Calibrate After Learning
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. Twice now, training a thinking model to give an answer at every step of its thinking stopped it learning a harder puzzle. So we separated the two jobs in time: first the model learns the puzzle with only its final answer trained, then a shorter second phase trains its answers along the way.
What we found. The order made the difference. Every run improved during the second phase, the opposite of what happened when both were trained together from the start. But every run still fell short of the bar we had set in advance for testing its stopping rule, because the first phase ended too soon: on this puzzle the solution arrives late in training, and we switched before it had.
Why it matters. The lesson generalises: some training goals that fight each other when pursued at once cooperate when pursued in sequence. The next test lets the model finish learning first.
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 precondition were committed (f04419d) before any run.
Program v2 Bucket S, item S17. Decisive computation: . Output: analysis/learn_then_calibrate.py. Reproduce with analysis/learn_then_calibrate.jsonpython analysis/learn_then_calibrate.py (about fifteen minutes on a throttled laptop CPU); --reuse re-derives every endpoint.
The question
On 16-entry parity, where adaptive thinking has room, training only a model's final answer learns the task and supervising its intermediate answers does not (S15 0.575, S16 0.612, against a best fixed budget of 0.833). S3's overthinker had learned first and been changed second. S17 does that on purpose: 3000 steps on the final answer only, then 1000 steps with every step's answer supervised, then stop on confidence.
Precondition, in code, fixed before execution: after the calibration phase, last-step accuracy within 0.05 of the best fixed budget, or the halting test is not run.
Kill test: at matched mean thinking steps, confidence halting does not beat S15's fixed-budget frontier.
Result: the precondition fails -- for a different reason than S15 and S16
| Seed | 9851 | 9857 | 9859 | 9871 | 9883 | 9887 | mean |
|---|---|---|---|---|---|---|---|
| after learning (3000 steps) | 0.582 | 0.562 | 0.602 | 0.647 | 0.714 | 0.698 | 0.634 |
| after calibration (+1000) | 0.727 | 0.730 | 0.658 | 0.724 | 0.722 | 0.781 | 0.724 |
0.724 against the 0.783 required, so the halting test was not run. But the table says something S15 and S16 could not:
- Calibrating after learning did not undo anything -- it helped. Every seed's last-step accuracy rose during the deep-supervised phase, by
0.09on average. Once the model has a partial solution, asking its intermediate steps to answer does not stop it improving. - The learning phase was too short. At
3000steps of final-answer training the model is at0.634; S15's identically trained fixed budget of twelve reached0.810at4000. On this task the solution arrives late, between the two, and S17 switched phases before it had.
One correction to the script before publishing: its message on a failed precondition read "the calibration undid the solution", which the data contradict. It now reads "below the learned threshold after calibration"; the decision logic is unchanged and --reuse reproduces the same numbers.
What stands
- The precondition fails, and the halting test was not run.
0.724after calibration against0.783required. - Learn-then-calibrate is the first schedule on this task where deep supervision helps rather than blocks:
+0.09during the calibration phase on every seed. - The failure is the phase boundary, not the method. The next version learns to convergence first -- which on this task means past
4000steps -- and gives the fixed-budget arms the same total training. That is S18, and it costs roughly twice this run.
Limits
- Compute is matched to S15's arms (
4000steps in all), which is why the learning phase was cut short; matching compute and letting the model converge first are in tension on a task that learns late. - Six seeds, one width, as in S15 and S16.
QUALIFIED 2026-09-26 by S18. The calibration phase raised last-step accuracy on every seed here because the model had not finished learning. Switched after6000final-answer steps, when it had, the same phase lowers last-step accuracy on four of six seeds (mean0.948to0.902). "Calibrating after learning helps" should read "calibrating before learning has finished keeps teaching the task". Text and numbers unchanged.
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.
- 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.
- 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.
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.