Research record

The Tuning Ran Off the Grid

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: What actually makes training cheaper? – One thing has worked: stopping part of the training early saved about 7% with no loss of quality. Everything else tested has been matched by a simpler or cheaper method -- and in two cases the clever method was only winning because it was quietly being given more.

In plain English

What we asked. We had shown that how batch size affects learning depends on the learning speed. So we tried to find the best learning speed for every batch size, and measure the effect there.

What we found. The search never found a best speed: at every batch size the fastest was the highest one we allowed, so the answer lies beyond what we tried. And simply doubling every speed changed the batch-size effect itself, which a true law would not do.

Why it matters. Two lessons. If you only reward speed, a search will always ask for more. And a published rule about batch size holds at the learning speed it was measured at.

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, 115 training runs (75 tuning, 40 measured). The design, tuning rule and kill test were committed (62feef2) before any run.

Program v2 Bucket T, item T10. Decisive computation: analysis/batch_law_tuned.py. Output: analysis/batch_law_tuned.json. Reproduce with python analysis/batch_law_tuned.py (about an hour on a throttled laptop CPU); --reuse re-derives every endpoint from the saved series.

The question

T8 found the batch exponent of steps-to-transition is -0.315 at a fixed rate and -0.571 [-0.585, -0.556] with the rate scaled by the square-root rule. T10 asks whether tuning the rate at every batch gives the rule's exponent. At each batch 16-256, rates 0.006 sqrt(B/64) m for m in 0.5, 0.75, 1, 1.5, 2 on three throwaway seeds; the tuned rate is the fastest mean step to held-out accuracy 0.5 with every seed reaching it. Then J8's eight receivers at the tuned rates.

At every batch size, the fastest learning rate was the largest one offered
At every batch size, the fastest learning rate was the largest one offered. Each cell is how many training steps a small model needed to get half its answers right, for one batch size (rows) and one learning rate (columns), averaged over three trial runs. Rates are multiples of a standard rule that raises the rate with batch. Every row is fastest in its rightmost column, so the search never found a best rate: the true optimum for speed lies beyond the grid. Speed alone keeps asking for a higher rate; an earlier study capped it by requiring the final accuracy not to drop.
Doubling every learning rate changed how steps fall with batch size
Doubling every learning rate changed how steps fall with batch size. Three ways of choosing the learning rate as the batch grows: keep it fixed, raise it by the standard square-root rule, or use twice that rule at every batch size. If the relationship were a clean law, doubling every rate would only shift the curve down. It also changed its slope. A batch-size exponent measured at one learning rate belongs to that rate.

Kill test, fixed before execution: the tuned exponent's interval overlaps the square-root rule's.

Result: the kill test does not fire, and the tuning did not find an optimum

BatchTuned multiplierStep to 0.5
162 (grid edge)127.5 [119.8, 135.2]
322 (grid edge)83.7 [77.8, 89.7]
642 (grid edge)59.2 [54.1, 64.4]
1282 (grid edge)42.0 [37.8, 46.2]
2562 (grid edge)30.4 [27.8, 33.1]
Exponent-0.514 [-0.533, -0.495]

Every batch chose the largest multiplier offered. The tuning rule reported it as a grid edge, as it was written to, so the "tuned" rates here are not optima: they are the square-root rule doubled, uniformly. The kill test's comparison is therefore between the rule and the rule times two, and those differ: -0.514 against -0.571, intervals apart.

Two consistency checks hold. The code's anchor (a T8 receiver rerun at multiplier 1) reproduced T8 exactly. And at batch 16 the doubled rule gives exactly T8's fixed rate (0.006 0.5 2), and the eight receivers reproduce T8's fixed-rate batch-16 cell to the step (127.5 [119.8, 135.2] both times).

What it shows anyway

  • A constant rescaling of the rate moves the exponent. If steps-to-transition were a clean power law in batch at any rate, doubling every rate by the same factor would shift the curve without changing its slope. It changed it by +0.057. The single-exponent summary depends on where on the rate axis it is measured -- the same bend T8 saw across batch, now seen across rate.
  • Speed alone keeps asking for a higher rate. O16's tuned 0.006 for batch 64 was chosen with a guard on final accuracy; T10's criterion had none, and at batch 64 twice O16's rate reached the level 16 steps sooner. A criterion without a quality guard is not the same tuning, and the two should not be mixed.

What stands

  • Kill test does not fire, on a comparison the tuning did not earn. The measured exponent, -0.514, is for the square-root rule doubled, not for a tuned rate.
  • The batch exponent moves with a uniform rate rescaling (-0.571 to -0.514), so a published exponent fitted at one rate describes that rate.
  • Generates T12: extend the grid upward with O16's accuracy guard until every batch has an interior optimum.

Limits

  • No interior optimum was found at any batch; the question T10 asked is still open.
  • One substrate, speed-only criterion, three throwaway 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.

accuracy
The fraction of answers a model gets right on questions it was not trained on.
exponent
The number in a power law that says how strongly one quantity responds to another. A bigger exponent means a steeper response to the same doubling.
held-out
Data the model was never trained on, kept back specifically to test it. Scoring a model on data it has already seen measures memorisation, not learning.
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.
power law
A relationship where one quantity changes by a fixed percentage whenever another one doubles, rather than by a fixed amount. Most scaling results in AI are stated this way.
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.
slope
How steeply one quantity changes as another does. A slope of one between a warning and the event it predicts means the warning shifts exactly in step with the event.

Want this measured on your data?

We build private models our clients own and run on their own infrastructure, and every engagement proves measured lift on the client's own tasks before we call it done. Start free with a readiness scorecard that tells you whether your data can support it, or book a short call.