Research record

One Step of the Ladder

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 decides when a model learns, and can you change it? – Settings dominate, data barely matters, and there is a brief window before the jump in which interrupting the model is unusually costly. Timing can be delayed but not brought forward.

In plain English

What we asked. Turn the learning speed up too far and a model stops learning. A 2025 paper predicts that for memory tasks this limit drops steadily as the model has to remember further back. We tested that with memory spans from 2 to 6 steps.

What we found. The limit did drop, but almost all of the drop came between remembering 2 steps and 3. From 3 to 6 it stayed the same within how finely we had spaced the speeds we tried. So the direction matches the paper, but the steady law is not established.

Why it matters. The lesson: before reading a trend off a handful of points, check whether one point is doing all the work, and whether it sits at the edge of what you tried.

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, 120 training runs of 3000 steps. The design and kill test were committed (74bb1bc) before any run; a throwaway run was disclosed in the pilot.

Program v2 Bucket T, item T21. Decisive computation: analysis/ghost_critical_rate.py. Output: analysis/ghost_critical_rate.json. Post-hoc, changing no verdict: analysis/ghost_critical_rate_posthoc.py -> analysis/ghost_critical_rate_posthoc.json.

The question

arXiv 2501.02378 (the ghost mechanism) finds that abrupt learning in RNNs on working-memory tasks has a critical learning rate that falls as an inverse power of the timescale being learned, with learning collapsing above it. T21 measures the critical rate against the lag of a copy task -- how far back the model must remember -- on J8's width-48 GRU: a random stream copied at lag 2-6, eight rates a factor 1.5 apart (0.003-0.051), three seeds, 3000 steps. A seed's critical rate at a lag is the largest rate at which it reaches held-out accuracy 0.5; the exponent is each seed's log-log slope on lag.

The fastest usable learning rate drops with memory length, only at the first step
The fastest usable learning rate drops with memory length, only at the first step. A small model learning to copy a symbol from a fixed number of steps earlier, tried at eight learning rates. Each point is the fastest rate at which one run learned. A recent paper predicts this should fall steadily as the memory gets longer. It falls from 2 steps back to 3, and at 2 the true limit is above anything we tried. From 3 to 6 it is flat within the coarse spacing of the rates tried, so the steady fall the paper predicts is not established here.

Kill test, fixed before execution: the exponent's interval includes zero or lies above it.

Result: the kill test does not fire

LagCritical rate (three seeds)
20.051, 0.051, 0.051 (top of the grid)
30.034, 0.034, 0.034
40.034, 0.034, 0.034
50.023, 0.034, 0.023
60.034, 0.034, 0.034

Exponent -0.437 [-0.656, -0.218]: the critical rate falls with the lag, as the ghost mechanism predicts.

What carries the exponent (post-hoc)

  • Lag 2 is censored: every seed learned at the largest rate offered, so its true critical rate is at least 0.051, perhaps well above.
  • Without lag 2, the exponent is -0.134 [-0.423, +0.154], an interval including zero. From lag 3 to 6 the critical rate sits at 0.034 on eleven of twelve points; the grid's factor-of-1.5 spacing cannot resolve a slope there.
  • So the fall rests on one step of the ladder (lag 2 to 3), and the censoring at lag 2 means the true drop there may be larger, not smaller. The direction agrees with the paper; the power law is not established.
  • Above the critical rate, runs fail by learning partway (14 runs reach above chance but not 0.5), not by staying at chance -- the paper's "no-learning zone" was not seen here.

What stands

  • Kill test does not fire. Exponent -0.437 [-0.656, -0.218].
  • The fall is carried by the step from lag 2 to lag 3; lags 3-6 are flat within the grid's resolution.
  • Generates T22: a finer rate grid (factor 1.2) extending above 0.051, over lags 2-8 with a longer budget.

Limits

  • Rate grid a factor 1.5 apart; one width; 3000 steps, which may cut off slow learning at low rates and long lags.

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.
exponent
The number in a power law that says how strongly one quantity responds to another. A bigger exponent means a steeper response to the same doubling.
GRU
Gated Recurrent Unit. A compact design for processing sequences one item at a time, with internal switches controlling what it keeps in memory.
held-out
Data the model was never trained on, kept back specifically to test it. Scoring a model on data it has already seen measures memorisation, not learning.
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.
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.
power law
A relationship where one quantity changes by a fixed percentage whenever another one doubles, rather than by a fixed amount. Most scaling results in AI are stated this way.
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.
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.
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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