A Random Table, and It Slows
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 helped on every task we had tried that follows a rule: adding, subtracting, XOR, and picking the larger of two symbols when that was hard. We tried a task with no rule at all: looking up the answer in a random table, made just as hard to learn.
What we found. The easy start slowed learning. It took about 1,500 more steps than ordinary training at the same learning rate, and about 3,000 more than ordinary training at its better rate.
Why it matters. So difficulty alone is not enough. The easier versions have to share a rule with the hard one, so that what is learned on them carries over. Practising a random table on easier cases did not.
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 of24000steps on sixteen fresh seeds. The design, four disclosed calibration runs and the kill test were committed (7575cf8) before any run.
Program v2 Bucket A, item A66. Decisive computation: . Output: analysis/table_mixture.py.analysis/table_mixture.json
The question
The easy warm-up speeds a recurrent network's learning of a hard two-read task for the modular sum, difference and XOR (A44, A57, A63/A67) and for a maximum that is hard for plain training (A62), and slowed an easy maximum (A60). All four operations have structure: a rule relates the answer to the inputs. Does the speed-up need structure, or only a hard two-input table to build? Here the target is a fixed random table with no rule at all.
Design: GRU, width 48, 20 symbols (the model's input and output layers sized for 20 in both arms), 24000 steps, sixteen fresh seeds 29001-29016. Hard target T[x[t-2]][x[t-7]], T a 20 x 20 table drawn from seed 6600 and saved in the output; easy warm-up on the same table at (2,3)/(2,4)/(2,5) for 2000 steps at rate 0.003. Plain with a 500-step learning-rate warm-up at peaks 0.003 and 0.005, the better compared. The size was chosen by calibration, disclosed before running, to make the table about as hard for plain training as the hard difference: 32 symbols did not reach 0.9 in 32000 steps, 16 were solved by plain at 3680, 20 at 5540 and 6780, 24 at 12660 and 14870. Kill test, fixed before execution: mixed minus the better plain peak includes zero or lies above it. Anchor, in code: the loop reproduces A57's first mixed run -- held.
Results
Arm (sixteen fresh seeds, random 20-symbol table) | Mean steps to 0.9 | Median | Solved by 24000 |
|---|---|---|---|
easy lags of the same table first (0.003) | 8124 | 8160 | 16 |
plain, peak 0.003 | 6575 | 6375 | 16 |
plain, peak 0.005 | 5084 | 4920 | 16 |
- Mixed minus the better plain peak (
0.005):+3039.4[+2328.3, +3750.4]steps; ratio of mean steps1.598. - At the same rate as the mixed arm (
0.003):+1548.8[+930.3, +2167.2]steps; the easy start was faster on only2of16seeds (computed from the committed output, same script'ssolved_at).
The kill test fires. On a random table as hard for plain training as the hard difference, the easy warm-up slows learning, against plain at either rate.
The better plain peak (0.005) is the top of the grid, so plain's optimum is not found. A higher plain rate could only make plain faster, which strengthens the result rather than weakening it. The mixed arm was not tuned (it never has been in this thread); that is the one lever that could reverse it, and A69 tests it.
What it says
Difficulty is not enough; the easy versions need to share structure with the hard task. The plain-training difficulty here (6575 steps at 0.003) sits beside the hard difference (6840 median), where the easy start halves the steps. What differs is that the sum, difference, XOR and maximum each follow a rule that holds at every lag, so learning it on near lags is learning it for the far one; a random table has only entries, and although the easy phase shows the network the very same entries, reading them at near lags did not help it read them at the far lag -- it cost 1500-3000 steps.
This refines, and does not withdraw, the A62 reading: the easy start helps when the hard task is hard for plain training and the easy versions share its rule. A62 separated difficulty from the operation for a structured task; A66 holds difficulty fixed and removes the structure. Whether a harder table would change it is A68.
What stands
- A66: kill test fires. Random
20-symbol table: mixed minus the better plain peak+3039.4[+2328.3, +3750.4]steps; at the same rate+1548.8[+930.3, +2167.2]; all seeds solve in all arms.
Limits
- One table (seed
6600), one size, width48, sixteen seeds. - The mixed arm ran only at
0.003(A69); plain's best peak is the top of its grid (only strengthens the result). - Fewer symbols also means a smaller model input and output layer than every other task in this thread (
20against32); both arms share it, so it does not bias the comparison, but it is a difference from the structured tasks.
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.
- calibration
- Working out an instrument's settings from runs whose answer you already know, so it can be used on a run whose answer you do not.
- 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.
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