The sudden jump in AI benchmarks was mostly in the scoring

Two papers scored the same model outputs

In 2022 a team led by Jason Wei gave a name to something the field had been noticing: some abilities seem to appear all at once. A small model cannot do a task at all, scoring no better than chance. Make the model larger and, past some size, the score climbs sharply. Wei and his coauthors called these emergent abilities, and defined the term precisely: "We consider an ability to be emergent if it is not present in smaller models but is present in larger models," so that "emergent abilities cannot be predicted simply by extrapolating the performance of smaller models."¹ They charted eight such abilities from few-shot prompting, each a flat line near chance that bends upward at a threshold of scale.¹ Three-digit addition, in their tables, appears at 13 billion parameters; two-digit multiplication and a 57-subject exam called MMLU appear only at 175 billion.¹

In 2023 Rylan Schaeffer, Brando Miranda, and Sanmi Koyejo at Stanford looked again. They did not dispute a single number. They took the same fixed model outputs and scored them differently, and argued that "for a particular task and model family, when analyzing fixed model outputs, emergent abilities appear due to the researcher's choice of metric rather than due to fundamental changes in model behavior with scale."² Their paper, "Are Emergent Abilities of Large Language Models a Mirage?", won an Outstanding Main Track Paper Award at NeurIPS 2023.³

Both accept that small models score low and large models score high. The whole dispute is about the shape of the line between those two points: whether it jumps or whether it rises smoothly. And a benchmark score is not the ability itself. It is a proxy, a number standing in for a capability no one can measure directly. The word "emergent" lives in the space between what a metric counted and what a reader takes it to have counted.

What exact-match accuracy does to a near-miss

Take a single arithmetic problem whose answer is the five-digit number 74510. A benchmark scores a model's answer with a rule, and the standard rule for arithmetic is exact-match accuracy: the answer scores 1 if every digit matches the target, and 0 otherwise.² There is nothing in between. A model that writes 74513, correct in four of its five digits, does not score four-fifths. It scores 0, exactly what a model that writes 29563 scores, because neither string is the target string.

Call a metric like this discontinuous: its output can only be 0 or 1, with no value between, however close the answer came. Now picture three models of increasing size, each a little better at the last digit than the one before. Under exact-match, every one that falls short scores 0, and the first that gets all five digits scores 1. Plot those scores against model size and you get a flat line that suddenly snaps to the top. That is the hockey stick. And here is the exact place a reader's intuition slips. The curve jumped, so it feels as though an ability switched on at that size. What actually happened is that a rule which reports nothing until an answer is perfect finally had a perfect answer to report.

Score the same answers for how close they got

Keep the same model outputs. Change only the ruler. Instead of exact-match, score each answer by token edit distance: count the single-character changes needed to turn the answer into the target, and give credit for the characters already right.² Now 74513 is one change away from 74510, so it keeps four-fifths of the credit. The answer 29563, four changes away, keeps one-fifth. The two models that scored an identical 0 a moment ago are now cleanly separated, and the separation matches how close each came.

Read the two score columns down the page. Exact-match sits at 0 through three improving models and then leaps to 1. The token score climbs at every step: 0.2, 0.4, 0.8, 1.0. Same outputs, same models, same underlying improvement. One ruler hides it until the final step, and the other shows it all along.

There is a reason the shapes differ so sharply, and it is arithmetic, not opinion. Suppose the model's chance of getting any one digit wrong is \varepsilon, and that it falls smoothly as the model grows. An answer of L digits is scored correct by exact-match only if every digit is right, so its expected accuracy is about (1-\varepsilon)^{L}. Raising a number below one to the fifth or tenth power drives it toward zero and holds it there while \varepsilon is still large, then lets it shoot up once the per-digit error gets small: a curve that looks flat, then sudden. Token edit distance instead adds up the per-digit successes, so it tracks 1-\varepsilon in a near-straight line. The same smoothly falling error rate produces a sudden curve under one metric and a gradual one under the other.² A later account of the debate put the intuition plainly: ask how well a model predicts the first digit, then the second, then the third, and for the sum 100 + 278 the answer 376 is much closer than −9.34, a difference that all-or-nothing grading throws away.⁴

Most of the jumps lived in two metrics

One worked example is not a proof about the field. Schaeffer and his coauthors went to the source most of Wei's emergent tasks were drawn from: BIG-Bench, a community benchmark of 204 tasks assembled by 450 authors across 132 institutions, each task shipped with its own preferred scoring metric.⁵ They counted where emergence showed up. More than 92% of the abilities anyone had called emergent appeared under just two of those metrics, Multiple Choice Grade and Exact String Match, both discontinuous.² Of the 39 preferred metrics in BIG-Bench, at most 5 produced any emergence at all.² When they took a task that looked emergent under Multiple Choice Grade and rescored it under Brier score, a continuous metric for the same predictions, the jump flattened into a ramp.²

The original authors had seen this coming. Wei's own paper, in its discussion, warns that "using exact string match as the evaluation metric for long-sequence targets may disguise compounding incremental improvements as emergence."¹ The mirage paper did not catch the field off guard so much as measure a caveat the field had already written down and moved past. That history matters for how much weight to give the correction: it is a sharpening of a known problem, not the exposure of a hidden one.

What the swap leaves standing

It would be easy to read all this as: emergence was fake. That is not what the evidence says, and Schaeffer's own words are careful about the boundary. The claim is scoped to "a particular task and model family, when analyzing fixed model outputs."² It does not assert that nothing ever changes qualitatively with scale, and it does not cover what happens during training. Three things survive the metric swap.

The first is the ability itself. Showing that a curve was smooth all along does not make the capability absent. It restores the opposite conclusion: the underlying skill was improving predictably with scale, and the sudden-onset story was hiding that. The models were never at zero capability; a metric that reports zero until an answer is perfect only made them look that way.

The second is the jump a user actually feels. If you need the sum and will accept only the correct sum, then a model that reaches 74513 has given you nothing, and the one that finally reaches 74510 has given you everything. Smooth improvement in the per-digit error rate still produces a sharp jump in useful behavior, because usefulness here is itself all-or-nothing. Wei's camp makes exactly this point: for a task like arithmetic, the right answer is all a user wants, so the discontinuous metric is the one that counts.⁴ The metric swap explains the mechanism and restores predictability of the skill. It does not make a near-miss useful.

The third is what we still cannot predict. Alex Tamkin, a researcher at Anthropic, cautions that this "is not the full story," that "we can't say that all of these jumps are a mirage," and that "you still have discontinuities."⁴ Even where the underlying skill is smooth, no one has shown how to say in advance which capability will cross the threshold of usefulness at which scale. That gap was named before the emergence debate began. Ganguli and coauthors at Anthropic described large models in 2022 as having "an unusual combination of predictable loss ... and unpredictable specific capabilities, inputs, and outputs."⁶ The mirage paper narrows the mystery by making the skill curves predictable. It does not close the surprise at deployment.