Source
Hoy et al. (2026), LIT-235.
What was actually shown
Decompose the displacement an ES run accumulates into two parts: the component lying in directions where the loss actually changes, and everything else. The second part is loss-invariant by construction, so nothing in the objective pushes back on it and it performs an unbiased random walk. The paper gives its size: the squared norm of the off-manifold displacement grows as
‖Δθ_off‖² ∝ σ² · d · T / N
with σ the perturbation scale, d the parameter dimension, T the number
of steps and N the population size. In a high-dimensional landscape where
most directions carry negligible curvature — which is what an LLM’s loss
surface is — this term dominates the total displacement.
What could have come out the other way. The scaling is a prediction with four handles, and the paper reports LLM weight matrices exhibiting the predicted random-walk behaviour with the theoretical scaling matching observation. It also predicts consequences that are separately checkable and were separately observed: the ES update direction should look like a random direction when probed on held-out tasks (it does, where GRPO’s looks sharply task-aligned); ES and GRPO directions should be nearly orthogonal (they are); the loss should be flat along the ES displacement (it is); and the two solutions should be linearly connected with no barrier despite all of that (they are, on four tasks).
The last is the one that would have been hardest to explain away. Two optimizers travelling in almost perpendicular directions, two orders of magnitude apart in distance, landing in a basin with no wall between them is a strange fact on any account except this one.
What this explains, and how much
It dissolves an argument three papers in this record were having without realising it. LIT-237 measured ES drift at roughly 1000× GRPO’s and concluded it causes catastrophic forgetting. LIT-230 measured it at roughly 40×, found the performance gains survive zeroing most of it, and concluded it is harmless. LIT-231 measured the same geometry and concluded the search is not finding anything at all. On this account all three are looking at the off-manifold walk: it is genuinely enormous, it genuinely carries almost no task information, and whether it is harmful is a question about what else you were measuring, not about the drift.
And it makes the drift controllable, which no previous document in this
line could. T and N are knobs a practitioner sets. Drift accumulates with
steps and falls with population size, so the same task accuracy bought with a
larger population and fewer steps costs less displacement. SOTA-213 is
that instruction, and LIT-235’s own continual-learning result — ES
“remains competitive sequentially when its iteration budget is controlled” —
is the first evidence it works.
On SOTA-154 it supplies something the practice had been missing in a different place from THEORY-006. That account says why there is anything worth finding near the pretrained weights; this says what the search does with the rest of the space while it looks.
The confirmation that promoted this
Schweighofer et al. (LIT-238) took the scaling as a prediction and
tested the handle this account is most useful for. Raising the ES population
from 30 to 128 cuts the update norm by about half — which is what an
inverse dependence of the squared norm on N predicts for a 4.3× increase —
and prior-task degradation falls monotonically across population sizes 30, 128
and 256 (their Table 1). Their own summary: “the update norm is indeed
inversely proportional to the population size.”
That is the promotion condition, met in the terms it was written in: an
independent group — no shared authors with LIT-235 — on a different
model, Qwen2.5-3B rather than Qwen3-4B, with N varied directly at fixed T
rather than the dependence inferred from the algebra.
One refinement arrived with it, and it sharpens the account rather than qualifying it. Even at population 256 or with an anchor penalty, ES update norms stay an order of magnitude above GRPO’s — yet the distributional shift on prior tasks becomes comparable to GRPO’s. So the harm is not carried by the size of the walk: “it is the randomness of the drift unconstrained by the target task that leads to prior task forgetting for ES, rather than the magnitude of updates alone.” Displacement is the thing that scales; what a displacement costs depends on whether anything constrained its direction.
What this does not say
It does not say the off-manifold walk is harmless. Loss-invariant means invariant for the objective being optimized. Everything the training reward does not measure — every prior capability, every held-out benchmark — is free to degrade along exactly those directions, and LIT-237 reports that it does, on a long enough horizon. The account explains why the damage is invisible to the training signal; it does not make it not damage.
The validation is still narrow even after the confirmation. Two models,
Qwen3-4B and Qwen2.5-3B, both below 5B, and the second paper varies N across
three values on one task. d and σ — the other two terms — have never been
varied against the prediction at all.
The decomposition is cleaner than any measurement of it can be. “On-manifold” and “off-manifold” are exact only where the loss is exactly flat; real directions have small nonzero curvature, and how the accounting degrades as curvature grows is not characterized here.
It does not adjudicate the failed replication. LIT-237 reports GRPO ahead of ES on three of four tasks at 1B–1.5B. Nothing in this account says who wins on accuracy; it says why the two winners look so different in parameter space when they tie.