Emergent Abilities and Metric Artefacts

Three-digit addition accuracy for GPT-3 sits near zero for every model up to 6.7B parameters, rises at 13B, and is close to perfect at 175B in the few-shot setting (Brown et al., 2020, Language Models are Few-Shot Learners, arXiv:2005.14165). Plot it against parameter count and you get a step function. Wei et al. collected dozens of such curves and defined an emergent ability as one "not present in smaller models but present in larger models", explicitly not predictable from smaller-scale extrapolation (Wei et al., 2022, Emergent Abilities of Large Language Models, arXiv:2206.07682, TMLR).

The claim mattered because it undermined the entire case for careful pre-deployment evaluation at small scale. If capabilities appear without warning, small-model evals cannot tell you what a large model will do.

The metric critique

Schaeffer, Miranda, and Koyejo argued that the sharpness is manufactured by the evaluation metric (Schaeffer et al., 2023, Are Emergent Abilities of Large Language Models a Mirage?, arXiv:2304.15004, NeurIPS 2023). The argument is mechanical and hard to dispute.

Take exact-match accuracy on \(L\)-digit addition. Suppose per-token error falls smoothly with scale, so the probability of getting a single token right is \(p(N)\), improving gradually with parameter count \(N\). Exact match requires every token correct:

Raising a smoothly improving quantity to the fifth power produces something that looks flat and then rises steeply. Nothing discontinuous happened in the model. The metric applied a sharp nonlinearity to a smooth signal.

The prediction that follows is testable: swap exact match for a continuous metric such as token edit distance or per-token log-likelihood, and the curve should become smooth on the same models and the same checkpoints. It does, on the great majority of the tasks originally cited as emergent. Schaeffer et al. also show they can induce apparent emergence in vision models, where nobody had claimed it, by switching to a discontinuous metric.

Two further mundane causes reinforce the effect. Small models are often evaluated with too few samples to resolve accuracies near zero, so the low end of the curve is noise rounded to zero. And the model sizes sampled are usually spaced by an order of magnitude, so any smooth transition spanning less than a decade of scale looks like a jump.

What survives

The critique is about sharpness and predictability, not about capability. Nobody disputes that large models do things small ones cannot; the question is whether the transition is a phase change or a threshold crossing on a smooth curve. Three things survive.

Exact match is often the metric you actually care about. A user who needs a correct 5-digit sum gains nothing from the model being smoothly closer. The smooth per-token curve is the better scientific description and the worse product description, and both descriptions are legitimate.

Some downstream behaviour still resists prediction. Predicting per-token loss from scale is reliable; predicting which benchmark score that loss corresponds to is not, and the mapping from loss to task performance remains poorly characterised. This is the sharpest version of the open problem, and it is not resolved by the metric argument.

Sudden behaviour changes exist in training, not only in scale. Induction heads form in a narrow window during training and coincide with a visible bump in in-context learning ability. That is a genuine phase transition in mechanism, measured on a continuous quantity, and it is the kind of emergence the metric critique does not touch.

When it breaks

The practical discipline this yields is specific. When a curve looks like a step, before concluding anything about the model, check whether the metric is discontinuous, whether the low-end points have enough samples to distinguish small from zero, and whether the x-axis spacing could hide a smooth transition. Report a continuous metric alongside the thresholded one; it costs nothing and it is what makes the claim falsifiable.

The residual risk is real and should not be argued away. Even under the metric account, capabilities cross usable thresholds at scales that were not tested, and a system that is smoothly improving toward a dangerous competence is not safer than one that jumps to it. The mirage argument changes the mechanism of surprise, not the fact of it. See scaling laws, reasoning evals and contamination, and eval error bars and statistics.