Research record

At Width 24, Undecided

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. The easy-sum speed-up had held at two sizes of model. We tried a third, half the size of the original, on a hard sum chosen to challenge it.

What we found. It leaned the same way: the typical run needed about 3,900 steps with the easy start against 5,200 without. But runs varied a lot, and with only one easier sum available as the warm-up, the difference was not clear of the noise.

Why it matters. Two sizes where it clearly holds, one where it leans the same way. We report it as undecided.

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 16000 steps at width 24 on sixteen fresh seeds. The design, the disclosed throwaways and the kill test were committed (4cd357e) before any run.

Program v2 Bucket A, item A56. Decisive computation: analysis/sum_mixture_narrow.py. Output: analysis/sum_mixture_narrow.json.

The question

The early warm-up of easier sums reaches the solution in about 42% fewer steps than the best plain recipe at width 48 (A44) and 46% fewer at width 96 (A53). A third, smaller width: 24.

The easy-sum start needs fewer steps at every width tried
The easy-sum start needs fewer steps at every width tried. For each model width, the average number of training steps the easy-sum start needed to solve its hard sum, divided by plain training's. Below 1 means fewer steps. Each width uses a hard sum chosen to sit at the edge of what that model learns. At widths 48 and 96 the easy start needs a little over half the steps, and both are clear of the noise. At width 24 (blue), with only one easy sum available, it leans the same way but is not yet clear.

Design: width 24; target (2, 4), chosen by throwaways as just past what width 24 learns in 8000 steps (it solves (2, 3) at step 2500 and not (2, 4)); 16000 steps so the plain run has room. The warm-up is a single easy pair, (2, 3) -- the generator requires lags of at least 2, so it is the only easier pair sharing the target's first offset. Mixed (2000 steps of (2, 3)) against plain with a 500-step learning-rate warm-up, both at 0.003; endpoint steps to 0.9 (never = 16000). Kill test, fixed before execution: mixed minus plain includes zero or lies above it. Anchor, in code: at width 48 the loop reproduces A40 -- held.

Results

Arm (width 24, sixteen fresh seeds)Median steps to 0.9Solved by 16000
easy warm-up (2, 3), then (2, 4)391513
plain, learning-rate warm-up517010
  • Mixed minus plain: -2131.2 [-5609.6, +1347.1] steps; ratio of mean steps 0.743.

The kill test fires. The warm-up leads on every summary -- median, solved count, ratio of means -- and the paired interval is wide enough to reach zero. At width 24 the speed-up is undecided.

What it says

Three things differ from the two widths where it held, and this pilot cannot separate them: the model is smaller; the warm-up is one easy pair rather than a mix (the only one available); and at this width a run either solves quickly or very late, which widens the interval (the six unsolved-by-the-plain-run seeds are counted at 16000). The direction agrees with widths 48 and 96; the size is smaller (ratio 0.743 against 0.578 and 0.544) and not established.

What stands

  • A56: kill test fires. Width 24: mixed minus plain -2131.2 [-5609.6, +1347.1] steps; solved 13 against 10.
  • Across widths: established at 48 and 96; undecided at 24 with a single-pair warm-up.

Limits

  • Sixteen seeds; a single easy pair; one target.

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.

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.
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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