The Harder the Task, the Bigger the Saving
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: Is the task we are studying actually hard? – Often it is not. A rule from 1990 with no parameters beats the trained model on the task most of these results were measured on, and what an intervention costs is set by the task's own structure.
In plain English
What we asked. Our easy-start recipe slowed learning on an easy version of a task and sped it up on a harder one. We wanted to see the whole picture, so we made five versions of the same task, each harder than the last.
What we found. The effect moved smoothly with difficulty. On the two easiest versions the easy start cost about a quarter more steps. From the middle version on it saved time, and on the hardest it saved 40%.
Why it matters. So there is a line: when ordinary training learns a task quickly, starting easy is extra work; when it struggles, starting easy pays, and pays more the harder the task. Where the line falls depends on the setup, but that it exists is the useful part.
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,96new training runs of24000steps plus64re-used from A60 and A62. The design and kill test were committed (68ad342,5b360db) before any run, including the replacement of the backlog's original kill test and the reason for it.
Program v2 Bucket A, item A65. Decisive computation: . Output: analysis/max_ladder.py.analysis/max_ladder.json
The question
The easy start slowed learning of an easy maximum (A60, lag 7) and sped up a harder one (A62, lag 9). Does its benefit grow steadily as the hard task gets harder for plain training, and where does it cross zero?
Design: GRU, width 48, rate 0.003; the hard task max(x[t-2], x[t-far]) at far lags 6, 8, 10 (new, sixteen fresh seeds each, 24000 steps) with 7 (A60) and 9 (A62) reused; sequence length 9 + far (nine scored positions); easy maxima on (2,3)/(2,4)/(2,5) for 2000 steps; plain with a 500-step learning-rate warm-up. Kill test, fixed before execution: Spearman between plain mean steps and mixed minus plain across the five rungs above -0.9. (The backlog's first kill test, "no sign change", was replaced before any run because the reused rungs already had opposite signs and it could not fire.) Anchor, in code: A62's first plain run reproduces -- held.
Results
| Far lag | Plain mean steps to 0.9 | Mixed minus plain (steps) | Share of plain's steps | Solved (mixed / plain) |
|---|---|---|---|---|
6 (new) | 4105 | +968.1 [+141.0, +1795.2] | +24% | 16 / 16 |
7 (A60) | 4946 | +1292.5 [+824.6, +1760.4] | +26% | 16 / 16 |
8 (new) | 7636 | -711.9 [-1276.9, -146.8] | -9% | 16 / 16 |
9 (A62) | 9151 | -2351.9 [-3449.3, -1254.4] | -26% | 16 / 16 |
10 (new) | 13520 | -5404.4 [-6658.9, -4149.9] | -40% | 16 / 16 |
- Spearman(plain mean, difference) =
-0.9; the one pair out of order is lags6and7, both positive. - The first rung wholly below zero is lag
8; linear interpolation puts the zero crossing where plain training needs about6680mean steps.
The kill test does not fire -- at its boundary. The preregistered rule fires above -0.9, and the observed value is exactly -0.9: one adjacent pair out of order, which the rule was written to allow. Reported as it is: the ordering is near-monotone, not perfect, and the exception sits among the rungs where the easy start costs time.
What it says
On one operation, varying only the lag, the easy start's effect moves smoothly from a cost to a large saving as the task gets harder for plain training: it costs a quarter of plain's steps where plain needs about 4000-5000, and saves 40% where plain needs about 13500. Every run in every cell solved the task.
The crossing (plain about 6700 steps at this width, rate and budget) sits close to where the structured tasks that benefited already were -- the hard difference's plain median was 6840 -- and to the random table's plain time (6575 at 0.003), where the easy start did not help. That fits the reading from A66 and A70: difficulty decides how much a shared rule is worth; without a shared rule there is nothing to gain at any difficulty tried so far.
A practical form, for this setup: if plain training takes well under the crossing, skip the easy start; the further above it, the more it saves. The crossing is in steps on this rig and is not a transferable constant.
What stands
- A65: kill test does not fire (at the boundary,
-0.9). Mixed minus plain moves from+968(lag6) to-5404steps (lag10); first rung below zero lag8; crossing near plain mean6680steps.
Limits
- Plain and mixed at rate
0.003throughout; neither arm tuned per rung (the rate thread's caveat). A70 found both arms best near0.008on the random table, so a rate sweep per rung could move the crossing. - Lag
7comes from A60, whose runs were16000steps (all solved, so the budget does not change them) and whose seeds differ from the new rungs'. One operation (the maximum), width48, sixteen seeds per rung. - Changing the lag also changes sequence length and the gap between the easy lags and the hard one.
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.
- GRU
- Gated Recurrent Unit. A compact design for processing sequences one item at a time, with internal switches controlling what it keeps in memory.
- interpolation
- Estimating a value between two measured points by drawing a straight line between them. It gives a finer answer than the measurements themselves, at the cost of assuming what happened in between.
- 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.
- 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.
- 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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