Research record

A Delay by Most Measures

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. Warming a small model up on one easy sum seemed to stop it ever learning a hard one. Was that a permanent trap, or just a slow start that our training budget cut off?

What we found. Mostly a slow start. Trained two and a half times longer, six of eight warmed-up runs learned the hard sum, several thousand steps later than runs with no warm-up, and both ended at the same average accuracy. By the count we fixed in advance, the warmed-up runs still trailed by one run at the finish line.

Why it matters. When results are all-or-nothing, where you stop counting can decide the story. Look at when things happen, not only whether they have happened by a deadline.

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, 16 training runs of 20000 steps. The design and the kill test were committed (d628789) before any run.

Program v2 Bucket A, item A41. Decisive computation: analysis/sum_trap_or_delay.py. Output: analysis/sum_trap_or_delay.json.

The question

A39 found a 2000-step warm-up of (2,3) alone leaves every seed near chance on (2, 7) at step 8000, worse than no warm-up. A trap (a solution the model cannot leave) or a delay (a slower start)?

The trap is mostly a delay: the warmed-up runs get there, later
The trap is mostly a delay: the warmed-up runs get there, later. Each line counts how many of eight runs have reached 90% accuracy on the hard sum by each step. One version warms up on the easy (2,3) sum first; the other does not. Earlier experiments stopped at step 8,000. At 8,000 steps no warmed-up run had solved it and the warm-up looked like a trap. Given longer, most get there, several thousand steps behind. Where you stop counting decides which story the numbers tell.

Design: A18's task and receivers at 0.003; the (2,3) warm-up arm and the plain run, both to step 20000. Kill test, fixed before execution: at step 20000 the (2,3) arm solves (>= 0.9) at least as many seeds as the plain run -- a delay. Anchor, in code: the first 8000 steps of each arm reproduce A39 and A32 exactly -- held on all eight seeds.

Results

ArmSolved at 8000Solved at 20000Reached 0.9 at some pointMean final accuracy
(2,3) warm-up0 of 84 of 86 of 80.824
plain, no warm-up2 of 85 of 85 of 80.826

First step at 0.9, per seed: (2,3) arm 19990, --, 17690, --, 12850, 10760, 19970, 12440; plain --, 9670, 11490, 6130, 5840, --, --, 18370.

The kill test does not fire -- by one seed. At step 20000 the (2,3) arm solves 4 of 8 against the plain run's 5, so by the fixed criterion it is a trap. Everything else points to a delay. The two arms end at the same mean accuracy (0.824 against 0.826); six (2,3) seeds reach 0.9 at some point, one more than the plain run; and they get there later -- the first at step 10760, where four plain seeds were there by 11490. Two of the (2,3) seeds cross 0.9 only in the last thirty steps of the budget.

What it says

On this evidence the far-pair warm-up is mostly a delay of several thousand steps, not a permanent trap -- and the fixed-in-advance count, which is the verdict, calls it a trap by one seed at a cut-off that two seeds crossed at the last moment. Both statements are true; the second is what the test was fixed to say. A comparison decided by one seed on a bimodal outcome is decided by where the budget ends.

For the thread: on modular sum, a warm-up of the wrong easy material costs thousands of steps; the right mixture saves them (A36, A40 running). Both are effects on when the model finds the solution, which is the thing a fixed-budget accuracy endpoint turns into a coin-flip near the edge.

What stands

  • A41: kill test does not fire, 4 against 5 solved at 20000.
  • Final accuracy is the same (0.824, 0.826) and 6 of 8 (2,3) seeds reach 0.9 at some point, later than the plain run's.

Limits

  • Eight seeds; one cut-off. A time-to-solve endpoint over a longer budget would read this more cleanly than a count at one step.

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.

accuracy
The fraction of answers a model gets right on questions it was not trained on.
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.

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