the part of the comparison that is done right.
“Competitive with GRPO” is the paper’s own phrasing for the LLM results, and it is the honest one. The Countdown figure where it reports 72.9% against 52.8% for GRPO and 66.8% for OpenES starts from a weaker base model (RWKV-7g7B against Qwen2.5-7B), which makes it a striking result and not a like-for-like one.
Zeroth-order pretraining is argued to be unsuitable, by this paper. It finds large population sizes necessary for pretraining performance and reads that as evidence that zeroth-order methods would not do for pretraining — worth recording because it is a negative result from the group with the most reason to want the opposite.
Standing in the anthology
The engineering half of the ES post-training line, where LIT-211 is the
existence half. LIT-211 showed that searching the full parameter space of a
billion-parameter LLM works at all; this shows it can be made to run at
inference-grade throughput, which is what turns SOTA-154 from a result into
something a practitioner could schedule. The two are one line and not rivals,
which is why extends: and not compared_against:.
It also sharpens what the line’s remaining question is. Once perturbations are structured and populations are enormous, the difference between this and the other members of the family is a choice about where the search budget goes — many cheap directions or few expensive ones — rather than about whether gradient-free post-training is viable.