On Fresh Seeds, the Mixture Wins
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 copy task, our easy-first warm-up turned out to be nothing a standard learning-rate warm-up could not do. On the adding task it had stayed ahead, but not clearly. We ran the decisive version: 32 brand-new runs, the easy-sum mix against the best ordinary recipe we had found, warm-up schedule included.
What we found. The mix won clearly: 91 percent accuracy against 65, and it solved the task on 26 of 32 runs against 12. On this task, easier data early does something a learning-rate schedule does not.
Why it matters. Whether a data curriculum helps depends on the task. Compare it against a tuned learning-rate warm-up before crediting it: on one of our tasks it failed that test, on the other it passed.
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,64training runs of8000steps on thirty-two seeds never used before. The design and the kill test were committed (f97b636) before any run.
Program v2 Bucket A, item A40. Decisive computation: . Output: analysis/sum_mixture_powered.py.analysis/sum_mixture_powered.json
The question
On the copy task the data-warm-up thread ended with no advantage over a tuned learning-rate warm-up (A33, A35). On modular sum, A36 found the early mixture ahead of the best plain alternative -- a 500-step learning-rate warm-up to 0.003, chosen from four tuned plain cells -- by +0.167 [-0.068, +0.401] on sixteen seeds: not established. A40 runs only those two cells on thirty-two fresh seeds, so neither arm's settings were chosen on the seeds that judge them.
Design: A18's task ((2, 7), 8000 steps), seeds 11001-11032. Mixed: 2000 steps of a shuffled mix of (2,3)/(2,4)/(2,5), then (2, 7), at 0.003. Rate warm-up: plain (2, 7) with a 500-step linear learning-rate warm-up to 0.003. Same compute. Kill test, fixed before execution: mixed minus the rate warm-up, paired, includes zero or lies below it. Anchor, in code: A36's loop reproduces its rate-warm-up run on A36's first seed -- held.
Results
| Arm (thirty-two fresh seeds) | Final (2, 7) accuracy | Solved (>= 0.9) |
|---|---|---|
easier sums mixed first, 0.003 | 0.905 [0.836, 0.974] | 26 of 32 |
plain with a learning-rate warm-up to 0.003 | 0.647 [0.542, 0.752] | 12 of 32 |
| mixed minus rate warm-up, paired | +0.258 [+0.149, +0.366] | higher on 26 of 32 |
Pooled with A36's sixteen seeds, as a description: +0.227 [+0.129, +0.326] over forty-eight.
The kill test does not fire. On seeds never used to choose either arm's settings, the early mixture of easier sums beats the best plain recipe found -- tuned rate and a learning-rate warm-up -- by a quarter of the accuracy scale, and solves the task on more than twice as many seeds.
What the data-mixture work now says
- On the copy task, easier data early is a learning-rate warm-up in disguise: once the plain run is tuned and given a rate warm-up, it adds nothing (A31-A35).
- On modular sum it is not. It beats a tuned plain run with a learning-rate warm-up (A40); its effect depends on which easy material and in what order -- two of the three easy sums alone delay learning by thousands of steps (A39, A41), and ending the warm-up on the farthest one is worse than no warm-up (A22). A learning-rate schedule cannot reproduce content effects like those.
The difference between the tasks is itself the finding worth carrying: a data warm-up has to be compared against a learning-rate warm-up before it is credited, and it can pass that test on one task and fail it on another.
What stands
- A40: kill test does not fire. Mixed minus the best plain run (rate warm-up to
0.003) on thirty-two fresh seeds:+0.258[+0.149, +0.366]; solved26against12.
Limits
- One task, one width (
48), one budget (8000steps); the plain run's warm-up was one ramp length (500) tuned over two peaks, and a longer budget narrows gaps that are partly delays (A41). - The mixed arm's rate (
0.003) was chosen as its best in A32; A40's fresh seeds remove the selection bias from the comparison but not the choice.
QUALIFIED 2026-09-28 by A42. Run to step16000on sixteen of these seeds, the plain run largely catches up (+0.087[-0.017, +0.190]). The advantage measured here at8000is mostly speed: the mixture reaches0.9at a median3555steps against9655(descriptive). Text and numbers above unchanged.
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.
- 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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