Research record

A Queue, Not a Graph

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 happens at the moment a model learns? – It builds machinery rather than selecting it, working through the task in a reproducible order and trying a simpler wrong rule on the way. The visible training curve cannot tell you which is happening.

In plain English

What we asked. Our last experiment showed a small model learns simple skills before the skills built from them, every time. But the order alone cannot tell you which skill is built from which. So we tried holding one simple skill back, giving the model no feedback on it for a while, to see which later skills would be slowed down.

What we found. If learning followed what depends on what, only the skills built on the held-back one should have waited. Instead almost everything the model normally learns afterwards waited, including a skill that does not use the held-back one at all, and it waited the longest. The later a skill usually comes, the more it was delayed.

Why it matters. That looks more like a queue than a family tree: hold up one item and everything behind it waits. We only noticed the queue pattern after seeing the results, so it is a guess until our next experiment tests it directly.

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, six seeds, 18 training runs of 3000 steps. The design, precondition and kill test were committed (b9e2135) before any run.

Program v2 Bucket O, item O12. Decisive computation: analysis/prerequisite_edges.py. Output: analysis/prerequisite_edges.json. Reproduce with python analysis/prerequisite_edges.py (about seventy-five minutes on a throttled laptop CPU); --reuse re-derives every endpoint from the saved series, and was checked to print the identical summary.

The question

O11 found acquisition order follows planted depth on every seed. But order recovers layers, not edges: every look-up arrives before every composite, so nothing in the order says C needs A rather than D. O12 asks for the edges by intervention.

Holding back one skill delays what comes after it, not what depends on it
Holding back one skill delays what comes after it, not what depends on it. Six skills: A, B and D are simple look-ups, C combines A and B, F combines B and D, and E builds on C. For the first 600 steps the model gets no feedback on skill A. Each bar is how much later each skill is learned than normal, averaged over six runs. If learning followed what depends on what, holding back A would slow C (which needs A) and leave F alone. Instead F is slowed the most, and so is D, which needs nothing. The delay grows with how late a skill is normally learned, like a queue.

The task is O11's graph plus a second depth-1 composite: look-ups A, B, D; C = A + B; F = B + D, which does not need A; and E = C + D. Three arms per seed: control; withhold-A, where A's own answers go unsupervised for steps 1-600 (its token and query marker stay in the input); and withhold-D, the same for D. If acquisition reflects edges, withholding A should delay C more than F.

Kill test, fixed before execution: under withhold-A, the per-seed paired difference delay(C) - delay(F) has an interval including zero.

Precondition, fixed before execution: C and F acquired on at least four of six seeds in every arm. It passes (F on 4 of 6 under withhold-D, all others 6).

Budget: 3000 steps, checked on a throwaway seed before the pilot was committed (F at 1140).

Result: the kill test fires -- in the wrong direction for edges

Acquisition step (first step past halfway from chance to perfect, and staying there), mean over the seeds that acquired it:

ArmBDACFE
control118 (6)437 (6)528 (6)1038 (6)1290 (6)2085 (6)
withhold-A152 (6)697 (6)877 (6)1345 (6)1802 (6)2288 (5)
withhold-D117 (6)938 (5)757 (6)1140 (6)1998 (4)2333 (3)

Delay against each seed's control, paired:

SkillNormal positionDelay under withhold-ADelay under withhold-D
B1st+33.3 [+22.5, +44.2]-1.7 [-9.6, +6.2]
D2nd+260.0 [+19.7, +500.3]+490.0 [-66.8, +1046.8] (5)
A3rd+348.3 [+166.4, +530.3]+228.3 [+31.9, +424.7]
C (needs A)4th+306.7 [+18.9, +594.4]+101.7 [-153.8, +357.2]
F (needs D)5th+511.7 [+147.7, +875.6]+735.0 [+316.0, +1154.0] (4)
E6th+162.0 [-564.3, +888.3] (5)+46.7 (3)

delay(C) - delay(F) under withhold-A is -205.0 [-580.5, +170.4]: the kill test fires. Withholding A delays F, which does not need A, more than it delays C, which does. It also delays D (+260), a look-up that needs nothing. The mirror, reported: withholding D delays F more than C (+517.5 [-96.4, +1131.4]), in the direction edges predict, but its interval includes zero and rests on four seeds.

Reading it: a queue, not a graph

Withholding a skill does not delay its descendants. It delays nearly everything the model would have learned after it, and under withhold-A the delay grows with a skill's normal place in the queue: D +260, C +307, F +512. Only B, learned first, is barely touched. That is what a model acquiring skills one after another would show -- hold back one early item and everything behind it waits -- and it is not what the dependency graph predicts. This reading is post hoc and the record does not test it; O17 does.

What O11 established still stands: acquisition order follows depth on every seed. What O12 adds is that intervening on a prerequisite does not reveal which skills depend on it on this substrate, because the intervention's effect is dominated by something that is not the graph.

What stands

  • Kill test fires. Withholding A delays F (no dependence) by +511.7 and C (dependence) by +306.7; the difference -205.0 [-580.5, +170.4].
  • Withholding one skill's supervision delays most skills learned after it, including ones that do not depend on it, and the delay grows with queue position under withhold-A.
  • Edges are not recovered by this intervention. O11's layers stand; the edge question is open.
  • Generates O17: is acquisition a serial queue?

Limits

  • Intervals are wide: acquisition times vary by hundreds of steps between seeds, and six seeds resolve delays of this size only coarsely.
  • withhold-D loses seeds (F on four, E on three), so the mirror is weak.
  • One intervention: withholding supervision for 600 steps. Blocking a skill's input (randomising its token) is a different intervention and might recover edges where this one does not.
  • The queue reading is post hoc; it explains the pattern after seeing it, which this programme's own rules (Q8) say to test before believing.

QUALIFIED 2026-09-26 by O17. This record's post-hoc "queue" reading is refuted: withholding G, a skill nothing depends on, does not delay the skills learned after it but speeds them (C -551.7, F -700.0). The measured delays here stand; the explanation offered for them does not. Competition for a shared budget is the leading alternative (O20). 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.

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.
post hoc
Worked out after the fact, rather than decided in advance. We report such checks separately and never let them decide a result, because it is far too easy to find a pattern once you already know the answer.
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.

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