Research record

Forty Percent Fewer Steps

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 earlier results suggested that on the adding task, a short start on easier sums gets a small model to the solution faster. We had only measured that after the fact. This time we fixed the measure in advance: how many training steps until it solves the hard sum.

What we found. On 32 fresh runs, the easy start reached the solution in about 3,600 steps; the best ordinary recipe, with its learning-rate warm-up, in about 7,800. On average that is about 40 percent fewer steps for the same cost per step.

Why it matters. A clear efficiency gain on this task, against a properly tuned baseline. On our other task the same idea gave nothing, which is why it is worth testing where it matters.

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, 64 training runs of 16000 steps on thirty-two seeds never used before. The design, the endpoint and the kill test were committed (18e2849) before any run.

Program v2 Bucket A, item A44. Decisive computation: analysis/sum_mixture_steps.py. Output: analysis/sum_mixture_steps.json.

The question

A42 found that on modular sum the plain run with a learning-rate warm-up largely catches up with the early mixture of easier sums given twice the budget, and -- post-hoc -- that the mixture reaches the solution much sooner. With steps to solve fixed as the endpoint in advance, on fresh seeds, is the mixture faster?

The easy-sum mix reaches the solution in about 40% fewer steps
The easy-sum mix reaches the solution in about 40% fewer steps. Each line counts how many of thirty-two runs, never used to tune either recipe, have reached 90% accuracy on the hard sum by each step. The measure, steps to solve, was fixed before any run. Both recipes cost the same per step. The typical run solves it in about 3,600 steps with the mix and 7,800 without: on average about 40% fewer steps, against the best ordinary recipe including a learning-rate warm-up.

Design: A40's two arms and loop on (2, 7) -- the mixture (2000 steps of (2,3)/(2,4)/(2,5), then (2, 7), at 0.003) and plain training with a 500-step learning-rate warm-up to 0.003, the best plain recipe found (A36) -- on thirty-two fresh seeds 14001-14032, 16000 steps. Endpoint: the first evaluation step at which (2, 7) held-out accuracy reaches 0.9; a seed that never does is counted at 16000. Kill test, fixed before execution: mixed minus the rate warm-up in steps to solve, paired, includes zero or lies above it. Anchor, in code: the loop reproduces A42's rate-warm-up run on its first seed -- held.

Results

Easier sums mixed firstPlain + learning-rate warm-up
median steps to 0.936157825
solved by step 1600029 of 3226 of 32
  • Mixed minus the rate warm-up, paired: -4062.5 [-5917.2, -2207.8] steps, the mixture sooner on 26 of 32 seeds.
  • Ratio of mean steps (mixed over rate warm-up): 0.578 [0.437, 0.742] (paired bootstrap, 10000 resamples).

The kill test does not fire. On seeds never used to tune either arm, the early mixture of easier sums reaches the solution in about 42% fewer steps on average (median: 54% fewer) than the best plain recipe with a learning-rate warm-up, at the same cost per step.

What the data-mixture work now supports

On modular sum, a brief early phase of easier versions of the task reaches the solution in roughly half to three-fifths of the steps of the best plain recipe found -- a tuned rate with a learning-rate warm-up -- measured in steps to a task criterion on fresh seeds (A44); it also wins on a second target pair with the plain run tuned there (A43, A45); and which easy material, in what order, matters (A22, A39). On the copy task the same idea is only a learning-rate warm-up in disguise (A31-A35). The standing lesson and the positive result are the same sentence: a data curriculum has to be priced against a tuned learning-rate warm-up, and on one of two tasks here it survives.

Still open: whether it survives a decaying rate (A47, running), whether the early phase matters or easy data throughout does as well (A48), and whether the plain run ever solves the harder target (A46, running).

What stands

  • A44: kill test does not fire. Steps to solve, mixed minus the rate warm-up: -4062.5 [-5917.2, -2207.8]; ratio of means 0.578 [0.437, 0.742].

Limits

  • One task family, one width (48), a small GRU, synthetic data. A constant rate after warm-up (A47 tests decay). Seeds that never solve are counted at the budget, which understates the gap.

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.
bootstrap
A way of estimating how uncertain a number is by repeatedly resampling the data you already have. Useful when the usual formulas do not apply.
curriculum
Training on easier examples first and harder ones later, like a school syllabus, rather than on everything at once.
GRU
Gated Recurrent Unit. A compact design for processing sequences one item at a time, with internal switches controlling what it keeps in memory.
held-out
Data the model was never trained on, kept back specifically to test it. Scoring a model on data it has already seen measures memorisation, not learning.
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.
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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