Research record

Order Can Make the Warm-Up Harmful

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: Is the task we are studying actually hard? – Often it is not. A rule from 1990 with no parameters beats the trained model on the task most of these results were measured on, and what an intervention costs is set by the task's own structure.

In plain English

What we asked. A recent paper found that the order in which a model sees easier material matters a great deal. On our copy task, order had made no difference. We tried it on the second task, adding numbers, with three easier sums before the hard one.

What we found. Order mattered, in an unexpected way. Shuffled together, the easier sums helped: six of eight runs learned the hard sum. Given hardest to easiest, none did, which is worse than no warm-up at all.

Why it matters. The same data can help or hurt depending on how it is arranged. What a model practises last before the real task seems to matter here.

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.

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EXPLORATORY. Not a preregistered study. Local CPU, 16 new training runs of 8000 steps plus 8 re-used. The design and the kill test were committed (01e727c) before any run; the rate was moved to 0.003 in a separate commit (49c865e), also before any run, after A32 found A18's 0.005 too hot for this task.

Program v2 Bucket A, item A22. Decisive computation: analysis/warmup_order.py. Output: analysis/warmup_order.json. Descriptive post-hoc: analysis/warmup_order_posthoc.py and its output.

The question

arXiv 2608.14936 ("Small Models Scout Bottleneck Order") reports that reversing its phase order, or collapsing it to a static mixture, removes most of a 31-56% token saving. A14 found order did nothing on the copy task, whose easy lags are one skill at graded difficulty. Modular sum's easy pairs (2,3), (2,4), (2,5) each need a different second offset. Does order matter there?

The same easy sums, in the wrong order, stop the model learning
The same easy sums, in the wrong order, stop the model learning. Every model spends its first 2,000 steps on the same three easier sums, then the hard one. Only the order differs: shuffled together, easiest to hardest, or hardest to easiest. Same compute and learning rate. Shuffled works best. Ending the warm-up on the easiest sum is worse than no warm-up at all: none of eight runs learns the hard task. On this task, what the warm-up ends on seems to matter.

Design: A18's task and receivers, 8000 steps, rate 0.003 (the mixed arm's tuned best, A32). The 2000-step warm-up is given shuffled (A32's mixed arm), increasing ((2,3), (2,4), (2,5), a third each) or decreasing (the reverse), then (2,7). Kill test, fixed before execution: increasing minus shuffled includes zero. Anchor, in code: shuffled reproduces A32's mixed runs at 0.003 -- held on all eight seeds.

Results

Warm-up orderFinal (2, 7) accuracyMinus shuffledSolved (>= 0.9)Minus plain run at 0.003
shuffled0.872 [0.677, 1.067]--6 of 8+0.342 [-0.013, +0.697]
increasing0.616 [0.336, 0.896]-0.256 [-0.541, +0.029]3 of 8+0.086 [-0.319, +0.491]
decreasing0.135 [0.032, 0.239]-0.737 [-1.008, -0.465]0 of 8-0.394 [-0.737, -0.052]
(plain run, no warm-up, A32)0.5302 of 8

The kill test fires: increasing minus shuffled includes zero. But order is far from irrelevant. Shuffled is best and increasing trails it on the point estimate; decreasing order -- ending the warm-up on the easiest sum -- does worse than no warm-up at all, solving the task on no seed. The same 2000 steps of the same three easy tasks can help or harm depending on their order.

What it says

This disagrees with the paper's direction (its ordered phases beat a static mixture; here a shuffled mixture beats both orders) and with the copy task, where order did nothing. What the two orders differ in is what the model was doing just before the switch: increasing ends on (2,5), nearest the target; decreasing ends on (2,3), furthest. Ending far from the target and then switching appears to leave the model somewhere it cannot get out of in the budget. That is a hypothesis this pilot cannot separate from "starting near the target"; a single-pair design can.

It also means the modular-sum mixture's advantage is not a warm-up's generic protection alone: a warm-up of the same length and material, in the wrong order, is actively harmful. Whether the mixture beats the best plain alternative is A36 (running); A39 asks whether one easy pair would do, as it did on the copy task (A25).

What stands

  • A22: kill test fires. Increasing minus shuffled: -0.256 [-0.541, +0.029].
  • A decreasing warm-up is harmful -- -0.737 against shuffled and -0.394 [-0.737, -0.052] against no warm-up, 0 of 8 solved.

Limits

  • Eight seeds on a bimodal outcome; one rate (0.003), one budget. The rate is the mixed arm's best, not the ordered arms'.

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.

accuracy
The fraction of answers a model gets right on questions it was not trained on.
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.
post hoc
Worked out after the fact, rather than decided in advance. We report such checks separately and never let them decide a result, because it is far too easy to find a pattern once you already know the answer.
seed
The number that fixes all the randomness in a training run. Same seed, same run. Running several seeds is how you tell a real effect from a lucky one.

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