Research record

Bigger Batch, Higher Limit

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. A common rule of thumb says that when you feed a model bigger batches of examples, you can raise its learning speed in proportion to the square root of the batch size. Some of our earlier experiments used that rule without checking it, so we checked it.

What we found. The fastest speed at which our model still learns roughly tripled from batches of 16 to batches of 256, and every run agreed. Given how finely we spaced the speeds we tried, that is consistent with the square-root rule.

Why it matters. In practice: the rule of thumb holds up here, so raising the learning speed with the square root of the batch size is a sensible default for models like this one.

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, 165 training runs of 3000 steps. The design and kill test were committed (44bf8da) before any run.

Program v2 Bucket T, item T23. Decisive computation: analysis/critical_rate_batch.py. Output: analysis/critical_rate_batch.json. Post-hoc, changing no verdict: analysis/critical_rate_batch_posthoc.py -> analysis/critical_rate_batch_posthoc.json.

The question

The batch-law thread (T8-T15) found the batch-size law depends on how the learning rate is set, and T8 and T10 used the square-root rule (rate proportional to sqrt(batch)), whose premise is that the largest usable rate grows as the square root of the batch. T22 measured that largest usable rate -- the critical rate -- against memory length. T23 measures it against batch size: T22's task and endpoint at lag 4, batch 16-256, rates a factor 1.25 apart (0.012-0.112), three seeds, 3000 steps.

Bigger batches tolerate higher learning rates, about as the square-root rule says
Bigger batches tolerate higher learning rates, about as the square-root rule says. A small model learning a copy task with batches of 16 to 256 examples. Each point is the fastest learning rate at which it still learned; all three runs agreed at every batch size. The dashed line is the growth a common rule of thumb assumes. The limit roughly triples from batch 16 to 256, close to the square-root rule. The spacing of the rates tried cannot tell it apart from slightly slower growth.

Kill test, fixed before execution: the exponent's interval includes zero. Anchor: at batch 64 the critical rate (0.0366) is within one grid step of T22's lag-4 value (0.0346). It holds.

Result: the kill test does not fire

BatchCritical rate (all three seeds)
160.0188
320.0234
640.0366
1280.0458
2560.0572

The critical rate grows with batch size, three-fold from batch 16 to 256, and every seed chose the same rate at every batch. The fitted exponent is +0.418.

Reading the exponent honestly

Because all three seeds landed on the same grid point at every batch, the per-seed interval is zero-width -- it reports the grid, not the uncertainty. Each true critical rate lies somewhere in its grid bin (at least the last rate that learned, below the next that did not). Allowing for that, the exponent is anywhere from +0.32 to +0.52, a range that contains 0.5. So the data are consistent with the square-root rule's premise and cannot distinguish it from a somewhat slower growth; a finer grid would be needed to say more.

What stands

  • Kill test does not fire. The largest usable learning rate grows with batch, as roughly batch^0.4 (between 0.32 and 0.52 once grid quantisation is allowed for).
  • The square-root rule's premise is consistent with this GRU, so the rule T8 and T10 used was a reasonable choice; the batch law's dependence on the rate policy (T15) is not a sign that the rule was mis-premised.
  • With T22: on this substrate the critical rate falls with memory length (lag^-0.53) and rises with batch (batch^0.4).

Limits

  • One lag, one width, rate grid a factor 1.25 apart, 3000 steps.

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.

batch size
How many examples the model looks at before updating itself once. Bigger batches give a steadier but more expensive update.
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.
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.
post hoc
Worked out after the fact, rather than decided in advance. We report such checks separately and never let them decide a result, because it is far too easy to find a pattern once you already know the answer.
quantisation
Rounding a model's numbers to fewer bits so it takes less memory and runs on smaller hardware, at some cost in accuracy. Spelled quantization in US usage.
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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