The Head Start Closes
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. More about this programme.
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. The day before this experiment we published a result with a break-even number: handing a trained model's internal machinery to fresh ones saves each of them real time, and pays for itself once about five have used it. That was measured at a single model size. Everything in this project that has taken the form of something happening at a particular moment during training has faded as models got bigger, so we tested it against size straight away.
What we found. It fades too. At the smallest size we tried, a fresh model saved about forty per cent of its own learning time. At the middle size, about thirty. At the largest, the honest answer is nothing: around six per cent, with a range of plausible values that includes zero. The break-even number we published holds at the size it was measured at and nowhere above it.
Why it matters. Two things are worth taking from this. The first is that the machinery still works, it just stops helping. A model handed weights from an untrained donor is still slowed down at every size, by about the same amount. So the larger model notices being handed somebody else's numbers; what disappears is the benefit of those numbers having learned anything. The second is the pattern. This is the fifth result in this project of that shape to fade as models grow, and the fifth to fade completely. Five is enough that we now treat it as what to expect rather than as a surprise, and it changes the order we do things in: test against size before building anything on a result, not after. We tested this one the day after publishing it, and that was still a day too late.
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. - Negative results are kept. Roughly half of what is published here says an idea did not work, including several of our own. Those pages are not failures, they are the output. 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, 4 receivers at 3 widths, no GPU, no cost.
Program v2 Bucket P, item P9, generated by P8. Decisive computation: . Output: analysis/donor_width.py. Reproduce with analysis/donor_width.jsonpython analysis/donor_width.py; --reuse re-derives every endpoint.
CORRECTED 2026-09-01 by P11. The headline is wrong as a statement about scale. This record reports that the head start "closes as models grow" and calls it the fifth instance of a pattern. It does not close as models grow. It closes as the model outgrows the task. P11 rebuilt the sweep with difficulty raised alongside width, so the control run's transition time stays near130instead of falling from135to59. On that ladder the head start is flat:-42.6%,-40.2%,-42.8%of the run at widths 24, 48 and 96, every interval overlapping. At width 96 it is-52.5steps against this record's-3.8-- fourteen times larger at the same model size, from nothing but making the task harder. Every number below reproduces exactly, and P11's anchor requires that. What is withdrawn is the interpretation: the fade was an artefact of sweeping width at fixed task difficulty, which makes the model progressively oversized and the analysis window progressively too wide.
The question
P8 is the programme's first efficiency claim with a break-even number: a matured donor saves each receiver 25.0 steps and pays for itself across 4.8 of them. It was measured at one width.
Every timing-shaped result in this archive has degraded with size. The critical-period window narrows with width and had vanished at the largest size tested; the decode probe's lead shrinks as models grow. A saving measured at width 48 and never swept is exactly the shape of claim this programme has repeatedly had to withdraw.
Kill test, fixed before execution: the head start's share of the receiver's own time-to-transition does not grow with width, and its interval includes zero at the largest width.
Anchor enforced in code: width 48 must land on P8's [-30.7, -19.3]. It does, at -27.5 [-32.1, -22.9].
What we found
The donor is trained to a fixed multiple of its own transition (1.4x) rather than a fixed step count, because 120 steps is a different stage of maturity at each width and a fixed count would confound donor maturity with width.
| Width | Receiver alone | Donor length | Head start | As a share of the receiver's own run |
|---|---|---|---|---|
| 24 | 130.0 | 177 | -52.5 [-60.5, -44.5] | -40.4% [-46.5%, -34.3%] |
| 48 | 88.8 | 119 | -27.5 [-32.1, -22.9] | -31.0% [-35.4%, -26.5%] |
| 96 | 58.8 | 80 | -3.8 [-7.7, +0.2] | -6.2% [-12.9%, +0.4%] |
The kill test fires. The head start falls monotonically with width and its interval includes zero at width 96, in steps and as a share alike. P8's saving is a small-model phenomenon.
Both endpoints were reported because they can disagree, a constant step saving is a shrinking share as models get faster, and a constant share is a shrinking step count. Here they agree, which is the strongest form the answer could take.
The harm does not close, only the benefit
The untrained-donor control still delays at every width: +36.2, +21.2, +21.2. So at width 96 a matured donor does nothing while an untrained one still costs +21.2 steps. The transplant machinery is working and the model still notices being handed foreign weights. What disappears is specifically the benefit of the donor having learned something.
What that does to P8's economics
P8's break-even of 4.8 receivers holds only at width 48. At width 96 there is no saving to amortise at any number of receivers, so the break-even is undefined rather than large. A correction banner has been appended to P8's record; its numbers are unchanged and reproduce.
The pattern this is the fifth instance of
- the critical-period window narrows with width and vanished at the largest size tested
- the decode probe's lead shrinks as models grow
- one gradient alarm fires earlier and earlier until it covers the whole run
- another cannot accumulate enough history before larger models have already learned
- and now the donor head start closes
Five results, one shape. **In this programme, a phenomenon defined by when something happens has never survived being made bigger. That is now enough instances to treat as a prior rather than a coincidence, and it is the strongest argument yet that the remaining timing-shaped items should be width-swept before** anything is built on them, not after.
Limits
- Three widths, four receivers each. A trend across three points, with the largest carrying the verdict. A fourth width above 96 would test whether it goes negative or merely flattens.
- Width 96 is still a 17,280-to-70,000 parameter model on a synthetic task. "Closes by width 96" is not "closes at scale"; it is a trend within a toy range, and the honest reading is that the burden of proof has moved rather than that the matter is settled.
- The transition endpoint is quantised to 5 steps. At width 96 the receiver transitions at
58.8, so a 5-step quantum is 8.5% of the run and the-3.8reading sits near that floor. - The donor's maturity multiple (
1.4x) is fixed and not swept. A more mature donor might hold up better at width, though P8 found longer donors buy little. - One task, one learning rate, one graft point.
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.
- confound
- A second explanation you did not control for. If bigger models both learn faster and score higher, then 'fast learners score higher' may be entirely about size and not about speed.
- critical period
- A stretch of time during which something has to happen for development to proceed normally. Borrowed from biology, where it describes windows in which a young brain must receive certain input.
- 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.
- 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.
- probe
- A small separate model trained to read information out of a bigger model's internals, used as a measuring instrument rather than as a product.
- 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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