Same Material, Same Time
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. Our earlier results suggested that a model's learning speed depends on how much material it sees per training step, not on whether that comes as many short examples or a few long ones. A first test was spoiled by an easy shortcut and a counting error, so we ran it again carefully.
What we found. Four very different packagings of the same amount of material took the same time to learn, within 2.4 percent. Four times the material was clearly faster, by an amount that matches a separate earlier measurement.
Why it matters. In practice, on this kind of task: choose batch size and example length for convenience. What matters is the total material per step.
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,41training runs (one anchor). The design, counts (checked in code against the task's own mask) and kill test were committed (459b4f9) before any run.
Program v2 Bucket T, item T16. Decisive computation: . Output: analysis/content_per_step_clean.py. Reproduce with analysis/content_per_step_clean.jsonpython analysis/content_per_step_clean.py (about forty minutes on a throttled laptop CPU); --reuse re-derives every endpoint from the saved series.
The question
T13 found batch size and sequence length interact as substitutes on a random-stream copy task. T14 tried to test whether scored content per step -- batch times scored positions per sequence -- is what sets the pace, and hit two faults: a miscount of scored positions and a cell whose endpoint could be reached on one easy position. T16 is the clean rerun: four cells of exactly 1408 scored positions per step, counted from the task's own mask, as batch 16, 32, 64, 128 at length 93, 49, 27, 16; every cell scores at least 11 positions per sequence. A contrast cell carries four times the content (batch 64, length 93).
Kill test, fixed before execution: the slowest equal-content cell's mean step exceeds the fastest's by more than 25%. Anchor: a batch-64, length-16 rerun reproduces T11. It holds.
Result: the kill test does not fire
| Batch x length | Scored per step | Step to 0.5 |
|---|---|---|
16 x 93 | 1408 | 129.2 [123.9, 134.5] |
32 x 49 | 1408 | 127.8 [121.1, 134.4] |
64 x 27 | 1408 | 127.5 [122.9, 132.0] |
128 x 16 | 1408 | 126.1 [121.6, 130.6] |
64 x 93 (contrast) | 5632 | 91.5 [87.5, 95.4] |
The four equal-content cells agree within 2.4% (slowest over fastest 1.024, against a limit of 1.25), across an eight-fold range of batch size and a six-fold range of length. The contrast cell, with four times the content per step, is faster than all four. On this task, how the content is packaged -- a few long sequences or many short ones -- does not matter; how much there is does.
The contrast gives an exponent against content per step of ln(91.5 / 127.5) / ln 4 = -0.24. T11 measured the same quantity independently, from length alone at a fixed batch, as -0.237 [-0.257, -0.217] once its count was corrected (T14). Two designs, one number.
What the batch-law thread now says
- The step at which this task is learned is set by scored content per step, with an exponent near
-0.24, whether the content arrives as more sequences or longer ones. - That is why batch and length interact (T13): they are two routes to one quantity, so a law with separate exponents for each describes one slice of the grid.
- The batch exponents in T8-T15 are this relationship seen through a learning-rate policy, which moves them by more than the model change does (T15).
What stands
- Kill test does not fire. Equal scored content per step:
126.1-129.2steps, within2.4%. - Four times the content:
91.5steps, exponent-0.24, matching T11's independent-0.237. - Practical reading: on this kind of task, choose batch size and sequence length for hardware convenience; the learning time depends on their product in scored positions.
Limits
- One task, one rate (
0.006, fixed), one model. At a rate scaled with batch the equivalence may not hold, since T8 showed the rate changes the batch exponent. - Content per step, not total content: the endpoint is in steps. Four times the content per step costs four times the compute per step for
0.72times the 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.
- 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.
Get new results as we publish them
Roughly monthly, one finding per email, in plain English first. Including the approaches that turned out not to work, which are usually the useful ones. No sales email.
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