Research record

The Mixture Gets There Sooner

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 adding task, starting with a mix of easier sums had beaten the best ordinary recipe at a fixed training length. Would the ordinary recipe catch up if given longer?

What we found. Mostly, yes. At twice the length, most runs of both recipes had learned the hard sum. But the mix got there much sooner: the typical run needed about 3,600 steps against about 9,700.

Why it matters. Not a better model in the end, a faster route to it, roughly a third of the training. That is an efficiency gain, and the next test fixes it as the thing measured.

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. The design and the kill test were committed (4dd2ac9) before any run.

Program v2 Bucket A, item A42. Decisive computation: analysis/sum_mixture_longer.py. Output: analysis/sum_mixture_longer.json. Descriptive post-hoc (steps to solve): analysis/sum_mixture_longer_posthoc.py and its output.

The question

A40 found the early mixture beating plain training with a learning-rate warm-up by +0.258 at step 8000 on thirty-two fresh seeds. A41 found that on this task a fixed budget partly reports timing. Does the gap survive twice the budget?

The easy-sum mix does not raise the ceiling; it gets there sooner
The easy-sum mix does not raise the ceiling; it gets there sooner. Each line counts how many of sixteen runs have reached 90% accuracy on the hard sum by each step, run to twice the earlier budget. One recipe is the best ordinary one, with a learning-rate warm-up; the other starts with a mix of easier sums. Given enough steps, most runs of both recipes get there. The mix gets there sooner: the typical run solves it in about 3,600 steps against about 9,700.

Design: A40's two arms and loop on its first sixteen seeds, to step 16000. Kill test, fixed before execution: mixed minus the rate warm-up at step 16000 includes zero or lies below it -- the mixture only gets there sooner. Anchor, in code: the first 8000 steps of every run reproduce A40 -- held on all sixteen seeds.

Results

Arm (sixteen seeds)Solved at 8000Solved at 16000Final accuracy at 16000
easier sums mixed first13150.980
plain with a learning-rate warm-up6120.894
mixed minus rate warm-up at 16000+0.087 [-0.017, +0.190]

The kill test fires. At step 16000 the gap is +0.087 with an interval reaching zero, the mixture higher on only 5 of 16 seeds -- most seeds in both arms have solved the task by then. Given twice the budget, the plain run largely catches up.

What the mixture does instead: it gets there sooner (descriptive, post-hoc, not the kill test). The median seed reaches 0.9 at step 3555 with the mixture and 9655 with the rate warm-up; paired, the mixture is sooner by 4495 steps [1469, 7521], on 13 of 16 seeds (seeds that never solve are counted at the budget, which understates the gap).

What it says

The kill test was written to separate "a better end point" from "sooner", and it says sooner. On modular sum the early mixture is not a higher ceiling within 16000 steps -- as it was not on the copy task once tuned -- but it reaches the solution in roughly a third of the steps of the best plain recipe. That is an efficiency claim in the units this programme prefers (steps to a task criterion, at matched compute per step), and it has only been measured after the fact here. A44 fixes it as the endpoint on fresh seeds.

What stands

  • A42: kill test fires. At step 16000, mixed minus the rate warm-up: +0.087 [-0.017, +0.190].
  • Steps to solve (descriptive): median 3555 against 9655; the mixture sooner by 4495 [1469, 7521] steps.

Limits

  • Sixteen seeds; the steps-to-solve comparison is post-hoc; one task and target pair (A43 runs a second pair).

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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