Research record

Plain Gets There Eventually

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 the harder of our two sums, ordinary training had not learned it on a single run in the time allowed, while the easy-sum mix learned it on most. Was ordinary training unable to learn it at all, or just slow?

What we found. Just slow. Given three times as long, it learned it on 10 of 16 runs. The typical run needed about 18,400 steps; with the easy-sum start, about 5,600.

Why it matters. The same story on both sums: the easy start does not unlock anything ordinary training cannot reach, it gets there in a fraction of the time.

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. The design and the kill test were committed (cc959a9) before any run.

Program v2 Bucket A, item A46. Decisive computation: analysis/sum_second_pair_longer.py. Output: analysis/sum_second_pair_longer.json. Descriptive post-hoc (steps to solve): analysis/sum_second_pair_longer_posthoc.py and its output.

The question

On (3, 8) no plain setting solved a single seed of sixteen in 8000 steps, while the early mixture of easier sums solved twelve (A45). On (2, 7) the plain run caught up given twice the budget (A42). Speed again, or something the plain run cannot reach?

On the harder sum, ordinary training gets there too, three times later
On the harder sum, ordinary training gets there too, three times later. Each line counts how many of sixteen runs have reached 90% accuracy by each step, run to three times the earlier budget. At the earlier stopping point ordinary training had solved none. Given long enough, ordinary training solves it on 10 of 16 runs; the mix solved 12, all by about 6,400 steps. The typical run needs about 5,600 steps with the mix and 18,400 without.

Design: A43's two arms on (3, 8) -- the mixture, and plain with a 500-step learning-rate warm-up to 0.003 -- on sixteen of A43's seeds, to step 24000. Kill test, fixed before execution: the plain arm solves (>= 0.9) at least 8 of 16 seeds by step 24000 -- the mixture's advantage is speed here too. Anchor, in code: the first 8000 steps of every run reproduce A43 -- held on all sixteen seeds.

Results

Arm (sixteen seeds, (3, 8))Solved by 8000Solved by 24000Median steps to 0.9Final accuracy
easier sums mixed first121255850.875
plain with a learning-rate warm-up010184200.780

The kill test fires. Given three times the budget the plain run solves (3, 8) on 10 of 16 seeds -- its first solves arriving between steps 8260 and 21710 -- so on this target too the mixture's advantage is speed, not a ceiling the plain run cannot reach.

How much faster (descriptive, post-hoc): the mixture's solving seeds get there between steps 3900 and 6400. Counting seeds that never solve at the budget, the mixture is sooner by 8118 [3813, 12423] steps on 12 of 16 seeds, a ratio of mean steps of 0.551 -- a slightly larger saving than A44's 0.578 on (2, 7). The four mixture seeds that had not solved it by step 8000 did not solve it by 24000 either.

What it says

Across both targets the same shape: the early mixture of easier sums reaches the solution in roughly half to three-fifths of the steps of the best plain recipe, and the plain recipe gets there eventually. On the harder target "eventually" is past the budget earlier experiments used, which is why A43 and A45 read as the plain run failing.

What stands

  • A46: kill test fires. The plain run solves (3, 8) on 10 of 16 seeds by step 24000.
  • Descriptive: median steps to solve 5585 with the mixture against 18420; ratio of mean steps 0.551.

Limits

  • Sixteen seeds; the steps comparison is post-hoc here (A44 fixed it on (2, 7)).

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.
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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