Source
Kaya and Hashemi (2026), LIT-232 — ARXIV-2609.10980; Ba et al. (2026), LIT-230 — ARXIV-2608.27351.
What the antithetic pair was for, and why it stops paying here
Standard practice evaluates both θ + σE and θ − σE for each direction and
subtracts. The subtraction cancels whatever the two evaluations share — the
reward offset, and every even-order term of the local expansion — which is a
real variance reduction, and it is why two-point zeroth-order estimators are
the default on supervised tasks.
The cancellation depends on the pair sharing randomness, and reasoning tasks break that. A supervised objective re-scores fixed data, so the paired evaluations differ only in the perturbation. A reasoning objective regenerates an autoregressive response, and an early-token divergence sends the two rollouts down different paths. LIT-230 measures exactly this: raw variance reduction on SST-2, but not reliably on regenerated GSM8K rewards, and no training-reward or held-out advantage from the second evaluation.
The replacement, which is cheaper than it sounds
LIT-232’s LOO-ROLL removes the population-level reward offset with a leave-one-out baseline instead of an antithetic partner. The point is that this baseline is free: it comes from the population mean that ES score centering already computes. No extra fitness evaluations, no extra model-sized state, no extra communication rounds, and the expected update field is unchanged before standardization.
So the same evaluation budget funds N independent directions where it
previously funded N/2 antithetic ones. At equal evaluation cost that
halves estimator MSE in transformer blocks.
Measured end to end across ten matched-wall-time post-training settings on models up to 8B: seven improvements in individual paired tests, three unresolved, no significant loss, five gains surviving Holm correction. GSM8K accuracy rises at both 0.6B and 8B.
Conditions, and one place this reverses
Reasoning and other regenerating objectives. The whole argument rests on the paired coupling being weak. On a supervised task that re-scores fixed data, the coupling holds, the antithetic estimator does its job, and LIT-230 measures the variance reduction working. Do not carry this across.
The two sources argue for slightly different things. Ba et al. use plain one-point estimation and find the second evaluation buys nothing. Kaya and Hashemi derive a leave-one-out baseline that provably preserves the expected field. The shared instruction is don’t spend two evaluations on one direction; the leave-one-out construction is the better-supported way to act on it, which is why it is the primary source.
It is a change to the estimator, not to the search. Population size, perturbation scale and reward normalization are separate decisions, and LIT-230 reports that the perturbation scale has a two-sided failure mode — too small overfits the sampled rewards into a local optimum, too large destabilizes training.
Where this sits
This is an implementation decision inside SOTA-154 rather than an alternative to it, and inside LIT-229’s low-rank machinery in particular — whose reference implementation ships the antithetic pairs this practice argues against. It is filed separately because it is a claim about the estimator, and someone running any ES variant faces it.