It Must Be an Early Phase
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. A research team made a hard arithmetic problem learnable by keeping easier examples in the training mix all the way through. Our easy sums had only ever been an early phase. Would keeping them in work as well?
What we found. No. As a short phase at the start, the easy sums let 13 of 16 runs learn the hard sum. Mixed in for the whole run, none did. There is a catch: mixed in, the hard sum was only a quarter of the training data, so the model also saw it much less.
Why it matters. The next test keeps easy sums in throughout but makes the hard sum three quarters of the data, so the two explanations can be told apart.
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,32training runs of8000steps on sixteen fresh seeds. The design and the kill test were committed (69db55a) before any run.
Program v2 Bucket A, item A48. Decisive computation: . Output: analysis/sum_mixture_throughout.py.analysis/sum_mixture_throughout.json
The question
arXiv 2410.03569 makes hard modular arithmetic learnable with a training distribution that keeps easier examples in throughout. Every modular-sum mixture here has been an early phase (A40, A44). Does it have to be?
Design: A18's task at 0.003, 8000 steps, sixteen fresh seeds 16001-16016. Early: 2000 steps of (2,3)/(2,4)/(2,5), then (2, 7). Throughout: every step draws one of (2,3), (2,4), (2,5), (2,7) at random for the whole run. Kill test, fixed before execution: early minus throughout includes zero. Anchor, in code: the early arm reproduces A40's mixed run on its first seed -- held.
Results
| Arm (sixteen fresh seeds) | Final (2, 7) accuracy | Solved (>= 0.9) |
|---|---|---|
| early phase, then the target | 0.904 [0.796, 1.011] | 13 |
| easy and hard mixed throughout | 0.076 [0.070, 0.083] | 0 |
| early minus throughout | +0.827 [+0.722, +0.933] |
The kill test does not fire. Keeping the easy sums in for the whole run leaves every seed near chance; the same material as an early phase solves the task on thirteen of sixteen.
A confound this design cannot remove
The arms differ in how much of the hard sum they see. Throughout, (2, 7) is a quarter of the data: about 2000 steps' worth, against 6000 in the early arm, and the plain recipe needs a median 7825 steps to solve it (A44). Under-exposure alone could leave the throughout arm at chance. Two things argue it is not only that -- the throughout arm is not merely slow but flat at chance (0.076), and A39 found the far easy pairs, trained on at length, delay learning on their own -- but neither separates the two readings. A50 does: easy sums kept in throughout at a quarter of the data, the hard sum at three quarters.
What it says
The recipe on modular sum is specific: a brief phase of easier sums sharing the target's structure, then the target alone. Mixing throughout -- the design in 2410.03569 -- did not work here in the form tested, which parallels the copy task, where mixing throughout also hurt (A17).
What stands
- A48: kill test does not fire. Early minus throughout:
+0.827[+0.722, +0.933]; solved13against0. - Confounded with hard-sum exposure (
6000against about2000steps); A50 separates them.
Limits
- One mixing proportion for the throughout arm; sixteen seeds; one budget.
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.
- confound
- A second explanation you did not control for. If bigger models both learn faster and score higher, then 'fast learners score higher' may be entirely about size and not about speed.
- 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.
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