Research record

The Room Was a Training Budget

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. Some AI models can decide how long to think about each question: less for easy ones, more for hard ones. That can only pay off if thinking a fixed amount is not already good enough. We built a puzzle where, it seemed, it was not, and spent four experiments trying to get a model to decide for itself how long to think.

What we found. This time we trained everything for longer, the same amount for every method. A model that always thinks for six steps then got 99.5% right, so there was almost nothing left for a smarter strategy to win. The gap we had built was the training being unfinished. Training the finished models to also answer early made their final answers worse.

Why it matters. The practical lesson: before building something clever to beat a simple method, train the simple method properly. Otherwise the thing you are beating is an unfinished baseline.

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, 54 training runs. The design, precondition and kill test were committed (e93c183) before any run.

Program v2 Bucket S, item S18. Decisive computation: analysis/converge_then_calibrate.py. Output: analysis/converge_then_calibrate.json. Reproduce with python analysis/converge_then_calibrate.py (about an hour and a half on a throttled laptop CPU); --reuse re-derives every endpoint from the saved evaluations, and was checked to print the identical summary.

The question

The thinking-budget thread asks whether a model that decides how long to think per input can beat a fixed thinking budget at the same average cost. S15 built a task with room for that -- 16-entry parity, where at 4000 training steps no fixed budget came near the ceiling (best 0.833) -- and found every recipe that supervises the intermediate answers from the start stopped the model learning. S17 learned first (3000 steps on the final answer) and calibrated after (1000 steps supervising every step's answer); the calibration raised last-step accuracy on every seed, but learning had not finished and the precondition failed.

Trained longer, a fixed amount of thinking reaches the ceiling
Trained longer, a fixed amount of thinking reaches the ceiling. A small model answers a puzzle after a fixed number of internal thinking steps. Grey is after 4,000 training steps, the length our earlier experiments used; blue is after 7,000. Each bar is the average of six models. At the shorter length no fixed amount of thinking came close to perfect, which is why we thought there was room for a model that decides how long to think. Trained longer, six steps of thinking is almost perfect. The room was the training being unfinished.
Teaching a finished model to answer at every step costs it accuracy
Teaching a finished model to answer at every step costs it accuracy. Six models trained until they had learned the puzzle (first bar of each pair), then given extra training to make every intermediate thinking step give a good answer too (second bar), so that they could stop early when confident. On four of the six models the extra training made the final answer worse. Earlier, when the models had not finished learning, the same step made them better, but only because it was still teaching them the puzzle.

S18 moves the switch past convergence and matches compute: 6000 final-answer steps, then 1000 calibration steps, against every fixed budget retrained to 7000 steps.

Precondition (S17's, against the new frontier): after calibration, last-step accuracy within 0.05 of the best 7000-step fixed budget. Kill test (S17's): at matched mean thinking steps, confidence halting does not beat the fixed-budget frontier.

Anchor, in code: each seed's accuracy at step 3000 of the learning phase equals S17's committed value exactly. All six do.

Result: the precondition fails, and the frontier moved

S15, 4000 stepsS18, 7000 steps
fixed budget 30.5500.870
fixed budget 40.6780.958
fixed budget 60.7810.995
best fixed budget0.833 (10)0.995 (6)

Per seed, the halting model:

SeedAfter 6000 final-answer stepsAfter calibrationChange
98510.8330.908+0.075
98570.9720.838-0.134
98590.9640.833-0.131
98710.9730.983+0.010
98830.9900.906-0.084
98870.9580.946-0.012
mean0.9480.902-0.046

0.902 against the 0.945 required: the precondition fails and the halting test is not run, as fixed in advance.

What the table says

  • S15's room was a training budget. At 4000 steps no fixed thinking budget came within 0.12 of the ceiling; at 7000 a budget of six reaches 0.995. The task did not have room for adaptive thinking; the models had not finished learning it. At matched, converged compute there is almost nothing left for per-input budgeting to win: the frontier is flat from six steps on.
  • S17's "calibrating after learning helps" was continued learning. On an unconverged model the calibration phase raised accuracy on every seed; on a converged one it lowers it on four of six (mean -0.046). What looked like cooperation between the two objectives was the second phase still teaching the task.
  • The thread's four failures in a row had a common cause. S15, S16, S17 and S18 each found the adaptive model had not learned what the fixed budgets had; the first three ran at 4000 steps, on a task whose fixed budgets had not converged there either. Sizing the budget against the slowest thing the test needs (the standing rule O6 and S17 earned) applies to the baseline too.

What stands

  • The precondition fails; the halting test is not run.
  • On 16-entry parity at 7000 steps, a fixed budget of six reaches 0.995: the room S15 built closes when training is long enough.
  • Calibrating a converged model's intermediate answers costs last-step accuracy (-0.046, four of six seeds down).
  • The thinking-budget thread closes here. No item is generated: every design that remains would be testing adaptive halting where a fixed budget is already at the ceiling, which S13 already did.

Limits

  • One task, one width (64), six seeds, S15's thresholds.
  • One calibration length (1000 steps) and one learning rate; a gentler calibration might keep more accuracy, but the frontier it would have to beat is at 0.995.
  • The fixed arms were retrained rather than extended, so they are not anchored to S15's; S15's numbers are quoted from its record.

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.
baseline
The thing you compare against. A result without one is not a result.
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.
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.
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.
learning rate
How big a step training takes each time it updates the model. Too small and nothing happens; too big and it never settles.
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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