Research record

One Jump, or Several?

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.

EXPLORATORY. Not a preregistered study. Local CPU, 10 training runs, no GPU, no cost.

Program v2 tier 3, items D2 (per token class) and A12 (per position), which are the same measurement applied to two ways of slicing the same runs. Decisive computation: analysis/acquisition_microscope.py. Output: analysis/acquisition_microscope.json. Reproduce with python analysis/acquisition_microscope.py in about ten minutes on a throttled laptop CPU.

The question, and why it matters now

Every measurement this project has made of the transition treats it as one thing: accuracy averaged over every scored position jumps from chance to ceiling. That average could be hiding a staircase.

What looked like one moment of learning is really four
What looked like one moment of learning is really four. The task asks a model to repeat a short pattern it has already seen. Measuring overall accuracy, the model appears to learn the whole thing in one sudden burst. Measuring each element of the pattern separately shows four bursts instead, about sixteen steps apart. The model learns the pattern in order: first element, then second, then third, then fourth. Averaging across all of them blurred four events into one. The order is almost perfectly repeatable across runs that share nothing but the task, which means the earliest element is an early warning for the rest. Averages hide structure, and here the structure was the finding.

It matters because D3 closed the control programme by showing the transition's timing cannot be steered. Structure inside the transition would be a different handle, and the program has none.

Kill test: all classes move together within a few steps.

"A few steps" is not scale-free, so it is made so: a stagger between classes counts only if it is large relative to how long a single class takes to transition. Two classes separated by 5 steps mean nothing if each takes 60 steps to cross.

Result 1: per position, there is a staircase, and it is the same one every time

delayed-copy, 13 scored positions, five seeds:

MeasureValue
Stagger between classes75.0 steps
A single class's own width52.0 steps
Stagger / width1.44
Order consistency across seeds+0.983

The classes resolve separately, and the order in which they resolve is almost perfectly reproducible between runs that share nothing but the task.

Result 2: what orders the staircase is not position

The per-position transition steps are not monotone in position: 40, 70, 95, 114, 54, 77, 91, 113, 74, 80, 88, 100, 79. "Later positions are harder" is simply false, and so is its opposite.

The script scores three candidate orderings rather than leaving the pattern to be spotted:

OrderingSpearman
Prefix element being predicted+0.910
Absolute position+0.302
Position within the period-0.196

delayed-copy repeats a prefix of length lag, so position p predicts prefix element (p + 1) mod lag. Grouping by that makes the staircase obvious:

Prefix elementPositionsMean transition step
03, 7, 11, 1561.8
14, 8, 1275.7
25, 9, 1391.3
36, 10, 14109.0
The model learns to reproduce the repeating prefix one element at a time, in order, roughly 16 steps apart. What looked like a single event is four, and the ordering is the sequence order of the thing being memorised.

Result 3: per lag, the same consistency without the separation

dispatch-copy-8lag, six lag classes:

MeasureValue
Stagger between classes105.0 steps
A single class's own width251.5 steps
Stagger / width0.42
Order consistency across seeds+0.910
Ordered by announced lag-0.886

By the scale-free criterion this is not a staircase: each class takes so long to transition that the classes overlap heavily. It is a ramp with a consistent internal ordering rather than a set of discrete steps.

And the ordering is counterintuitive: rho = -0.886 against the announced lag means longer lags are acquired first. Lag 6 and 7 transition around steps 80 and 90; lags 2 and 3 around 162 and

  1. Whatever makes a short lookback easy for a human is not what makes it easy for this model.

What the two views agree on

The two decompositions disagree about whether to call it a staircase, and agree about the thing that matters more: the acquisition order is highly reproducible in both (+0.983 and +0.910). Whether the steps are separated enough to resolve depends on how wide each step is, which is a property of the task. The existence of a consistent order does not.

That is the internal structure the program lacked. Concretely:

  • A11 gains a candidate. A12's own note says that if acquisition propagates, the earliest class is a candidate leading indicator for the full transition. It does propagate, reproducibly, and the earliest class transitions ~47 steps before the latest.
  • A14 gains a handle. Position-dependent difficulty is real and ordered, so a curriculum over prefix elements is now a well-defined intervention rather than a guess.
  • It complements F2 without duplicating it. F2 found information present in the state ~23 steps before the model can use it. This finds parts of the output arriving before other parts. Both are "early predicts late", measured on different objects.

Limits

  • One architecture (GRU), one width, five seeds, two tasks.
  • Both orderings are correlational. Nothing here shows that the early classes cause the late ones; a curriculum experiment or a per-class freeze would be needed, and D1's freeze machinery is the obvious tool.
  • The 1.0 threshold on stagger-over-width is a choice, made before the runs but not preregistered. The two tasks land at 1.44 and 0.42, comfortably either side, so the verdict does not turn on a borderline call, but a task landing near 1.0 would need a better rule.
  • The dispatch task's six usable classes exclude lag 8, which did not clear the sample-count floor on every seed.

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