The Level Was Not the Problem
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 makes training cheaper? – One thing has worked: stopping part of the training early saved about 7% with no loss of quality. Everything else tested has been matched by a simpler or cheaper method -- and in two cases the clever method was only winning because it was quietly being given more.
In plain English
What we asked. Last time a model's loss curve predicted its sudden jump in accuracy well when the vocabulary stayed the same, and badly when it changed. We guessed the reason: the loss starts from a different height for each vocabulary. So we measured it against a level set by the vocabulary instead.
What we found. It made no difference. The prediction stayed just as poor across vocabularies. With a large vocabulary the loss falls a long way before accuracy jumps; with a small one accuracy jumps first. They are simply measuring different things.
Why it matters. So our explanation was wrong, and the simple formula stays the better free way to predict the jump across different tasks.
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. No training: N20's committed curves, re-scored. The script and kill test were committed before it was run.
Program v2 Bucket N, item N25. Decisive computation: . Output: analysis/loss_vocab_normalised.py. Reproduce with analysis/loss_vocab_normalised.jsonpython analysis/loss_vocab_normalised.py (seconds).
The question
N20 found that held-out loss crossing the midpoint of its own fall predicts when accuracy crosses 0.5 to 4.8 steps within vocabulary 32 but 15.7 across N6's grid, worse than N14's formula (9.6), and read the failure as the loss curve starting at the log of the vocabulary. The standing rule prefers a level fixed by the task over one normalised by the run. N25 fixes it: the loss crossing is the first evaluation at which held-out loss falls to half the natural log of the vocabulary size, with N20's leave-one-cell-out lead and N14's scoring unchanged.
Kill test, fixed before execution: the error still exceeds 9.6 steps.
Result: the kill test fires
| Loss crossing | Cell error, all 17 cells | Within vocabulary 32 |
|---|---|---|
| N20: midpoint of the run's own fall | 15.69 [3.15, 28.22] | 4.8 |
N25: half of ln V, fixed by the task | 15.83 [4.16, 27.49] | 5.97 |
The vocabulary columns that broke N20 break this too: the lead from loss crossing to accuracy crossing is +104.7 steps at vocabulary 128 (N20: +107.7) and -6 to -12 at vocabulary 8 (N20: -12 to -15). Moving the loss level to one set by the vocabulary changes almost nothing.
What this says
N20's explanation -- that the loss curve's starting height moved the midpoint -- is not what breaks the loss signal. With the level fixed by the task the leads barely move, so across vocabularies held-out loss and held-out accuracy are tracking different things: at vocabulary 128 the loss falls a long way (the model improving its probabilities over a large vocabulary) long before argmax accuracy reaches 0.5, and at vocabulary 8 accuracy reaches 0.5 before the loss has fallen far. A free instrument calibrated on one vocabulary does not transfer to another, and the offline formula remains the best free instrument across N6's grid.
What stands
- Kill test fires. A task-fixed loss level scores
15.83steps, no better than N20's15.69. - The loss signal's vocabulary dependence is not a normalisation artefact; the thread closes here with the formula ahead across vocabularies and the loss signal ahead within one.
Limits
- One alternative level (
0.5 ln V), fixed in advance; others were not tried, deliberately, to avoid searching levels until one fits. - N6's grid only.
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.
- argmax
- Short for 'the argument that maximises'. A model outputs a score for every possible next token; the argmax is simply whichever one scored highest. Accuracy is measured on the argmax, which is why accuracy is a thresholded quantity: only the winner counts, and by how much it won is discarded.
- calibrated
- A model is calibrated when its confidence matches how often it is right: answers it gives with 90% confidence should be right about 90% of the time.
- 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.
- normalisation
- Dividing a measurement by something else to make it comparable across cases. What you divide by is a choice, and it can change the answer as much as the data does.
- vocabulary
- The set of distinct symbols a model can read and produce.
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.