Research record

A Harder Table, and Still Slower

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. On tasks that follow a rule, the easy-start recipe saved more the harder the task. On a random lookup table it was slower. We asked whether a harder table would change that.

What we found. It did not. On a table about twice as hard, the easy start was still about 3,000 steps slower, at a difficulty where it had saved a quarter of the steps on a task with a rule.

Why it matters. So the two conditions are separate. The task has to be hard, and the easier versions have to share a rule with it. Difficulty alone is not enough.

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, 64 training runs of 32000 steps on sixteen fresh seeds. The design, a disclosed calibration and the kill test were committed (325cbac) before any run.

Program v2 Bucket A, item A68. Decisive computation: analysis/table_harder.py. Output: analysis/table_harder.json.

The question

On a random 20-symbol lookup table the easy start was slower than plain training at every rate, by +1976.2 [+1486.8, +2465.7] steps with both arms at their best rate (A70). For the maximum, a harder version turned a slow-down into a saving (A62, A65). Does a harder table do the same?

A harder random table, and the easy start is still slower
A harder random table, and the easy start is still slower. Two random lookup tables, one with 20 symbols and a harder one with 24. Each point is a recipe at its best learning rate. Making the table harder roughly doubles the work for both recipes, and the easy start stays behind by 2,000 to 3,000 steps. On tasks with a rule, the same increase in difficulty turned the easy start into a saving; without a rule it did not.

Design: A66's loop with a 24-symbol random table (seed 6600), 32000 steps, sixteen fresh seeds; both arms rate-tuned from the start at 0.005 and 0.008 (A70's optimum and the rate below it); best of each arm, paired. Kill test, fixed before execution: best mixed minus best plain includes zero or lies above it. Anchor, in code: A70's plain 0.008 run on its first seed reproduces -- held.

Results

Arm (sixteen seeds, random 24-symbol table)Mean steps to 0.9MedianSolved by 32000
easy start, 0.005135291345016
easy start, 0.008128551218516
plain, 0.005109971079016
plain, 0.0089858984016
  • Best mixed (0.008) minus best plain (0.008): +2996.9 [+1498.7, +4495.1] steps; ratio of mean steps 1.304.

The kill test fires. On a table that plain training finds about twice as hard as the 20-symbol one, the easy start is still slower, by about 3000 steps.

What it says

Difficulty does not rescue a task without a rule. Plain training needs about 9900 steps here -- inside the range where, on the maximum, the easy start saved a quarter of the steps (lag 9, plain 9151, -26%; A65). On the table it costs 30% instead. Across A65, A66, A70 and A68, the pattern is now two-sided: with a rule shared between the easy and hard versions, the saving grows with difficulty; without one, the easy start costs time at both difficulties tried.

What stands

  • A68: kill test fires. Random 24-symbol table: best mixed minus best plain +2996.9 [+1498.7, +4495.1] steps, both at 0.008.

Limits

  • Both best rates are the top of a two-rate grid (0.008). On the 20-symbol table both arms were slower at 0.012 (A70), which suggests but does not show that 0.008 is near the optimum here too.
  • One table per size; width 48; sixteen seeds.

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.
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.
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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