Memorised, Never Generalised
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 decides when a model learns, and can you change it? – Settings dominate, data barely matters, and there is a brief window before the jump in which interrupting the model is unusually costly. Timing can be delayed but not brought forward.
In plain English
What we asked. 'Grokking' is a famous effect: train a network over and over on a small fixed set of arithmetic problems, and long after it has memorised them it suddenly learns the real rule. All our experiments so far used fresh problems every step, so we tried a small fixed set.
What we found. Our model memorised the problems within about a hundred steps and never solved a new one in ten thousand, whatever the setting. A standard trick that helps grokking, weight decay, slowly wore away the memorised answers without anything better taking their place.
Why it matters. The sets were probably far too small: grokking happens near the amount of data a model needs to find the rule. The next experiment moves up to that point.
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,24training runs of10,000steps. The design and kill test were committed (0615361) before any run; one streaming throwaway run was made first and is disclosed.
Program v2 Bucket E, item E5. Decisive computation: . Output: analysis/grokking_bridge.py. Reproduce with analysis/grokking_bridge.jsonpython analysis/grokking_bridge.py (about an hour on a throttled laptop CPU); --reuse re-derives every endpoint from the saved curves.
The question
Every run in this programme drew fresh data at every step, so memorising the training set was impossible by construction. Grokking (Power et al., 2022, arXiv 2201.02177) is the best-studied sudden-learning phenomenon in the literature: on a small fixed training set of a modular-arithmetic task, with weight decay, a network first fits its training set and only much later generalises. E5 asks whether this rig produces it.
Task: modular sum (x[t-2] + x[t-4] mod 32), J8's width-48 GRU, AdamW at 0.005; a streaming throwaway run learned it by step 2000. Grid: fixed pools of 8, 16, 32, 64 sequences (12 scored sums each), weight decay 0 and 1.0, three seeds, 10,000 full-batch steps. A run groks if training accuracy reaches 0.99 while held-out accuracy is below 0.5, and held-out accuracy later reaches 0.9 at least three times as late.
Kill test, fixed before execution: no cell has two of three seeds that grok.
Result: the kill test fires
| Pool | Weight decay | Grokked | Memorised by step | Best held-out accuracy (seed 8101) |
|---|---|---|---|---|
8 | 0 / 1 | 0/3 / 0/3 | 50 | 0.034 / 0.035 |
16 | 0 / 1 | 0/3 / 0/3 | 50 | 0.033 / 0.036 |
32 | 0 / 1 | 0/3 / 0/3 | 50-100 | 0.036 / 0.041 |
64 | 0 / 1 | 0/3 / 0/3 | 100 | 0.033 / 0.038 |
(Chance is 1/32 = 0.031.)
Every run memorises its training set within 50-100 steps and none ever generalises: held-out accuracy stays within a point of chance for all 10,000 steps. With weight decay the memorised solution also erodes: in every one of the twelve weight-decay runs, training accuracy later falls well below 0.99 (lowest values after step 1000 between 0.26 and 0.65), and nothing general replaces it.
Why this is not the end of the question
The bounded search the kill test named contains no grokking. Two features of the design make that a statement about this search rather than about the rig, and both are stated here rather than discovered later:
- The pools are far below what the task needs. The streaming run that learned the task saw about
64,000sequences by step1000; the largest pool here holds64. Grokking in the literature sits at the edge of data sufficiency, where a network can eventually find the general rule from the data it has; these pools may be too far below that edge for any delay to end. - A recurrent model can memorise whole sequences. With
8-64distinct sequences it can key on each sequence's opening tokens and never learn the sum at all.
E10 tests the edge directly: larger pools, up to a size where the model generalises, and whether a delay appears just below it.
What stands
- Kill test fires. Pools of
8-64sequences, with or without weight decay: memorised in50-100steps, never generalised in10,000. - Weight decay erodes memorisation here without producing generalisation.
Limits
- One task, one width, one rate,
10,000steps. Power et al.'s delays can run to10^5steps and more. - The pool range sits far below the streaming run's data.
FOLLOWED UP 2026-09-27 by E10. Larger pools (256-16384) find the edge: with weight decay the model generalises from1024sequences, without it from4096, and in every such run it generalises no later than it memorises. No grokking in either record. Text and numbers above unchanged.
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.
- AdamW
- A widely used training algorithm that adapts how big a step it takes for each individual parameter. The default in most modern AI training.
- grokking
- When a network that has memorised its training examples suddenly, much later, learns the general rule and starts getting new examples right.
- GRU
- Gated Recurrent Unit. A compact design for processing sequences one item at a time, with internal switches controlling what it keeps in memory.
- 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.
- 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.
- weight decay
- A common training setting that gently pulls a model's internal numbers toward zero, used to stop it over-fitting.
- 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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