Differences Help Too
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. Easy sums unrelated to a hard sum still sped up learning it, and we guessed that was because they practise addition. So we swapped addition for subtraction in the easy examples.
What we found. Easy subtraction helped too: about 900 steps sooner than ordinary training. Easy addition may help a little more, but the gap between them is within noise.
Why it matters. What carries over may be the shape of the task, remembering two symbols and combining them, rather than the specific operation. We have updated the earlier page to say so.
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,48training runs of8000steps on sixteen fresh seeds. The design and the kill test were committed (550e0b1, inv0.279.0) before any run.
Program v2 Bucket A, item A52. Decisive computation: . Output: analysis/sum_operation.py.analysis/sum_operation.json
The question
A49 found easy sums that share no offset with the target (2, 7) still reach the solution about 1500 steps sooner than the plain recipe, and read that half of the mixture's saving as practising the operation. If it is the operation, easy tasks of the same shape with a different operation should help less.
Design: target (2, 7) at 0.003, 8000 steps, sixteen fresh seeds 19001-19016. Sums: A49's unshared pairs (4,5)/(4,6)/(5,6) for 2000 steps. Differences: the same pairs and inputs with the target (x[t-a] - x[t-b]) mod 32, computed in the pilot. Plain: a 500-step learning-rate warm-up. Endpoint: steps to 0.9 (never = 8000). Kill test, fixed before execution: sums minus differences includes zero or lies above it. Anchor, in code: the sums arm reproduces A49's unshared run on A49's first seed -- held.
Results
| Arm (sixteen fresh seeds) | Median steps to 0.9 | Solved by 8000 |
|---|---|---|
| unshared easy sums | 4870 | 13 |
| unshared easy differences | 5635 | 11 |
| plain, learning-rate warm-up | 7560 | 9 |
| Paired difference in steps to solve | |
|---|---|
| sums minus differences | -718.8 [-1663.5, +226.0] |
| sums minus plain | -1650.6 [-2340.9, -960.3] |
| differences minus plain | -931.9 [-1738.9, -124.8] |
The kill test fires. Sums lead differences by about 700 steps on the point estimate, and the interval reaches zero: whether the easy tasks need the target's own operation is undecided. Easy differences also beat the plain recipe (-931.9 [-1738.9, -124.8]).
What it says
A49's "operation" half is not shown to be about addition specifically. What the unshared easy tasks share with the target is also a shape -- read two symbols from the recent past and combine them into one answer mod 32 -- and easy differences share that shape too. Modular difference and modular sum are also close relatives (subtracting is adding the negative), so this design could not have separated "same operation" from "a closely related one" sharply. The reading that survives: on modular sum, easy tasks that exercise the target's two-read-and-combine structure speed it up, and tasks that also share one of its reads speed it up more (A49). On the copy task there is no such structure to exercise beyond a single read.
What stands
- A52: kill test fires. Sums minus differences:
-718.8[-1663.5, +226.0]steps -- undecided. - Easy differences beat the plain recipe by
931.9[124.8, 1738.9]steps.
Limits
- Sixteen seeds; one alternative operation, and a close relative of the target's.
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.
- 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.
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