Against the Best Plain Run, Not Established
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 second task, adding numbers, starting with easier sums had stayed ahead of plain training at every learning rate. This time we gave plain training its best settings, including the standard warm-up schedule, and ran sixteen of each.
What we found. The easier-sums start solved the hard sum on 11 of 16 runs; the best plain recipe on 6. But because runs mostly either succeed or fail outright, that gap in average accuracy is not yet clearly outside the noise.
Why it matters. Not established, leaning positive. The next test runs just those two recipes on thirty-two new runs to settle it.
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,64new training runs of8000steps plus16re-used. The design and the kill test were committed (8e4af86) before any run.
Program v2 Bucket A, item A36. Decisive computation: . Output: analysis/sum_mixture_settled.py.analysis/sum_mixture_settled.json
The question
A32 left the modular-sum mixture undecided: above the plain run at every rate, but with the plain run's optimum at the grid edge, eight seeds on a bimodal outcome, and no learning-rate warm-up arm -- the arm that matched every data warm-up on the copy task (A33). Against the best plain alternative, with sixteen seeds, does the mixture win?
Design: A18's task, 8000 steps, sixteen seeds (J8's receivers and donors). Plain (2, 7) at 0.001 and 0.002; plain with a 500-step linear rate warm-up to 0.003 and to 0.005; the mixed arm at 0.003. Kill test, fixed before execution: mixed minus the best of the four plain cells includes zero or lies below it. Anchor, in code: plain at 0.002 on the first receiver reproduces A32 -- held.
Results
| Cell (sixteen seeds) | Final (2, 7) accuracy | Solved (>= 0.9) |
|---|---|---|
plain, 0.001 | 0.239 [0.109, 0.369] | 0 |
plain, 0.002 | 0.570 [0.388, 0.752] | 4 |
plain, rate warm-up to 0.003 | 0.686 [0.514, 0.859] | 6 |
plain, rate warm-up to 0.005 | 0.587 [0.391, 0.783] | 6 |
mixed, 0.003 | 0.853 [0.731, 0.975] | 11 |
The kill test fires. Mixed minus the best plain cell (the rate warm-up to 0.003; its optimum is found, 0.001 being far worse) is +0.167 [-0.068, +0.401], the mixture higher on 10 of 16 seeds. The mixture's advantage over the best plain alternative is not established.
What the numbers do say. The point estimate still favours the mixture, and it solves the task on 11 of 16 seeds against 6 for the best plain run. A learning-rate warm-up closed a good part of the gap A32 showed (0.570 to 0.686 in mean, 4 to 6 solved) without closing all of it. On the copy task the rate warm-up closed it entirely (A35); here, on this sample, it has not -- and A22 found the mixture's order matters on this task, which a warm-up's generic protection would not explain.
What it says
The honest reading is not established, leaning positive. Outcomes are bimodal, so the mean is a blunt instrument and sixteen seeds are few. One more, sharper test is worth its cost: A40 runs only the two cells that matter -- the mixture and the rate warm-up at 0.003 -- on thirty-two further seeds, with the kill test fixed on the paired difference as here. If that fails too, the modular-sum result joins the copy task's.
What stands
- A36: kill test fires. Against the best plain alternative (a rate warm-up to
0.003), the mixture is+0.167[-0.068, +0.401],10of16seeds higher. - Solved:
11of16with the mixture,6of16for the best plain run. Descriptive; not the kill test.
Limits
- One ramp length (
500steps), two peak rates; sixteen seeds on a bimodal outcome.
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.
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