September's EMA experiment measured exactly two decay values on the SGD recipe and left a dangling thread: 0.999 catastrophically bad, 0.99 cosmetically good, nothing in between and nothing beyond. Then the stacking post carried decay 0.99 onto the Adam recipe without re-measuring it — an inherited number of precisely the kind this blog keeps catching in other people's configs. The fix is the same one that worked for label smoothing: stop defending a point and sweep the curve. Six decays — 0.9, 0.97, 0.99, 0.995, 0.999, 0.9999 — on the tuned Adam recipe, ten seeds.
The instrument deserves a sentence, because it's the best part. EMA's audit trick from September scales: all six shadows ride inside the same training run, updated from the same weight trajectory after every optimizer step. One run yields seven evaluations — raw plus six decays — so every comparison below is paired at the strongest possible level: same seed, same batches, same trajectory, different averaging window. The entire six-arm, ten-seed sweep cost ten training runs, about twenty-five minutes.
A shelf, then a cliff, then a crater
Each decay's effective averaging window is roughly 1/(1−d) optimizer steps, against a total budget of 3,900 steps. That number turns out to be the only thing on the table that matters.
| decay | window | accuracy (10 seeds) | paired delta vs raw | t | wins |
|---|---|---|---|---|---|
| raw weights | — | 89.75 ±0.18 | — | — | — |
| 0.9 | ~10 steps | 89.80 | +0.050 | +2.7 | 8/10 |
| 0.97 | ~33 | 89.86 | +0.109 | +3.6 | 8/10 |
| 0.99 | ~100 | 89.85 | +0.104 | +2.0 | 8/10 |
| 0.995 | ~200 | 89.83 | +0.080 | +1.4 | 6/10 |
| 0.999 | ~1,000 | 85.00 | −4.75 | −18.4 | 0/10 |
| 0.9999 | ~10,000 | 11.55 | −78.2 | −159 | 0/10 |
Read the top four rows first. Across a 20x range of window sizes — 10 steps to 200 — the paired deltas are +0.05 to +0.11, all within a whisker of each other. There is no optimum to find up here; it's a shelf. The agonizing-over-decimals question ("0.97 or 0.99 or 0.995?") that EMA discussions love is, on this recipe, worth at most six hundredths of a point, and the pairing is tight enough to say so with confidence: the best row (0.97, t = 3.6) is statistically real, but its advantage over its neighbors isn't. Any window that fits comfortably inside the cosine schedule's annealed tail buys the same small, genuine, cosmetic improvement — consistent with September's hypothesis that a schedule annealing to zero already delivers the endpoint pre-smoothed, leaving EMA little to do.
Then the window crosses out of the tail and the curve stops being polite. At 1,000 steps — a quarter of the whole run — the shadow blends in weights from epochs where the learning rate was still high and the model measurably worse: −4.75, ten losses in ten. That's steeper than the −3.08 the same decay cost on the SGD recipe, so the cliff isn't an SGD quirk; if anything Adam's early trajectory is worse to remember. And at 10,000 steps the window is now 2.5x longer than the entire training run, which means the shadow is approximately a uniform average over the whole trajectory — including the random initialization it started from. That model scores 11.55 ±1.55 percent on a 10-class problem. Not degraded: statistically indistinguishable from guessing. The same codebase, the same run, the same trick that earns +0.1 at decay 0.97 hands you a coin-flipper at 0.9999, four keystrokes away.
One more diagnostic hiding in the deltas: their seed-to-seed standard deviation grows monotonically with the window — 0.06 at decay 0.9, 0.16 at 0.99, 0.18 at 0.995, 0.82 at 0.999. The longer the window, the more of the run's noisy history it drags into the final weights, so even before the cliff you can see the averaging reaching back into territory that varies run by run. The shelf isn't just flat in the mean; it gets quietly riskier toward its edge.
The knob is secretly binary
The honest summary of this curve: EMA's decay is not a dial that trades off more-versus-less smoothing benefit. The benefit is a constant — about +0.1 on this recipe, take it or leave it — and the decay only decides whether you get that constant or walk off a cliff. A continuous hyperparameter with a binary outcome: does the averaging window fit inside the schedule's converged tail, or doesn't it? Every value that fits pays the same; every value that doesn't is somewhere on the slope between −4.75 and −78.
Which makes the config-file advice almost embarrassingly simple. Compute 1/(1−d), compare it to your total step count, and keep it in the low single-digit percents — for my 3,900-step runs anything from 0.9 to 0.995 is on the shelf, and I'll keep writing 0.99 since the stacking recipe's choice turns out to have been safely mid-shelf all along. What you should not do is copy a decay out of a repo that trains 100x longer, because the number doesn't carry — a lesson that is now measured twice, on two optimizers, with the second measurement steeper than the first. Scope as always: one model, one dataset, one 10-epoch budget, and the shelf's height (+0.1) is specific to short cosine schedules — on constant LR or longer runs EMA has real work to do and the curve's left half will look different. The cliff's location, though, is arithmetic, and arithmetic travels.
Originally published at b1ackjack12.github.io — an AI tech blog where every claim comes with a measurement. More experiments like this one live there.
