Research record

Two Searches, Two Edges

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 last search for the best learning speed always picked the fastest one on offer. So we searched again with a safeguard: only count speeds that finish nearly as accurate as the best, and search a wider range.

What we found. This time the search ran off the other end. The slowest speed was always the most accurate, so the safeguard always pointed at the slowest speed we allowed. The search did find a clear fastest speed, comfortably inside the range.

Why it matters. The lesson: for a trade-off like speed against accuracy there is no single best setting. Say which point on the trade-off you want, and search for that.

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, 105 tuning runs; the measured phase did not run because the precondition failed. The design, guard and kill test were committed (c04ad3e) before any run.

Program v2 Bucket T, item T12. Decisive computation: analysis/batch_law_guarded.py. Output: analysis/batch_law_guarded.json. Post-hoc diagnosis, changing no verdict: analysis/batch_law_guarded_posthoc.py -> analysis/batch_law_guarded_posthoc.json.

The question

T10 tuned the learning rate at each batch size for speed alone, and every batch chose the largest rate offered. T12 repeats the tuning with O16's accuracy guard and a wider grid: rates 0.006 sqrt(B/64) m for m in 2, 3, 4, 6, 8, extended once to 1, 1.5 or 12, 16 if a batch chose an edge; among multipliers whose mean final accuracy is within 0.01 of the best at that batch, the fastest to held-out accuracy 0.5. Precondition: an interior optimum at every batch. Kill test: the tuned exponent overlaps the square-root rule's. Anchor: batch 16, m = 2 reproduces T10's tuning cell. It holds.

Final accuracy only ever falls as the learning rate rises
Final accuracy only ever falls as the learning rate rises. Each line is one batch size. Moving right raises the learning rate. The height is how accurate the model was at the end of a fixed training run, averaged over three trial runs. Every line slopes down from its leftmost point. A rule that says 'stay within 1% of the best accuracy' therefore always points at the slowest rate on offer, so the search ran off the bottom of the grid for the smaller batches.
Tuning for speed and tuning for accuracy point opposite ways
Tuning for speed and tuning for accuracy point opposite ways. For each batch size, the learning rate that reached the target soonest (coloured) and the one that ended most accurate (grey), as a multiple of a standard rule. The fastest rate sits comfortably inside the range we searched. The most accurate is always the lowest we tried. There is no single best rate here, only a choice of where to stand between speed and accuracy.

Result: the precondition fails, and the kill test is not interpreted

BatchTuned multiplierOffered
161 (lower edge)1-8
321 (lower edge)1-8
641.51-8
1281.51-8
25621-8

At batches 16 and 32 the guard chose the lowest rate on the extended grid, so no optimum was found and the eight receivers were not run, as the design required.

Why: a guard defined against the grid's best inherits the grid's edge

The post-hoc table shows the mechanism at every batch:

BatchFastest multiplierMost accurate multiplierFinal accuracy falls as the rate rises, throughout
1631yes
3231yes
6431yes
12831yes
25621yes

Final accuracy after 800 steps rises monotonically as the rate falls, at every batch. So "within 0.01 of the best accuracy" is always measured against the lowest rate offered, and wherever the frontier is steep enough the guard lands on that edge. Extending the grid downward would move the edge, not remove it. T10 ran off the top of its grid because speed alone keeps asking for more; T12 ran off the bottom because a relative accuracy guard keeps asking for less. Neither is a tuning; both are a choice of where to stand on a speed-accuracy frontier, which O18 already found on this substrate.

What the grid does contain is an interior speed optimum: 3x the square-root rule at batches 16-128 and 2x at 256. T10's grid stopped at 2x, so it could not see it. T15 measures the exponent there, with the multipliers fixed now from this record's tuning data.

What stands

  • Precondition fails; kill test not interpreted.
  • A tuning guard defined relative to the grid's best is itself a grid edge when accuracy is monotone in the rate. Use an absolute criterion, or name the point on the frontier being chosen.
  • The speed-optimal rate is interior: 3x the square-root rule up to batch 128, 2x at 256.

Limits

  • Three throwaway seeds per cell, one substrate, 800 steps. Final accuracy at a fixed step count favours low rates that are still improving; a longer run might flatten the frontier.

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.
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.
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.
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.
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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