Research record

Tuned on Its Own Target, Plain Never Solves It

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. On a second hard sum, the easy-sum mix had beaten ordinary training, but ordinary training was using settings tuned on the first sum. Maybe it just needed its own settings.

What we found. It did not help. We tried four settings on the second sum itself; none let ordinary training learn it on a single one of sixteen runs in the time allowed. The mix learned it on twelve.

Why it matters. The next question is whether ordinary training ever gets there with much more time, or whether the mix is doing something it cannot.

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, 48 new training runs of 8000 steps plus 32 re-used from A43. The design and the kill test were committed (46bf0b9) before any run.

Program v2 Bucket A, item A45. Decisive computation: analysis/sum_second_pair_tuned.py. Output: analysis/sum_second_pair_tuned.json.

The question

A43 found the early mixture beating plain training with a learning-rate warm-up on target (3, 8) by +0.632, with the plain arm's settings tuned on (2, 7). With the plain run tuned on (3, 8) itself, does the mixture still win?

Tuned on the second sum itself, ordinary training still never solves it
Tuned on the second sum itself, ordinary training still never solves it. Four settings of ordinary training, tried on this sum itself, and the easy-sum mix, sixteen runs each at the same training length. Error bars are 95% confidence intervals. None of the ordinary settings solves it on a single run in this budget; the mix solves it on 12 of 16. The earlier result did not depend on tuning ordinary training on the other sum.

Design: A36's four plain cells on (3, 8), sixteen of A43's seeds, 8000 steps; the rate-warm-up-to-0.003 cell and the mixed arm re-used from A43. Kill test, fixed before execution: mixed minus the best plain cell includes zero or lies below it. Anchor, in code: the re-run rate warm-up reproduces A43 on the first seed -- held.

Results

Cell (sixteen seeds, target (3, 8))Final accuracySolved (>= 0.9)
plain, 0.0010.049 [0.045, 0.053]0
plain, 0.0020.102 [0.051, 0.154]0
plain, rate warm-up to 0.0050.092 [0.073, 0.111]0
plain, rate warm-up to 0.003 (best)0.207 [0.088, 0.326]0
easier sums mixed first0.868 [0.750, 0.986]12

The kill test does not fire. Mixed minus the best plain cell is +0.661 [+0.503, +0.819]. The best plain cell on (3, 8) is the same one tuned on (2, 7), and its optimum is inside the grid. No plain setting tried solves (3, 8) on any of sixteen seeds in 8000 steps; the mixture solves it on twelve.

What it says

A43's result does not depend on carrying the plain run's settings across targets. On (3, 8) the plain recipe is past its edge in this budget at every setting tried, and the mixture is not. Given A42 -- on (2, 7), a longer budget let the plain run catch up -- this is most naturally read as the same speed difference on a harder target, where "sooner" becomes "within the budget at all". A44 (running) measures steps to solve on (2, 7).

What stands

  • A45: kill test does not fire. Mixed minus the best plain cell on (3, 8): +0.661 [+0.503, +0.819]; solved 12 against 0 at every plain setting.

Limits

  • Sixteen seeds, one budget; four plain settings, one ramp length; whether the plain recipe solves (3, 8) given much longer is not tested.

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.
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.

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