Mixing First Makes It Learnable
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 finding -- that a random mix of easier tasks early makes a model better at the hard one -- came from one kind of task. A result like that has failed on a second task before, so we tried a completely different one: adding up two symbols from earlier in a sequence, made just hard enough that this small model usually cannot learn it.
What we found. Trained on the hard version alone, only one run in eight learned it. With a quarter of the same training spent first on a random mix of easier versions, six in eight learned it completely, and every run did better. The effect carried over, and here it was the difference between learning the task and not.
Why it matters. In practice: when a model struggles to learn a hard task, try spending some of its training on a varied mix of easier versions first. 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 of8000steps. The design, endpoint and kill test were committed (34bde48) before any run; throwaways choosing the task were disclosed in the pilot.
Program v2 Bucket A, item A18. Decisive computation: . Output: analysis/sum_mixture.py.analysis/sum_mixture.json
The question
A15 found that a random mix of easier copy lags for the first quarter of training raises final hard-lag accuracy by +0.215 at matched compute, on fresh seeds. A positive on one task has failed a second before here (O5's growth saving, O27/O28). A18 runs A15's comparison on a different task family: modular sum, target = x[t-a] + x[t-b] mod 32, with the hard target (2, 7) -- chosen by throwaways as the edge of what this width-48 model can learn in the budget ((2, 6) is learned fully, (2, 8) never). Fixed trains on (2, 7) throughout; mixed draws (2, 3), (2, 4) or (2, 5) at random for the first 2000 of 8000 steps, then (2, 7). Eight seeds, rate 0.005, endpoint (2, 7) held-out accuracy at step 8000.
Kill test, fixed before execution: mixed minus fixed has an interval including zero or lying below it.
Result: the kill test does not fire
| Seed | Fixed (2, 7) | Mixed first |
|---|---|---|
| 1 | 0.06 | 1.00 |
| 2 | 0.65 | 1.00 |
| 3 | 0.19 | 1.00 |
| 4 | 0.15 | 0.94 |
| 5 | 0.99 | 1.00 |
| 6 | 0.09 | 0.50 |
| 7 | 0.10 | 0.50 |
| 8 | 0.07 | 0.94 |
| Mean | 0.286 | 0.860 |
Paired difference +0.574 [+0.301, +0.847]. Mixed ends higher on every seed.
What it shows
At the edge of what the model can learn, the early mixture decides whether it learns at all. Trained on the hard sum throughout, one seed of eight solves it within the budget and five stay near chance. With a quarter of the same compute spent on a random mix of easier sums first, six of eight solve it (0.94-1.00) and the other two reach half. The effect is larger here than on the copy task (+0.215) because the fixed arm mostly fails outright.
With A14 (ordering does nothing) and A15, the result so far: a random mix of easier variants of a task, early in training, makes a hard version learnable at no extra compute, on two task families. A16 and A17 are testing whether it is a higher ceiling or a head start, and whether ongoing variety does the same.
What stands
- Kill test does not fire. On modular sum, mixed minus fixed final accuracy
+0.574[+0.301, +0.847], every seed higher. - The early-mixture gain travels to a second task family, which O5's growth saving did not.
- At the capability edge it is the difference between learning and not learning in the budget.
Limits
- One width, one rate, one budget per task; the hard targets were chosen at the edge of learnability, where any help is most visible. Whether it helps on tasks well within reach is not tested (A15's lag-
8task was also near the edge). - Eight seeds; the fixed arm is bimodal, so the mean hides a learned-or-not split.
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.
- 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.
- 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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