Research record

A Harder Maximum, and It Helps Again

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. Our easy-start recipe slowed learning when the task was to output the larger of two remembered symbols, and we read that as the recipe only working for arithmetic. But that task was also easy for ordinary training. So we made it harder by moving one symbol further back.

What we found. On the harder version the easy start helped again, saving about a quarter of the steps, and every run learned the task either way.

Why it matters. So what mattered was how hard the task was, not what kind of task it was. We have corrected the earlier page and our headline finding. The easy start is worth trying when there is something genuinely hard to learn.

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, 32 training runs of 24000 steps on sixteen fresh seeds. The design, a disclosed calibration throwaway and the kill test were committed (8660125) before any run.

Program v2 Bucket A, item A62. Decisive computation: analysis/max_harder.py. Output: analysis/max_harder.json.

The question

A60 found that with max(x[t-2], x[t-7]) as the hard task, the easy warm-up slowed learning by 1292.5 [824.6, 1760.4] steps, where for modular sums and differences it halves them. But that maximum was also easy for plain training (median 4595 steps, against 6840 for the hard difference), so A60 could not say whether the operation or the difficulty decided it. On a maximum that is harder for plain training than the hard difference, does the easy warm-up still slow learning?

On a harder version of the same task, the easy start helps again
On a harder version of the same task, the easy start helps again. The task is to output the larger of two remembered symbols. On the left the second symbol is 7 steps back and ordinary training finds it easy; on the right it is 9 steps back and ordinary training takes about twice as long. On the easy version the easy start costs time; on the harder one it saves about a quarter of the steps. What mattered was how hard the task was for ordinary training, not which operation it was.

Design: GRU, width 48, rate 0.003, 24000 steps, sixteen fresh seeds 27001-27016. Hard task max(x[t-2], x[t-9]) at sequence length 18 (nine scored positions, as at (2, 7) and length 16); chosen by a two-seed throwaway, disclosed before running, in which plain first reached 0.9 at a mean 9110 steps. Easy warm-up of maxima on (2,3)/(2,4)/(2,5) for 2000 steps -- the same easy set as A60. Mixed against plain with a 500-step learning-rate warm-up; steps to 0.9. Kill test, fixed before execution: mixed minus plain includes zero or lies above it (the operation, not the difficulty, decides). Anchor, in code: with the far lag back at 7, the patched loop reproduces A60's plain run on its first seed -- held.

Results

Arm (sixteen fresh seeds, hard maximum (2, 9))Median steps to 0.9Solved by 24000
easy maxima first670516
plain, learning-rate warm-up906516
  • Mixed minus plain: -2351.9 [-3449.3, -1254.4] steps; ratio of mean steps 0.743.

The kill test does not fire. On a maximum that plain training finds harder than the hard difference, the easy warm-up reaches the solution about a quarter sooner, with an interval wholly below zero and every seed solving in both arms.

What it says

A60's reversal was about difficulty, not the operation. The same operation that the easy warm-up slowed at (2, 7) -- where plain training solved it in 4595 median steps -- it speeds up at (2, 9), where plain needs 9065. The maximum is not a group operation and not modular arithmetic, so the finding is not "specific to modular arithmetic", as A60's record and the v0.290.0 top-findings list said; A60 now carries a banner. The better description on the evidence so far: the easy start helps a recurrent network when the hard task is hard for plain training, and can cost time when it is not. Two easy tasks do not yet say where the line is.

The effect is smaller here (ratio 0.743) than for the sum and difference (0.48-0.58). Whether that is the operation, the wider gap between the easy lags and the hard one, or the difficulty itself is not separated.

What stands

  • A62: kill test does not fire. Hard maximum (2, 9): mixed minus plain -2351.9 [-3449.3, -1254.4] steps; ratio 0.743; 16 of 16 solve in both arms.
  • A60's interpretation is corrected by banner: its measurement stands; "specific to modular arithmetic" does not.

Limits

  • The plain rate (0.003) was not re-tuned for the maximum, in A60 or here; the sum's tuned rate was carried over, as in A57. A lower plain rate on the easier (2, 7) maximum, or a higher one here, could move either result.
  • Changing the far lag also changed the sequence length (to keep nine scored positions) and widened the gap between the easy lags (3-5) and the hard one (9); difficulty is moved by one lag change, not by an independent knob.
  • One operation at two difficulties; sixteen seeds each.

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.

calibration
Working out an instrument's settings from runs whose answer you already know, so it can be used on a run whose answer you do not.
GRU
Gated Recurrent Unit. A compact design for processing sequences one item at a time, with internal switches controlling what it keeps in memory.
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.
recurrent
A design that reads a sequence one item at a time, carrying memory forward. The main alternative is attention, which looks at everything at once.
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.
width
How many internal numbers a model uses at each layer. The usual way we vary model size in these experiments.

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