Emergent Abilities: Real Phenomenon or Measurement Artefact?

“Emergent abilities” is one of the few claims about language models with a sharp, published counter-argument. Both sides are worth holding, because the disagreement is about measurement and the resolution changes how you should read every capability curve you are shown.

The original claim

Wei et al. (2022), “Emergent Abilities of Large Language Models”, defined an emergent ability as one that is absent in smaller models and present in larger ones, and which therefore cannot be predicted by extrapolating the performance of the smaller ones. Their evidence was a set of tasks whose accuracy sits at chance across several orders of magnitude of training compute and then rises sharply past some threshold.

The claim mattered because it sits awkwardly with scaling laws. Loss falls smoothly and predictably; if capabilities arrive in steps, then the smooth thing being predicted does not tell you what you actually want to know, and no amount of small-scale experimentation forecasts what a larger model will be able to do.

The metric critique, derived

Schaeffer, Miranda and Koyejo (2023), “Are Emergent Abilities of Large Language Models a Mirage?”, argued that the sharpness is frequently manufactured by the choice of metric rather than present in the model. The mechanism is arithmetic, and you can do it in one line.

Take a task scored by exact match on an answer that is k tokens long. Suppose per-token accuracy is p and errors are roughly independent. Then the metric being plotted is:

  exact_match = p^k

k = 5, and p improving smoothly:

  p = 0.50  ->  0.031
  p = 0.60  ->  0.078
  p = 0.70  ->  0.168
  p = 0.80  ->  0.328
  p = 0.90  ->  0.590
  p = 0.95  ->  0.774

A smooth, unremarkable improvement in p from 0.5 to 0.9 turns into a nineteen-fold jump in the reported score, and it looks like a step if your model sizes happen to land on either side of it. Nothing discontinuous happened inside the model. The exponent did the work.

The authors’ test of this is the useful part: re-score the same model outputs with a continuous metric — token-level edit distance, Brier score, or the log-likelihood assigned to the correct answer — and the curves become smooth. Same models, same outputs, different y-axis, no emergence. Multiple-choice accuracy behaves the same way for a related reason: it is a threshold on an underlying continuous margin, and thresholds turn gradual crossings into abrupt ones.

Other things that fake a jump

• Contamination. If a benchmark leaked into the training data of the larger model and not the smaller one, you get a jump that is about the corpus, not the capability — benchmark contamination is the standard treatment.
• Prompt sensitivity. A prompt format that a larger model parses and a smaller one does not produces a capability curve that is partly a formatting curve. Reported scores can move substantially with wording alone; see prompt sensitivity.
• Sparse sampling of scale. Three model sizes cannot distinguish a step from a steep smooth rise. Many published curves have few points, spaced by an order of magnitude each.
• Post-training differences. Comparing a base model to a preference-tuned one at a different size confounds two variables — see base versus instruct.

What survives

The critique is narrower than its headline. It shows that many reported emergences are consistent with smooth underlying improvement under a discontinuous metric. It does not show that the underlying curves are always smooth, and it does not claim to have checked every case.

More importantly, one part of the original claim is untouched by any of it. Whether or not the model’s internal curve is smooth, the question a practitioner asks — can this model do the job — is a threshold question, and thresholds are crossed abruptly. If your pipeline needs the whole answer correct, then p^k is your metric, and its behaviour is your reality regardless of what the smooth version of it looks like.

Predictability is the other survivor. Even if p improves smoothly, you cannot forecast when it will cross the level your product needs without knowing k, the task and the metric. So the practical warning stands: testing a small model and extrapolating is unsafe in both directions.

It is worth being clear about what would settle the disagreement, since both papers are arguing about the same charts. A genuine discontinuity would show up as a jump in a continuous metric — the log-likelihood of the correct answer, say — across densely sampled model scales in one family trained on one recipe. That experiment is expensive and only a handful of organisations can run it, which is a large part of why the question has stayed open rather than being resolved by data.

What it means for your evaluation

The lesson transfers directly to how you build your own eval. Score with a continuous metric when you want to see progress and detect regressions early — partial credit, token overlap, or the probability of the correct answer via logprobs. Score with the harsh, discontinuous, business-shaped metric when you want to know whether you can ship. They will disagree, and the disagreement is information rather than noise: a model improving on the continuous metric while flat on the strict one is approaching a threshold it has not reached.

And treat any capability chart with an accuracy y-axis and three points on the x-axis as a claim about a metric, not a claim about a model — which is the same caution that makes published benchmarks poor predictors of your own results.