Research record

A Ratio That Could Not Decide

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: What actually happens at the moment a model learns? – It builds machinery rather than selecting it, working through the task in a reproducible order and trying a simpler wrong rule on the way. The visible training curve cannot tell you which is happening.

In plain English

What we asked. We are trying to find out why teaching a small model an extra, unneeded skill slows its other skills: because the extra skill takes up room, or because teaching it pulls on the model every step. This time we taught the extra skill on half the examples, and checked first that it would still be learned.

What we found. If room is the cause, the slowdown should stay the same; if pull is the cause, it should halve. For most of the models it roughly halved. But we had chosen to measure it as a ratio for each model, and on one model the baseline ran backwards, so its ratio divided by a negative number and swamped the average. The test we fixed in advance came out undecided.

Why it matters. The lesson is about measurement, not models: a ratio of two noisy differences can explode when its bottom half is near zero. The next attempt uses more models and a steadier measure.

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, six seeds, 7 training runs of 3000 steps. The share was set from a throwaway run and the pilot committed (3c74ffd) before any run.

Program v2 Bucket O, item O23. Decisive computation: analysis/competition_mechanism_half.py (O22's script at a 50% share). Output: analysis/competition_mechanism_half.json. Reproduce with python analysis/competition_mechanism_half.py (about forty minutes on a throttled laptop CPU); --reuse re-derives every endpoint from the saved series, and was checked to print the identical summary.

The question

Teaching a model one skill nothing needs (G) slows its later skills (O20), and doubling the width barely changes the share (O21). Is it room (G occupies capacity once learned) or pull (G's loss acts on the shared weights every step)? O22 tried to cut the pull tenfold and G was never learned. O23 cuts it in half, the smallest share at which a throwaway run (seed 9999, before commit) learned G: at 25% it did not, at 50% it did, at step 910.

One model's reversed baseline made the whole ratio meaningless
One model's reversed baseline made the whole ratio meaningless. For each model, how much of the slowdown caused by an unneeded skill remains when that skill is taught on half the examples. One explanation predicts about 1, the other about 0.5. The last model learned more slowly without the skill than with it, so its ratio divides by a negative number. Four models sit between 0.2 and 0.5, pointing one way. One sits near 2, and the model with the reversed baseline sits above 4 and drags the average past 1. A per-model ratio of two noisy differences was the wrong measurement, and the question stays open.

Endpoint, O22's: per seed, the share of F's full slowdown that remains, (F with half G - F without G) / (F with full G - F without G). Room predicts about 1; pull about 0.5. Kill test, O22's, fixed before execution: the mean share's interval includes 1. Precondition: G learned on at least four seeds. It passes: 6 of 6.

Result: the kill test fires -- on an interval too wide to mean anything

SkillFull GHalf GNo GRemaining share, per-seed mean
C185812901203+0.477 [+0.054, +0.900]
F231318281433+1.275 [-0.371, +2.921]
E2730 (4)21761868+0.251 [-0.976, +1.478] (3)

F's interval includes 1, so the kill test fires. It also includes 0.5, and 0, and very nearly 3. It cannot tell room from pull.

Why, per seed:

SeedFull GHalf GNo GDenominatorShare
94331950249013605901.92
943723801540131010700.21
94392100171013507500.48
946126101760113014800.43
946325401620101015300.40
9467230018502440-1404.21

On seed 9467, F came later with no G than with full G, so the denominator is negative and the ratio is meaningless -- and it dominates the mean. This is the standing rule, written down since J8, that a ratio needs a determinate denominator -- and this design broke it. A per-seed ratio of two noisy differences was the wrong endpoint for acquisition times that vary by hundreds of steps.

What the rest of the table suggests, post hoc and not a verdict

  • C's share is 0.48 [0.05, 0.90], excluding 1: half the pull, about half the slowdown.
  • By means rather than per-seed ratios, F's share is (1828 - 1433) / (2313 - 1433) = 0.45.
  • On the four seeds with large denominators the shares are 0.21-0.48.

All three point toward pull. None is the preregistered endpoint, and the preregistered endpoint fired, so the record's verdict is that O23 did not settle it.

What stands

  • The kill test fires as preregistered (F +1.275 [-0.371, +2.921]), and the endpoint is too unstable to support either reading.
  • Room or pull remains open, with C and the ratio of means leaning to pull.
  • Generates O24: the same comparison with twelve seeds and a ratio-of-means endpoint with a bootstrap interval, fixed in advance.

Limits

  • Six seeds, acquisition times spread by hundreds of steps, and one seed with a reversed denominator.
  • At a 50% share the two readings predict 1 against 0.5, a narrower separation than O22's planned 1 against 0.1.

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.

bootstrap
A way of estimating how uncertain a number is by repeatedly resampling the data you already have. Useful when the usual formulas do not apply.
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.
post hoc
Worked out after the fact, rather than decided in advance. We report such checks separately and never let them decide a result, because it is far too easy to find a pattern once you already know the answer.
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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