The Warm-Up Holds at a Larger Width
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 warm-up result came from one small model. Bigger models find the same task easier, so to test a bigger one fairly we also made the task harder, until the bigger model found it about as hard as the small one had.
What we found. The warm-up still helped: 61 percent against 56 on the hard task, on six of eight runs. That is a quarter of the gain the smaller model showed. But both versions were still improving when training stopped, and the gap between them was still growing.
Why it matters. So the effect is not a quirk of one model size, and how large it is at scale is still open. The next step is simply to train longer and watch the gap.
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,16training runs of6000steps. The design, the disclosed calibration throwaways and the kill test were committed (eed9c84) before any run.
Program v2 Bucket A, item A19. Decisive computation: . Output: analysis/warmup_width.py.analysis/warmup_width.json
The question
Every data-mixture result so far (A15, A16, A18, A20) is at width 48. P11's rule: a width sweep must raise difficulty with width, or the larger model finds the task easy and any effect fades by construction. Does the warm-up hold at width 96, on a target at the edge of what width 96 can learn?
Calibration throwaways, disclosed in the pilot before running (one seed, 6000 steps): at length 16 and rate 0.01, width 96 learned lag 10 and then collapsed, and lag 14 was solved through a one-position shortcut (T14's trap). At length 32 and rate 0.005, lag 8 was solved (0.98), lag 12 reached 0.5 only at step 4050 and lag 16 ended at 0.51. Lag 12 was chosen.
Design: width 96, random-stream copy at length 32, rate 0.005, batch 64, 6000 steps, J8's eight receiver seeds. Fixed: lag 12 throughout. Shuffled: lags 3, 6, 9 at random for the first 1500 steps (A15's 2/4/6 for lag 8, scaled by 12/8), then lag 12. Endpoint: lag-12 held-out accuracy at step 6000, paired per seed.
Kill test, fixed before execution: shuffled minus fixed includes zero or lies below it.
Results
Lag-12 accuracy (mean of 8) | Step 2000 | Step 3000 | Step 5000 | Step 6000 |
|---|---|---|---|---|
fixed lag 12 | 0.401 | 0.457 | 0.533 | 0.563 [0.547, 0.579] |
shuffled early, then lag 12 | 0.400 | 0.475 | 0.574 | 0.614 [0.576, 0.651] |
The kill test does not fire: shuffled minus fixed is +0.051 [+0.011, +0.090], higher on 6 of 8 seeds.
But the gain is about a quarter of width 48's (+0.215 in A15, +0.258 with A20's shorter warm-up), and it is still opening: the gap is -0.001 at step 2000, +0.018 at 3000, +0.041 at 5000 and +0.051 at 6000, with both arms still climbing (fixed +0.03, shuffled +0.04 over the last 1000 steps). At width 48, running longer widened the gap from +0.215 to +0.304 (A16). A 6000-step budget reads this task mid-climb, so this is the gap part-way through learning, not at convergence. Generates A24 (the same at 15000 steps).
What it says
The direction travels to a larger model on a task scaled to it. Whether the size does is not yet known: a smaller gain at width 96 could mean the effect shrinks with scale, or that this budget reads a slower task earlier in its learning. Those two readings make different predictions for a longer run, which is what A24 tests.
What stands
- A19: kill test does not fire.
+0.051[+0.011, +0.090]at width96, lag12, step6000;6of8seeds higher. - The gain is a quarter of width
48's at this budget and was still widening when the run ended.
Limits
- One larger width; the warm-up length (
1500) was A15's, not A20's shorter optimum, and the easy lags were scaled by a rule chosen for this design, not tuned. - The rate (
0.005) was chosen by one throwaway, not a sweep. 6000steps reads the target mid-climb in both arms.
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.
- calibration
- Working out an instrument's settings from runs whose answer you already know, so it can be used on a run whose answer you do not.
- held-out
- Data the model was never trained on, kept back specifically to test it. Scoring a model on data it has already seen measures memorisation, not learning.
- 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.
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