Sun et al. (2026) — ARXIV-2602.01003
Key takeaways
The gap it closes is standard ES’s, not GRPO’s. Standard ES averages 75.97% on GSM8K across the four models; ESSAM reaches 78.27%. Against the RL baselines it is a tie — PPO 77.72%, GRPO 78.34% — which the paper states plainly rather than dressing up. The GRPO arm is LIT-127’s algorithm, run alongside PPO on the same four Qwen2.5 models, and its 78.34% average is the highest of the four methods, 0.07 points above ESSAM. The honest headline is that a sharpness-aware ES matches RL at inference-level memory, not that it beats it.
The mechanism is SAM transposed into zeroth order. Sharpness-aware minimization normally needs a gradient to find the adversarial neighbour. ESSAM uses the reward-weighted ES aggregate instead: move the parameters in the direction that would increase sharpness, recompute perturbations and rewards at that neighbouring point, then apply the resulting direction to the original parameters. The effect is to prefer flat regions without ever computing a gradient.
Memory is the point and the numbers are large. ESSAM holds the same GPU memory footprint as plain ES — inference level, since only forward passes are required — which the paper reports as a 10–18× reduction against PPO and GRPO. That is the “10× space-efficiency” figure LIT-231 cites this paper for.
It is a direct answer to an observed weakness. The motivation is that ES underperforms on mainstream mathematical reasoning benchmarks like GSM8K, and the fix targets generalization rather than optimization speed — the paper’s own diagnosis is that plain ES overfits its sampled rewards.
The ES it modifies is LIT-211’s. The paper takes Qiu et al.’s full-parameter ES, its z-score reward normalization and its memory-saving implementation, and adds the neighbour step to its update, after arguing that plain ES’s GSM8K shortfall comes from being driven toward sharp minima. It also objects to LIT-211’s data set-up as non-standard: 200 training examples used as a whole, without shuffling or mini-batches, and 2,000 for evaluation.
What the evidence does not cover
One benchmark. GSM8K, four Qwen2.5-Instruct models at 0.5B, 1.5B, 3B and 7B. No second task, no second family.
No ablation isolating the SAM step from the extra evaluations it costs. The two-stage update evaluates perturbations twice per iteration; whether the gain comes from sharpness-seeking or from the additional sampling is not separated, which matters given that SOTA-211 is about exactly how ES should spend a doubled evaluation budget.
The flat-minima argument is inherited rather than tested. The claim that flatter solutions generalize better is imported from the SAM literature; no sharpness measurement is reported for the resulting checkpoints.
Standing in the anthology
A second way of spending an ES evaluation budget, and it points the other way from SOTA-211. That practice says do not spend two evaluations on one direction — the antithetic pair’s second evaluation buys nothing when responses are regenerated. ESSAM spends a second round of evaluations too, on something else entirely: probing a neighbouring point to steer toward flat regions. The two are not in conflict, and the contrast is the useful part — the question for an ES practitioner is not whether to spend more evaluations but on what, and the record now holds two answers with different evidence behind them.
It is also a small corroboration of the scale pattern THEORY-006 predicts, from a paper not looking for it: the per-model table is where standard ES is weakest at the small end, and the paper’s framing of ES as overfitting its sampled rewards at small scale is what a low density of task-improving perturbations would look like from the inside.