It Replicates on a Second Target
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 one surviving positive result, a mix of easier sums before a hard one, had only been tested on a single hard sum. Would it hold on another?
What we found. It did, more strongly. On a different hard sum, with the easy sums shifted to match, the mix solved the task on 25 of 32 fresh runs; the best ordinary recipe, with a learning-rate warm-up, on 2.
Why it matters. A result that survives a second target is worth much more than one that does not. The ordinary recipe was tuned on the first sum, so the next check tunes it on this one.
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 fresh seeds. The design, a disclosed two-seed throwaway and the kill test were committed (4e39459) before any run.
Program v2 Bucket A, item A43. Decisive computation: . Output: analysis/sum_mixture_second_pair.py.analysis/sum_mixture_second_pair.json
The question
A40 found the early mixture of easier sums beating plain training with a learning-rate warm-up on modular sum -- all on one target pair, (2, 7). Does it replicate on another?
Design: target (3, 8); easy mix (3,4)/(3,5)/(3,6) (A18's shifted by one) for 2000 steps; A40's loop and settings otherwise (0.003, 8000 steps; the plain arm with a 500-step linear rate warm-up). Thirty-two fresh seeds, 12001-12032. Kill test, fixed before execution: mixed minus the rate warm-up includes zero or lies below it. Anchor, in code: with the task set back to (2, 7), the loop reproduces A40 -- held. A two-seed throwaway, disclosed before running, had placed (3, 8) at or past the edge of what the plain recipe learns in the budget.
Results
| Arm (thirty-two fresh seeds) | Final (3, 8) accuracy | Solved (>= 0.9) |
|---|---|---|
| easier sums mixed first | 0.884 [0.809, 0.959] | 25 of 32 |
| plain with a learning-rate warm-up | 0.252 [0.153, 0.351] | 2 of 32 |
| mixed minus rate warm-up, paired | +0.632 [+0.503, +0.762] | higher on 30 of 32 |
The kill test does not fire. On a second target pair the mixture beats the best plain recipe on 30 of 32 fresh seeds, and solves the task on 25 where the plain recipe solves 2.
What it says
The modular-sum advantage is not a property of one target. It is larger here than on (2, 7) (+0.632 against +0.258), and the reason is visible in the plain row: (3, 8) is harder for the plain recipe (2 of 32 solved against 12 of 32), so at a fixed 8000 steps more of the mixture's speed shows up as a difference in accuracy. A42 found that on (2, 7) most of the gap is speed rather than ceiling; the same is likely here, and A44 (running) measures steps to solve directly. The two together would support the claim this thread can now make: on modular sum, an early mixture of easier sums reaches the solution much sooner than the best plain recipe, learning-rate warm-up included -- on two target pairs, on seeds never used for tuning.
What stands
- A43: kill test does not fire. Mixed minus the rate warm-up on
(3, 8):+0.632[+0.503, +0.762]; solved25against2.
Limits
- One width, one budget; the plain arm's rate and warm-up were tuned on
(2, 7)(A36), not(3, 8), and(3, 8)may sit further past the plain recipe's edge. A fixed-budget accuracy gap on a harder target mixes speed and ceiling.
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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