Research record 34 of 39

The Warning Is a Share of the Run

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.

In plain English

What we asked. We can read a model's internal state and tell that it is about to get much better at its task. An earlier experiment showed the catch: how far ahead that warning arrives varies a lot from run to run, and a warning you cannot rely on is not much use. But if we could predict which runs get a long warning and which get a short one, it would become useful again. So we looked for anything measurable very early in training, long before anything happens, that tells us how much warning this particular run will give.

What we found. Nothing did. We tested seven different early measurements against eighteen runs and none of them predicted anything, once we accounted properly for the fact that testing seven things gives you seven chances to get lucky. The one we most expected to work, a head start the model already has before training begins, predicted nothing at all.

Why it matters. The useful discovery came from a check we had built to keep ourselves honest. The warning is the gap between two moments, and we wanted to be sure we were not just predicting the second one. It turned out that almost all the variation comes from that second moment moving around, while the warning itself is remarkably steady. That led us to compare runs trained about three times longer, and the warning scaled with them: measured in steps the two disagree by nearly three times, measured as a share of the run they nearly agree. So we had been quoting it in the wrong unit. It is not twenty-odd steps, it is about a quarter of the way through training, and anyone who trained for a different length and expected twenty-odd steps would have been misled by us. None of this needed a single new training run.

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.
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  • 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, no training at all, no GPU, no cost.

Program v2 Bucket I, item I2. Decisive computation: analysis/lead_predictors.py. Output: analysis/lead_predictors.json. Reproduce in seconds with python analysis/lead_predictors.py, reading the series G6 committed and the summaries I1 committed.

The question

G6's real finding was the spread: the decode probe warns 12 of 12 runs at a 45-step horizon, 7 of 12 at 25, the size of its own published lead, and 1 of 12 at 10. An indicator with a wide per-run spread is unusable. An indicator whose spread is predictable is usable again, because the alarm can be conditioned on whatever predicts it.

The warning is a share of the training run, not a fixed number of steps
The warning is a share of the training run, not a fixed number of steps. We can read a model's internal state and tell it is about to improve. We had always quoted that warning as a number of steps. These are two sets of runs on the same task, one trained about three times longer than the other. The left pair shows the warning each got in steps. The right pair shows the same two numbers as a share of how long training took, rescaled so both pairs fit on one axis. Measured in steps the two disagree by nearly three times. Measured as a share of the run they almost agree. So the warning is not a fixed quantity we can promise in steps, it is roughly a quarter of the way through training, and quoting it in steps would mislead anyone who trains for a different length. We found this while checking a different question, and it cost nothing: it is a re-analysis of numbers two earlier experiments had already saved.

Kill test: no early quantity correlates with the per-run lead beyond seed noise. Then the spread is irreducible and the 45-step window is the honest claim.

Result: the kill test fires

Seven quantities, all computed at or before step 100: what a live detector would have, and 170 steps before the transition, against the per-run lead across 18 runs:

Predictorr vs leadr vs probe crossingr vs model crossing
gradient norm, calibration mean-0.298-0.401-0.480
model accuracy, calibration mean-0.219+0.119-0.076
probe accuracy, calibration slope+0.076-0.091-0.007
gradient variance, calibration mean+0.072-0.090-0.009
probe accuracy, calibration mean-0.067+0.059-0.008
probe minus model, calibration mean+0.058-0.002+0.039
probe accuracy at step 1+0.009+0.106+0.077

Family-wise 95% critical value: 0.598, from 20,000 permutations taking the largest absolute correlation across all seven predictors per draw. Seven predictors against eighteen runs will produce a "significant" correlation by chance, so the null a predictor has to beat is the best that noise produces, not the average. Nothing comes close.

Notably, the probe's own step-1 reading predicts nothing (r = +0.009). That was the most natural candidate: F2 observed the probe already reads 0.1761 against the model's 0.0368 at step 1, and F3 explained it as a reservoir effect. If that head start varied usefully between runs, the lead would vary with it. It does not.

The confound check is the more useful half

The design tested the obvious confound rather than assuming it away: the lead is model crossing - probe crossing, so if the probe's crossing barely moves, predicting the lead is really predicting when the model learns.

That is exactly what is happening, and it is worth more than the null:

Value
lead vs model crossing+0.743
lead vs probe crossing+0.049
spread of probe crossing7.0 steps
spread of model crossing10.4 steps

The probe's crossing time is the stable one. Run-to-run variation in "how much warning you get" comes almost entirely from the event moving, not from the warning moving. The probe is closer to a clock than to a variable-quality forecaster.

And the lead is not a step count

That reframing is testable against runs at a different learning rate, because I1's arms sit at a transition near 85 and G6's near 270, a factor of about three:

ConfigurationTransitionLeadLead as a fraction of the transition
AdamW, lr 0.001 (G6, 18 runs)270.0+64.80.240
AdamW, lr 0.005 (I1/F2, 5 runs)85.2+23.50.276
SGD, lr 1.686.0+32.40.377
SGD + momentum, lr 0.281.1+25.10.309

Under AdamW, a 3.2x change in the time to the transition changes the absolute lead by 2.8x and the fraction by 15%. Within G6's population the fraction also varies less than the lead does (8.8% against 11.4%).

So F2's headline +23.5 steps is better read as "about a quarter of the way through training". That is a different claim with different consequences: the warning does not shrink to nothing on longer runs, and quoting it in steps will mislead anyone who trains for a different length.

It also sharpens I1. I1 recorded the larger SGD lead as unexplained, noting the arms differ in learning rate as well as optimizer. The transitions turn out to be nearly matched (86.0 against 85.2), so SGD's larger lead is not a longer-training-run effect: the fraction itself is larger (0.377 against 0.276). The learning-rate confound still blocks attributing that to the optimizer, but "it is just a later transition" is now ruled out.

Verdict

  • The kill test fires. No early quantity predicts the per-run lead. Conditioning the alarm on an early reading is not available, and G6's 45-step window stands as the honest operating point.
  • The spread is mostly not the probe's. It is the transition moving, and the probe's own timing is the more stable of the two.
  • The lead should be quoted as a share of training, not a step count. Roughly 0.240.28 of the time to the transition under AdamW across a threefold change in training length.
  • This costs nothing to have found. It is entirely a re-analysis of series two earlier pilots committed, which is the argument for the standing rule that says to save them.

Limits

  • 18 runs, one task, one width, one architecture. The family-wise null is honest about seven predictors, but with n = 18 the test only has power against fairly strong relationships, a real correlation of 0.3 would not be detected here. The null is "nothing strong", not "nothing".
  • Seven predictors is not all predictors. Everything here is a summary of the two logged series. The initialisation spectrum, the weight norms and anything requiring a re-run were not available and are the obvious next candidates.
  • The scaling table has four configurations and only two learning rates, one of them with five runs. "The fraction is stable across training length" rests on two AdamW points and should be treated as a hypothesis with supporting evidence rather than an established scaling law.
  • The fraction differs by optimizer (0.240.28 AdamW, 0.310.38 SGD family), and the arms differ in learning rate too, so nothing here attributes that difference to the optimizer.

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.
AdamW
A widely used training algorithm that adapts how big a step it takes for each individual parameter. The default in most modern AI training.
architecture
The blueprint of a model: what components it has and how they connect. Two models can be the same size and completely different architectures.
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.
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.
optimizer
The algorithm that decides how to change the model given the gradient. AdamW and SGD are two common choices and they behave differently.
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.
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.
SGD
Stochastic Gradient Descent. The simplest training algorithm: take a step in the direction the gradient points, every time, with no adaptation.
slope
How steeply one quantity changes as another does. A slope of one between a warning and the event it predicts means the warning shifts exactly in step with the event.
variance
How spread out a set of numbers is. Rising variance in a signal means it is becoming more erratic.
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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