Research record

The Optimizer's Memory Did Not Matter

Ongoing research. This is an experimental result from active work, not a settled conclusion. The numbers are what we measured and the method is described so you can judge it, but the programme is still running and later experiments may revise what it means.

A note on the language in these records. This is a working laboratory notebook for research into training AI models more cheaply and efficiently, so you will read that an approach did not work, that a result did not hold up, or that one method was worse than another. That is the research doing its job, not a verdict on the engineering we deliver to clients. Ruling an approach out is how the search narrows, and these are the pages that teach us the most: nearly every technique we now rely on came from understanding why something else fell short. Testing our own ideas at least as hard as anyone else's is the point of publishing them. More about this programme and why we run it.

Part of a bigger question: What actually makes training cheaper? – One thing has worked: stopping part of the training early saved about 7% with no loss of quality. Everything else tested has been matched by a simpler or cheaper method -- and in two cases the clever method was only winning because it was quietly being given more.

In plain English

What we asked. The Adam optimizer, used to train most modern models, keeps a running memory of how large its recent updates were. A 2025 paper recommends making that memory last longer or shorter as the batch size changes. We tried it on our batch-size experiment.

What we found. It changed nothing: every result matched the original to within a fraction of a step. Our models learn the skill in about a hundred steps, and that memory takes several hundred steps to make a difference.

Why it matters. In practice: in short training runs, this is not a setting worth tuning. The learning rate is.

The rest of this page is the technical record: the design, every number, and the limits. It is written for a reviewer, and you do not need it to have understood the result above.

New here? How to read a research record
  • Start at the verdict. Every record states, before the experiment was run, what result would have made us abandon the idea. That is the "kill test". Then it says whether the test fired. Nothing gets reinterpreted after the fact.
  • Numbers in square brackets are uncertainty. 23.4 [18.1, 28.7] means our best estimate is 23.4 and the true value is probably somewhere in that range. If a range includes zero, we cannot claim an effect.
  • Results that rule an idea out are kept. Roughly half of what is published here says an approach did not work, including plenty of our own. Those pages are the output, not a shortfall: knowing which direction is a dead end is what lets the next experiment go somewhere better, and most of what we now rely on came out of understanding why something else fell short. Work that only publishes what worked is not measuring anything.
  • Read the Limits section. Every record ends with what it does not show. It is the most honest part of any experiment and usually the shortest.
  • Pro tip: the figures near the top are designed to carry the result on their own. If you read nothing else, read the caption under each one, which says what it shows and what to take from it.
EXPLORATORY. Not a preregistered study. Local CPU, 33 training runs (one anchor) plus T8's 8 batch-64 runs. The design and kill test were committed (6acc1f4) before any run.

Program v2 Bucket T, item T17. Decisive computation: analysis/batch_law_beta2.py. Output: analysis/batch_law_beta2.json. Reproduce with python analysis/batch_law_beta2.py (about twenty minutes on a throttled laptop CPU); --reuse re-derives every endpoint from the saved series.

The question

arXiv 2507.07101 (Marek, Lotfi, Somasundaram, Wilson and Goldblum) argues that Adam's second-moment decay, beta2, should be scaled with batch size so that its half-life is fixed in tokens rather than in steps, and that with this change small batches train as well as or better than large ones per unit of compute. Every run in this programme used the default 0.999 at every batch. T17 reruns T8's fixed-rate batch sweep with beta2(B) = 0.999 (B / 64)**, which holds the half-life in examples at the batch-64 default's.

Rescaling Adam's memory with batch size changed nothing here
Rescaling Adam's memory with batch size changed nothing here. The Adam optimizer keeps a running average of how large recent updates were. A recent paper recommends adjusting how long that memory lasts as the batch size changes. We retrained the batch-size experiment both ways. The two lines lie on top of each other. Our models learn the skill within about a hundred steps, before that memory setting has had time to matter. In short runs it is not the setting to tune.

Kill test, fixed before execution: the exponent overlaps T8's fixed-rate interval [-0.329, -0.301]. Anchor: batch 64 through the optimiser wrapper reproduces T8 exactly. It holds. Prior: low.

Result: the kill test fires

Batchbeta2Step to 0.5T8 (beta2 = 0.999)
160.99975127.4 [119.6, 135.1]127.5
320.9995094.6 [89.1, 100.1]94.7
640.9990075.375.3
1280.9980061.6 [59.4, 63.9]61.6
2560.9960153.1 [51.5, 54.8]52.9
Exponent-0.313 [-0.328, -0.299]-0.315

No batch moved by more than 0.2 steps. Scaling beta2 with batch leaves the batch law where it was.

Why, and what it does and does not say

The prior was written in advance: the transition here arrives within 50-130 steps, while beta2's half-life is 693 steps at the default and longer at small batches. Over that window Adam's bias correction divides by 1 - beta2^t, which makes the second-moment estimate close to a plain running mean of the squared gradients whatever beta2 is. So the change the paper recommends has not yet had time to act.

This does not test the paper's claim, which is about long language-model runs where the half-life is short against the run. It says only that in short runs where the event of interest comes early, beta2 is not a lever, and that none of T8-T15's batch exponents was an artefact of leaving it at its default.

What stands

  • Kill test fires. With beta2's half-life fixed in examples the exponent is -0.313 [-0.328, -0.299], indistinguishable from T8's -0.315.
  • T8-T15 are robust to the beta2 convention.
  • Practical reading: in a run whose key event arrives within a few hundred steps, beta2 is not worth tuning; the learning-rate policy is (T15).

Limits

  • 800-step runs; the transition within the first 130 steps. Longer runs are where beta2 could matter.
  • One substrate, beta1 fixed at 0.9.

Terms on this page

Every piece of vocabulary this record uses, in plain language. Generated from the text above, so it cannot drift out of step with it.

batch size
How many examples the model looks at before updating itself once. Bigger batches give a steadier but more expensive update.
exponent
The number in a power law that says how strongly one quantity responds to another. A bigger exponent means a steeper response to the same doubling.
gradient
The direction and amount by which each of a model's internal numbers should change to do slightly better. Training is repeatedly following it.
kill test
A condition written down before running the experiment that says what result would make us abandon the idea. Fixing it in advance is what stops a disappointing result being reinterpreted as an encouraging one.
learning rate
How big a step training takes each time it updates the model. Too small and nothing happens; too big and it never settles.

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