The Sum's Baseline, Tuned Both Ways
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. When we compared the easy-start recipe with ordinary training on the sum, ordinary training's best learning rate was the lowest we had tried. A lower one might have been better still, so we tried two.
What we found. Both were slower. Ordinary training is best in the middle of the range, and the easy start still reached the solution in about half the steps.
Why it matters. So the comparison now stands against ordinary training tuned in both directions.
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,32new training runs of12000steps plus96re-used from A73. The design and the kill test were committed (ecf0f9d) before any run.
Program v2 Bucket A, item A75. Decisive computation: . Output: analysis/sum_twenty_lower.py.analysis/sum_twenty_lower.json
The question
A73 found the easy start ahead of plain training on the sum mod 20 by -3300.0 [-4617.4, -1982.6] steps, with plain's best rate (0.003) at the bottom of its grid. Does a lower plain rate close the gap?
Design: plain at 0.002 and 0.0015, A73's seeds and 12000-step budget; the best of all five plain rates against A73's best mixed cell, with the edge check looking at both ends of the grid. Kill test, fixed before execution: best mixed minus best plain includes zero or lies above it. Anchor, in code: A73's plain 0.003 run reproduces -- held.
Results
| Plain rate | Mean steps to 0.9 | Median | Solved (of 16) |
|---|---|---|---|
0.0015 (new) | 7891 | 7880 | 15 |
0.002 (new) | 6864 | 6960 | 16 |
0.003 (A73) | 6471 | 5895 | 15 |
0.005 (A73) | 8392 | 9295 | 8 |
0.008 (A73) | 11558 | 12000 | 1 |
easy start, best (0.005, A73) | 3171 | 2960 | 16 |
- Plain's best rate stays
0.003, now inside the grid (worse on both sides). - Best mixed minus best plain:
-3300.0[-4617.4, -1982.6]steps, unchanged.
The kill test does not fire. A73's caveat is closed: with symbols and model matched to the random table, and both arms tuned to interior optima, the easy start takes about half the steps on the sum.
What stands
- A75: kill test does not fire. Plain's best rate on the sum mod
20is0.003(interior); the easy start's lead of-3300steps stands.
Limits
- One modulus, width
48, sixteen seeds; the mixed arm's grid was0.003-0.008(best interior at0.005).
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.
- 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.
Get new results as we publish them
Roughly monthly, one finding per email, in plain English first. Including the approaches that turned out not to work, which are usually the useful ones. No sales email.
Double opt-in: we send a confirmation link and add nobody who does not click it. One-click unsubscribe on every email.