Mixing First Lifts the Ceiling
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. Last time we noticed something we had not been looking for: a model that spent its first stretch of training on a random mix of easier memory tasks ended up better at the hard one. A surprise like that needs its own test, so we repeated it on eight new training runs, deciding in advance exactly what we would measure.
What we found. It held up, and more strongly: 79 percent accuracy on the hard task against 58, for exactly the same amount of compute. Working through the easier tasks in order had not helped, so it is the mixing, not the ordering, that matters.
Why it matters. In practice: before spending all your training on the one task you care about, try mixing in varied easier versions of it early. It cost nothing extra here.
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,16training runs of6000steps on seeds A14 did not use. The design, endpoint and kill test were committed (7fc97ab) before any run.
Program v2 Bucket A, item A15. Decisive computation: (A14's code). Output: analysis/lag_mixture.py.analysis/lag_mixture.json
The question
A14 found that an easy-to-hard lag staircase does not speed learning a lag-8 copy task at matched compute, and, post hoc, that a shuffled mixture of lags 2, 4, 6 for the first 1500 steps ended +0.145 higher on lag-8 accuracy at step 6000. A finding noticed after the fact needs its own test. A15 reruns A14's fixed and shuffled arms on eight fresh seeds (J8's donor seeds), with the endpoint -- lag-8 held-out accuracy at step 6000 -- fixed in advance.
Kill test, fixed before execution: shuffled minus fixed has an interval including zero or lying below it.
Result: the kill test does not fire
| Arm | Final lag-8 accuracy |
|---|---|
fixed lag 8 throughout | 0.575 [0.492, 0.657] |
shuffled lags 2/4/6 for 1500 steps, then 8 | 0.790 [0.765, 0.815] |
| Paired difference | +0.215 [+0.135, +0.296] |
On fresh seeds the effect replicates, and is larger: spending the first quarter of training on a random mix of easier copy lags leaves the model 21 points more accurate on the hard lag at the end, at identical compute, with a third of the run-to-run spread. A14's arms reproduce closely (shuffled 0.790 in both records).
What it is and is not
- It is not a curriculum. A14's staircase gave the model the same easier lags, in order, and gained nothing (
+0.027[-0.084, +0.137]). The ordering does not help; mixing does. - It is the first positive "which data" result here to survive a preregistered test on fresh seeds, and it is priced at matched compute against the plain alternative (training on the target task throughout).
- What it is, mechanistically, is open. Two readings fit: interleaving varied lags forces a general copy mechanism rather than one tuned to a single offset; or it is simply a better starting point that the fixed arm would reach with time. A16 asks the second (does the fixed arm catch up with a longer budget?), A17 the first (does mixing all lags throughout do as well?).
What stands
- Kill test does not fire. An early shuffled mixture of easier lags raises final lag-
8accuracy by+0.215[+0.135, +0.296]at matched compute on fresh seeds. - Mixing, not ordering, is what helps (with A14).
Limits
- One task family, one width (
48), one rate,6000steps. Lag8sits near this model's capacity limit.
REPLICATED ON A SECOND TASK 2026-09-28 by A18. On modular sum at the edge of learnability, an early random mix of easier sums raises final hard-task accuracy by+0.574[+0.301, +0.847]at matched compute (six of eight seeds learn it, against one of eight trained on the hard task alone). 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.
- curriculum
- Training on easier examples first and harder ones later, like a school syllabus, rather than on everything at once.
- 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.
- 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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