For the Maximum, It Slows Learning
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. The easy-start speed-up held for adding and for subtracting two remembered symbols. We tried a task that is not arithmetic: output the larger of the two.
What we found. It reversed. Every run learned the task either way, but starting on easier versions made it slower, by about 1,300 steps on average.
Why it matters. So the easy start is not a general recipe for tasks that combine two things. It helps with modular arithmetic, which a recurrent network has to build a whole table for. We have narrowed our headline finding 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,32training runs of16000steps on sixteen fresh seeds. The design, a disclosed throwaway and the kill test were committed (a0719c3) before any run.
Program v2 Bucket A, item A60. Decisive computation: . Output: analysis/max_mixture.py.analysis/max_mixture.json
The question
The easy warm-up roughly halves the steps a recurrent network needs for a hard two-read task when the task is modular addition (A44) or modular subtraction (A57) -- both invertible group operations. Does it hold for a combine that is neither: the maximum?
Design: GRU, width 48, rate 0.003, 16000 steps, sixteen fresh seeds. Hard task max(x[t-2], x[t-7]) over symbol indices; easy warm-up of maxima on (2,3)/(2,4)/(2,5) for 2000 steps; A57's loop with the target swapped. Mixed against plain with a 500-step learning-rate warm-up; steps to 0.9. Kill test, fixed before execution: mixed minus plain includes zero or lies above it. Anchor, in code: with sum targets, the loop reproduces A40 -- held.
Results
| Arm (sixteen fresh seeds, hard maximum) | Median steps to 0.9 | Solved by 16000 |
|---|---|---|
| easy maxima first | 6270 | 16 |
| plain, learning-rate warm-up | 4595 | 16 |
- Mixed minus plain:
+1292.5[+824.6, +1760.4]steps; ratio of mean steps1.261.
The kill test fires, and the direction reverses. Every seed in both arms solves the task, and the easy warm-up makes it slower, by about 1300 steps on average, with an interval wholly above zero. (The disclosed one-seed throwaway had leaned the other way, 5190 against 6350 -- a reminder of what one seed can say.)
What it says
The speed-up is not a property of every two-read-and-combine task. It holds for modular addition and subtraction (A44, A53, A57) and reverses for the maximum. What differs is not the shape but the operation: a sum or difference mod 32 depends on both inputs everywhere and must be computed as a table, which easy sums help a recurrent network lay down (A49, A52); the maximum is easier for plain training (it solves in 4595 steps against 6840 for the hard difference), and two thousand steps of easy maxima appear to cost time without building anything the target needs. This narrows the positive finding: easy versions help recurrent networks learn modular arithmetic of two remembered symbols; they are not a general recipe for two-input tasks. The top-findings lists and the outside-venue draft now say so.
What stands
- A60: kill test fires. Hard maximum: mixed minus plain
+1292.5[+824.6, +1760.4]steps -- the warm-up slows it.
Limits
- One non-group operation; sixteen seeds; the maximum was also an easier task for the plain recipe, so "operation" and "difficulty" are not separated here.
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.
- 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.
- recurrent
- A design that reads a sequence one item at a time, carrying memory forward. The main alternative is attention, which looks at everything at once.
- 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.
Get new results as we publish them
Roughly monthly, one finding per email, in plain English first. Including the approaches that turned out not to work, which are usually the useful ones. No sales email.
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