Emergent abilities, or a mirage of the ruler? How exact-match manufactures a cliff from a smooth skill

Scaling laws say a model's loss falls as a smooth, forecastable power law. But downstream skills can behave differently: on many tasks a model scores essentially 0% across a huge range of sizes, then — past some threshold — accuracy leaps. That's an "emergent ability" (Wei et al. 2022), and it's unsettling, because you can't read the jump off the smooth loss curve. Then came the counter-argument (Schaeffer et al. 2023, "Are Emergent Abilities a Mirage?" ): much of that sudden jump is an…