Source
Srivastava et al. (2022), LIT-077 — BIG-bench, 204 tasks across three model families from millions to hundreds of billions of parameters, with expert human raters.
Nanda et al. (2023), LIT-085 — the grokking analysis, which reverse-engineers one network and recovers the continuous progress underneath its discontinuity.
Schaeffer et al. (2023), LIT-471 — read as NOTE-220 — the direct argument, which rescores fixed model outputs, counts which metrics the published claims sit under, and then manufactures emergence on demand in vision models that had never shown it.
The claim being checked is LIT-470, which is worth reading first: it raises the metric explanation itself and declines it for two stated reasons, one of which is still standing.
The grokking line, for the third check: Power et al. (2022), LIT-538, which named the phenomenon and measured its data dependence; Liu, Michaud and Tegmark (2022), LIT-540, which induces it outside algorithmic data and eliminates it on demand; Varma et al. (2023), LIT-539, which predicts and then observes ungrokking; and Kumar et al. (2023), LIT-537, which adds the kernel-alignment axis.
The claim
A capability that appears suddenly at some scale may be appearing suddenly in your measurement rather than in the model. Before treating a jump as a finding about learning, ask three things.
Is the metric all-or-nothing over multiple steps? BIG-bench’s categorisation is direct: tasks that improve gradually “commonly involve a large knowledge or memorization component, whereas tasks that exhibit breakthrough behavior at a critical scale often involve multiple steps or components, or brittle metrics.” A task scored only when every step is right improves invisibly until the last step lands, and then appears to jump. Nothing about the model was discontinuous.
Is the metric discontinuous? This is a separate question and it is the one that catches most cases. Multiple Choice Grade scores 1 when the correct option holds the highest probability mass and 0 otherwise — a step function over a continuous quantity, with no long target and no compounding involved. Of Wei et al.’s hand-annotated BIG-Bench emergent abilities, >92% sit under Multiple Choice Grade or Exact String Match: one discontinuous, one nonlinear. Asking only the first question would have cleared the classification tasks, which is exactly the mistake LIT-470 §5.1 made when it argued the metric explanation could not cover them.
Is the discontinuity a property of the regime? Grokking — delayed
generalization long after memorization — is the most-cited mysterious training
phenomenon of its period, and it is a regime a run is put into, not a fact
about a task. LIT-085 finds it disappears above roughly 60% data on
modular addition; LIT-538, the paper that named it, already reported
that converged accuracy is flat across a range of training fractions while the
time to reach it explodes as the fraction falls. But data fraction is one
axis of three. LIT-540 induces grokking on MNIST, IMDb and QM9 by
shrinking the training set and inflating the initialization scale — at
standard initialization there is none on any of them — and eliminates it on
algorithmic data by constraining the weight norm. LIT-537 adds a third
axis, the alignment between the initial neural tangent kernel and the target,
which is computable on any task as centered kernel alignment. The full account
is THEORY-069.
So the check is not “was the data starved” but move the regime and see whether the discontinuity moves with it. LIT-539 supplies the sharpest version: ungrokking, in which a network that has already grokked regresses to near-random test accuracy when trained on a smaller dataset, at a sharp threshold, with an endpoint independent of the weight decay. A capability a model gives back when you shrink its training set is not a capability the model acquired at a scale.
What a positive check looks like
Usually it is cheap, and this document used to say otherwise. The test is to change the scoring function and hold the model’s outputs fixed. Rescoring InstructGPT/GPT-3’s arithmetic outputs with Token Edit Distance turns the emergent curve smooth without regenerating anything; rescoring LaMDA under Brier Score — a proper scoring rule BIG-bench already computes — removes its emergence on the tasks where Multiple Choice Grade showed it. If you own the outputs, this is an afternoon.
A second cheap test comes free with it: add test data. Composing a per-token probability down to a small number leaves small models with a score that is nonzero and below your resolution, and a zero you cannot resolve looks like inability. More test data alone put every InstructGPT/GPT-3 model above chance.
The expensive case is real but narrower than it looked. LIT-085’s
progress measures — restricted loss and excluded loss — are computed by
projecting onto or removing the five key frequencies the network was
reverse-engineered to be using, and they are meaningless without that
reverse-engineering. That is the cost of recovering a continuous measure when
no continuous metric over the outputs exists. It is not the cost of the
check in general.
Conditions
LIT-077 is a categorisation across 204 heterogeneous tasks, not a controlled
experiment, and it puts no number on what share of observed emergence is
artefactual. LIT-085 is one modular-addition task on a one-layer transformer
with weight decay λ = 1 — the authors call the generalisation to emergence “a
proof of concept” and it is nonetheless how the paper is usually cited.
The grokking sources are narrow in a way the third check has to carry. LIT-538 and LIT-539 are algorithmic tasks throughout — modular arithmetic and binary operation tables — and LIT-539’s circuits are identified against a known trigonometric construction that no realistic task has. LIT-540’s results outside algorithmic data change two things at once, a much smaller training set and an inflated initialization, so the axes are established jointly rather than separately, and every such signal is described by its authors as weaker than on algorithmic data. What the check licenses is “move the regime and look”, not a prediction about which knob will turn out to matter.
LIT-471 is the strongest of the three and still does not license the
conclusion. It says so itself: “nothing in this paper should be interpreted as
claiming that large language models cannot display emergent abilities”. Its
demonstration that a metric can manufacture a sharp curve establishes
sufficiency, not necessity, and its meta-analysis counts metrics rather than
adjudicating claims. Caballero et al. and Michaud et al. both hold that some
emergence is real, and neither is refuted.
One objection survives all three sources. LIT-470 §5.1 noted that the quality of intermediate reasoning steps jumps too, which is not a property of how a final answer is scored. Nobody has answered it, and this record has independent reasons (SOTA-278) to distrust reading traces as evidence of anything — so the objection is open on both sides at once.
None of these sources licenses “emergence is not real”. They license asking, and they name three specific things to ask about.
Known implementations
- BIG-bench’s linearity vs breakthroughness axis is the categorisation itself
- BIG-bench ships Brier Score alongside Multiple Choice Grade on the same tasks, so the continuous counterpart is already computed for anything scored there