The Weighting 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. In our last experiment, training a thinking model to give an answer at every step of its thinking stopped it learning a harder puzzle, because its early answers could not possibly be right yet and trying to make them right swamped the learning. The obvious fix is to train the early answers less and the later ones more. We tried exactly that.
What we found. It barely helped. The model reached about 61% where a model trained only on its final answer reached 81%. We had said in advance that we would only test when-to-stop rules on a model that had actually learned the puzzle, so that test was not run.
Why it matters. Two different ways of training the early answers have now both failed the same way, which says the problem is not the balance but the timing. The next test learns the puzzle first, with only the final answer trained, and teaches the early answers afterwards, which is what happened by accident in the one version that worked on the easier puzzle.
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, S15's six seeds. The design, kill test and learning precondition were committed (18fbf54,cdde27f) before any run.
Program v2 Bucket S, item S16. Decisive computation: . Output: analysis/weighted_step_halting.py. Reproduce with analysis/weighted_step_halting.jsonpython analysis/weighted_step_halting.py (about fifteen minutes on a throttled laptop CPU); --reuse re-derives every endpoint.
The question
S15 built a task where adaptive thinking has room -- 16-entry parity, fixed budgets reaching 0.833 -- and found that supervising every one of twelve thinking steps with equal weight left the model at 0.575: early steps that cannot answer took most of the gradient. S9 had shown early answers must be trained to be trustworthy. S16 keeps both lessons: every step's loss weighted in proportion to its index, so early steps are still trained while later ones carry most of the signal.
Precondition, in code, fixed before execution: the model's last-step accuracy must reach the best fixed budget minus 0.05, or it has not learned the task and the halting test is not run.
Kill test, fixed before execution: at matched mean thinking steps, confidence halting does not beat the fixed-budget frontier.
Result: the precondition fails -- the model does not learn
| Seed | 9851 | 9857 | 9859 | 9871 | 9883 | 9887 | mean |
|---|---|---|---|---|---|---|---|
| last-step accuracy | 0.624 | 0.542 | 0.660 | 0.577 | 0.590 | 0.681 | 0.612 |
0.612 against the 0.783 required and the best fixed budget's 0.833. Weighting toward later steps improves on S15's uniform weighting (0.575) by about four points and does not come close to learning the task. The halting test was not run, as fixed in advance; the kill test is undecided because the thing it would test does not exist.
What this adds to S15
Two supervision schedules, the same failure. Uniform weight over twelve steps and weight rising with the step index both leave the model near 0.6, while a model trained only on its final answer -- S15's fixed budget of twelve -- reaches 0.810 at the same width, steps and data. Any substantial pressure on the intermediate answers, on this task, stops the model finding the solution. S13's recipe worked on the easy task because there the intermediate answers could mostly be right; on a task with room they cannot, and asking for them costs the learning.
The remaining route is to separate the two jobs in time, which is what S3 did by accident: learn the task with the final answer only, then train the intermediate answers to be calibrated, in a short fine-tune that should not undo a solution already found. That is S17.
What stands
- The precondition fails. Step-weighted deep supervision does not learn
16-entry parity (0.612against a best fixed budget of0.833); the halting test was not run. - The tension S15 found is not about the weighting. Uniform and rising weights both fail; only final-answer training learns.
- Generates S17: learn first, calibrate after.
Limits
- One weighting schedule besides S15's; a schedule that starts at zero on early steps and ramps up over training is S17's idea by another route, and was not tried here.
- Width and budget fixed at S15's. A larger model might absorb the intermediate pressure.
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.
- 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.
- deep supervision
- Training a model to give a correct answer at every intermediate stage, not only at the end, so an early answer can be trusted.
- gradient
- The direction and amount by which each of a model's internal numbers should change to do slightly better. Training is repeatedly following 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.
- parity
- Whether a count is odd or even. A classic test puzzle for models, because the answer flips with every single item and cannot be guessed from a rough impression.
- 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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