Emergence
Abilities that appear suddenly at scale rather than improving gradually — the most cited claim about large models, and a NeurIPS best paper says it's a measurement artefact.
When not to use it
- As evidence of unpredictability, without checking the metric. That argument leaned on emergence and the evidence moved.
- When your metric is exact-match. You built the cliff. It isn't in the model.
- As a claim about the model's nature. The model improved smoothly; the scoring didn't.
- To dismiss all sharp transitions. Induction head formation is a real candidate, observed mechanistically.
Reach for something else instead
- Continuous metrics — edit distance, per-token accuracy, log-likelihood. The curve is smooth underneath.
- Mechanistic evidence — look inside. That's where real phase transitions have been found.
- Scaling laws — the smooth, predictable thing that was there all along.
This entry is part of a longer guide: What is AGI?
Same model, same smooth improvement. Only the metric changes.
The grey line is per-token accuracy — the model's real, gradual improvement. Nothing about it jumps. The green line is only how we score it. Exact match demands every token be right, so it computes pN: near zero while p is middling, then a cliff. Switch to a metric that gives partial credit and the cliff is gone. Schaeffer et al. make this argument with real benchmark data; this is the mechanism behind it, computed live.
The full account
The claim, and why it landed so hard
Wei and colleagues made the claim precisely in 2022: an ability is emergent if it is not present in smaller models but is present in larger models, and therefore could not have been predicted by extrapolating from smaller models. They catalogued dozens of tasks with the same shape — flat at chance across several orders of magnitude of scale, then a sharp rise.
The claim mattered far beyond the paper because of what it implied about planning. If capabilities appear without warning at scales you haven't reached, you cannot know what a model will do until you build it. Every safety argument that depends on measuring a small model and extrapolating collapses. So does every business case that depends on knowing what the next run buys. Emergence was cited in policy documents, in lab safety frameworks, and in the case for treating frontier training runs as categorically different from ordinary engineering.
The mirage argument
Schaeffer, Miranda and Koyejo asked in 2023 whether the cliff was in the model or in the ruler, and their answer won NeurIPS best paper: the metric creates the discontinuity.
The mechanism is almost embarrassingly simple once stated. Take a task scored by exact match on a multi-digit arithmetic problem. The model must get every digit right; one wrong digit scores zero. Now suppose the per-token probability of being correct improves smoothly with scale — which it does, and which you can measure. Exact-match accuracy is that smooth per-token probability raised to the power of the number of tokens. Raising a smoothly rising quantity below 1 to a high power produces a curve that hugs zero and then lifts sharply. The sharpness is the exponent, not the model.
Their prediction is what makes it science rather than commentary: swap the nonlinear metric for a smooth one — per-token likelihood, edit distance, partial credit — and the cliff should vanish on the same model outputs, with no retraining. It does. They also ran it in reverse, applying nonlinear metrics to vision models where nobody had claimed emergence, and manufactured emergent-looking curves on demand. The figure on this page does the same thing live: toggle the metric, watch the cliff appear and disappear on identical underlying data.
Why "mirage" is too strong
The tidy version of this page would stop there, and it would be misleading. Two things complicate it.
The first is that the choice of metric is not arbitrary. If you want a model that outputs the correct four-digit answer, exact match is the metric that describes your product. Partial credit on three of four digits is a real improvement in the model and no improvement at all in the thing you're shipping. So the discontinuity is an artefact of the measurement and simultaneously real in the deployment, and a user experiences the cliff whether or not the log-likelihood underneath it was smooth. Schaeffer's result explains the shape; it does not make the shape irrelevant to anyone waiting for the model to become usable.
The second is that not everything dissolves. Some behaviours — chain-of-thought helping at all rather than hurting, code generation crossing a threshold of executability — still look discontinuous to users under metrics nobody chose adversarially. The honest 2026 position is the unsatisfying one: partly measurement artefact, partly real, with the boundary between them unresolved.
| Wei et al. (2022) | Schaeffer et al. (2023) | |
|---|---|---|
| Claim | Abilities appear sharply, unpredictably, with scale | The sharpness comes from the metric |
| Evidence | Dozens of tasks with cliff-shaped curves | Same outputs, smooth metric, no cliff — and manufactured cliffs in vision |
| What survives | The curves are real and reproducible | The mechanism is right |
| What doesn't | The inference to unpredictability | "Mirage" — the cliff is real where exact match is what you ship |
The framing that was better all along
Ganguli and colleagues had made the sharper distinction in early 2022, before either paper, and it has aged better than both: loss is predictable; which capabilities that loss buys is not.
That threads the needle. Scaling laws genuinely do predict cross-entropy several orders of magnitude out, with an accuracy unusual anywhere in machine learning. Nothing predicts which task a given loss makes possible. Those are different claims, and the emergence argument conflated them — Wei by inferring unpredictability of capability from discontinuity of metric, Schaeffer by demonstrating the metric artefact and being read as though he had shown capabilities are predictable, which he did not.
So the practical position is: you can forecast the loss curve of your next run. You cannot forecast what it will be able to do. That was true before Wei, remained true after Schaeffer, and is the actual state of the field.
The pattern worth carrying off this page
Grokking is the same story. A model memorises, sits at chance for thousands of steps, then abruptly generalises — until Nanda reverse-engineered the network and found the generalising circuit forming gradually across the whole plateau. Continuous process, discontinuous metric, apparent moment of insight.
Two of the field's most striking "capability appeared suddenly" phenomena have now dissolved into measurement artefacts under closer inspection. That should set your prior for the third one. When something in machine learning looks like a phase transition, the first question is what is being plotted on the y-axis, and the second is whether the person plotting it chose the metric before or after seeing the shape.
Further reading
- Wei et al. (2022), Emergent Abilities of Large Language Models — the claim, and the paper everyone cites.
- Schaeffer, Miranda & Koyejo (2023), Are Emergent Abilities of Large Language Models a Mirage? — NeurIPS Best Paper; it's the metric. Read both.
- Anderson (1972), More Is Different — what emergence means when it means something.
- Ganguli et al. (2022), Predictability and Surprise in Large Generative Models — the sharper framing: loss is predictable, which capabilities that loss buys is not.
- Srivastava et al. (2022), Beyond the Imitation Game (BIG-bench) — the benchmark most emergence claims were measured on, and its own analysis of breakthrough behaviour.
Primary sources, listed so you can check the claims on this page rather than take them on trust.
Where people go wrong
- Citing emergence without citing Schaeffer. The rebuttal won Best Paper and is less known than the claim.
- Concluding the model changed abruptly. Your metric had a cliff; the model had a slope.
- Assuming no sharp transitions exist. Induction heads form abruptly — the evidence is internal, not behavioural.
- Forgetting exact match is often what users need. The experience is real; the explanation was wrong.
At a glance
Often compared with
Where this sits
A destination. 8 concepts lead here, and nothing in the corpus depends on it.
Computed from the prerequisite graph, not assigned. How this works