That definition is based on how the paper approached it and seems to be a generally accepted definition. I just read a bit of the paper, but seems to highlight that how we've been evaluating LLMs has a lot more to say about their emergent capabilities than any actual outcome.

That was my feeling reading the paper. I feel that LLMs are overhyped but the issue of linear vs super linear growth in metrics is a different issue and can't be a refutation of what has traditionally been thought of as emergent properties. In other words, this is refutation by redefinition.

It's not the definition in the paper. Here is the context:

The idea of emergence was popularized by Nobel Prize-winning physicist P.W. Anderson’s “More Is Different”, which argues that as the complexity of a system increases, new properties may materialize that cannot be predicted even from a precise quantitative understanding of the system’s microscopic details.

What this means is, that we cannot, for example, predict chemistry from physics. Physics studies how atoms interact, which yields important insights for chemistry, but physics cannot be used to predict, say, the table of elements. Each level has its own laws, which must be derived empirically.

LLMs obviously show emergence. Knowing the mathematical, technological, and algorithmic foundation, tells you little about how to use (prompt, train, ...) an AI model. Just like knowing cell biology will not help you interact with people, even if they are only colonies of cells working together.

The paper talks specifically about “emergent abilities of LLMs”:

The term “emergent abilities of LLMs” was recently and crisply defined as “abilities that are not present in smaller-scale models but are present in large-scale models; thus they cannot be predicted by simply extrapolating the performance improvements on smaller-scale models”

The authors further clarify:

In this paper, [...] we specifically mean sharp and unpredictable changes in model outputs as a function of model scale on specific tasks.

Bigger models perform better. An increase in the number of parameters correlates to an increase in the performance on tests. It had been alleged, that some abilities appear suddenly, for no apparent reason. These “emergent abilities of LLMs” are a very specific kind of emergence.