The account
Grokking — training accuracy saturating long before validation accuracy leaves chance — is a regime a training run can be put into and taken out of. It is not a property of algorithmic datasets, and it is not a fundamental feature of overparameterized learning. Three separate knobs have been shown to control it, each demonstrated in both directions.
This is what the third check in SOTA-200 rests on. Because the discontinuity is set by the regime rather than the task, moving any of these knobs and watching whether the jump moves with it tests whether a capability was acquired at a scale or produced by the run’s conditions.
Training-set size — or something fused with it. LIT-538 measures it in
the paper that named the phenomenon: converged accuracy is flat across a range
of training fractions while the time to reach it explodes as the fraction
falls — in the vicinity of 25–30% on S₅, removing 1% of the data raises
median steps-to-generalize by 40–50%, while steps-to-fit stay at 10³–10⁴.
LIT-085 puts a threshold on it: above roughly 60% data on modular
addition, grokking is gone and generalization is immediate.
Both vary the fraction of a fixed universe of examples, which is one knob moving two things — how much data there is, and what proportion of the possible examples it covers. LIT-667 has two knobs and turns them separately: on knowledge-based reasoning, holding the inferred/atomic ratio fixed and scaling the training set changes nothing, while moving the ratio at fixed size moves grokking speed monotonically. A ratio of that kind is not defined on modular arithmetic, so this does not overturn the measurements above; it does mean they could not have told which of the two they were measuring. The knob is real. What it is a knob on is open.
Initialization scale relative to the generalizing weight norm.
LIT-540 induces grokking on MNIST (depth-3 MLP, 1k examples, Kaiming
weights scaled by α > 1), on IMDb with an LSTM at α = 6, and on QM9
with a GCNN at α = 3. At the standard initialization there is no grokking on
any of them. Run the other way, constraining the model to a small-weight-norm
sphere nearly eliminates grokking on algorithmic data.
Initial kernel–task alignment. LIT-537 sweeps an output-scale
parameter α and shows it makes grokking more dramatic or removes it entirely,
and shows that worse alignment between the initial NTK’s top eigenvectors and
the labels produces more intense grokking — and, because feature learning is
then necessary rather than optional, a lower final test loss. Alignment is
computable on any task as centered kernel alignment.
Why this is Active when the mechanisms are not
The record holds three rival accounts of why — THEORY-072, THEORY-071 and THEORY-070 — and none is settled; one of them exists because it is an explicit counterexample to the other two. They disagree about the mechanism and they do not disagree about this. A dataset-size condition appears in all four of the algorithmic-data papers, including in LIT-537’s own list of three conditions, which is the paper arguing hardest against the others.
A claim that survives the disagreement of every account of the thing it describes is in a different evidential position from any of them.
The fifth source is the exception that has to be stated. LIT-667 does not disagree that the regime can be moved; it disagrees about what the first knob is, and unanimity among four papers that could not separate size from composition is not evidence about which of the two it was.
What it is not
Not “grokking is an artefact”. Ungrokking (LIT-539) is a real, sharp, reproducible behaviour, and the representations LIT-538 visualizes are real structure. The phenomenon happens; it happens in a regime.
Not “three knobs is the list”. Three are established. Weight decay strength changes the timing in two of the accounts without being one of these axes — LIT-667 measures that directly, and raising it accelerates grokking — and LIT-538 reports operations that never generalize at any data fraction, which no knob here explains.
Not “and now there are four”. The inferred/atomic ratio is not being added as a fourth axis, because on the reading THEORY-071 now takes it is the first axis seen properly: both are ways of making the memorising solution more expensive. Counting it twice would claim an independence nobody has shown.
Not a licence to read across the demonstrations. Every result outside algorithmic data in LIT-540 changes two things at once — a much smaller training set and an inflated initialization — so the axes are established jointly rather than separately, and the paper says so.
What would change this
A demonstration of delayed generalization at standard initialization, on a standard-sized dataset, with no knob turned — that is, grokking arriving unbidden in an ordinary training run. Nothing in these five papers is that, and the one setting where it occurs unbidden is the small algorithmic dataset, which is itself a regime choice.
LIT-667 narrows what is left. An 8-layer GPT-2 at a standard initialization, AdamW at weight decay 0.1, nothing inflated and nothing constrained — and generalization arrives roughly 50× after the training set is fit. The model and the optimizer are ordinary there. What is engineered is the data: a synthetic knowledge graph with a chosen ratio of derived to atomic facts. So the remaining gap in this section is no longer “grokking needs a doctored initialization”; it is that every setting in which anyone has watched grokking has a data distribution somebody chose.