The LSTM's Best Rate, and the Speed-Up Holds
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. On a second kind of network (an LSTM), our easy-start recipe beat ordinary training, but ordinary training had not been given its best learning rate yet. We tried higher rates to find it.
What we found. Its best rate is 0.008: above that, ordinary training fails on almost every run. At that best rate, the easy start still reached the solution about 3,800 steps sooner on average and solved it on 15 runs out of 16, against 10.
Why it matters. So the speed-up holds on two kinds of recurrent network, each compared with the best ordinary recipe we could find. How big it is on the LSTM is less certain than on the GRU.
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,32new training runs of16000steps plus96re-used from A58 and A59. The design and the kill test were committed (d663d16) before any run.
Program v2 Bucket A, item A61. Decisive computation: . Output: analysis/sum_lstm_higher.py.analysis/sum_lstm_higher.json
The question
A59 tuned the plain LSTM on the hard modular sum (2, 7) over learning-rate peaks 0.002 to 0.008. The best was the top of the grid, so the tuning had not found an optimum, and the easy-sum warm-up's lead over it (-3763.1 [-7359.8, -166.5] steps) could still have been an untuned baseline. Does a higher rate close the gap?
Design: the plain LSTM with a 500-step learning-rate warm-up to peaks 0.012 and 0.016, A58's sixteen seeds, 16000 steps. The best of all six plain peaks (lowest mean steps to 0.9) is compared with A58's mixed runs, paired. Kill test, fixed before execution: mixed minus the best plain cell includes zero or lies above it; a best peak at 0.016 is reported as not found. Anchor, in code: re-running A59's 0.008 cell on the first seed reproduces it -- held.
Results
| Plain LSTM, peak rate (sixteen seeds) | Mean steps to 0.9 | Median | Solved by 16000 |
|---|---|---|---|
0.002 (A59) | 12192 | 15265 | 8 |
0.003 (A58) | 12678 | 16000 | 5 |
0.005 (A59) | 11124 | 16000 | 7 |
0.008 (A59) | 9181 | 6235 | 10 |
0.012 (new) | 15038 | 16000 | 2 |
0.016 (new) | 16000 | 16000 | 0 |
| easy sums first (A58) | 5418 | 4120 | 15 |
- Best plain peak:
0.008, now inside the grid. Above it the plain LSTM gets rapidly worse: two seeds of sixteen solve at0.012, none at0.016. - Mixed minus the best plain cell:
-3763.1[-7359.8, -166.5]steps (unchanged from A59, because the best cell is the same one).
The kill test does not fire. The plain LSTM's tuned rate is found, and the easy-sum warm-up still reaches the solution sooner, on 15 seeds against 10.
What it says
A59's open question was whether the plain LSTM's best rate lay above the grid. It does not: the optimum is 0.008, and past it the plain run fails. So the LSTM result is now measured against a found optimum, and the recurrent-network speed-up holds on a second recurrent architecture, with the plain baseline tuned, including its learning-rate warm-up. The interval is wide and its upper end is close to zero (-166.5), because the best plain cell is bimodal: ten seeds solve early (median 6235) and six not at all. Its size is less certain than on the GRU (ratio of means 0.590 here).
Choosing the best of six plain cells on the same seeds the comparison uses favours the plain arm, so this selection works against the finding.
What stands
- A61: kill test does not fire. The best plain LSTM rate is
0.008(interior); mixed minus it-3763.1[-7359.8, -166.5]steps; solved15against10of16.
Limits
- One task (the modular sum
(2, 7)), width48, sixteen seeds. The interval's upper end is near zero, and the plain arm's failures are counted at the budget (16000), so the mean difference is partly a difference in how often each arm solves at all. - The rate grid is coarse between
0.008and0.012; an optimum between them is not excluded.
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.
- architecture
- The blueprint of a model: what components it has and how they connect. Two models can be the same size and completely different architectures.
- baseline
- The thing you compare against. A result without one is not a result.
- 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.
- LSTM
- Long Short-Term Memory. An older and larger relative of the GRU, also gated, also for sequences.
- recurrent
- A design that reads a sequence one item at a time, carrying memory forward. The main alternative is attention, which looks at everything at once.
- 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.
- settled
- A run has settled when it has stopped improving. Measurements anchored to a run's own best score are unreliable until it has, because that best score is still moving.
- 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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