Emergence as a mirage. Watch a metric invent a cliff.

A single smooth improvement in skill, scored by an all or nothing metric, can look like an ability that switches on at some scale. Drag the marker to read any point. Then drag the answer length and watch the cliff appear out of a curve that never bends.

Scale (log10 params)
11.00
Per token accuracy
0.900
Exact match accuracy
0.122
Answer length L
20
20 tokens

The lesson. Distrust any emergence claim built on an all or nothing metric. The lesson is not that emergence is fake, real reorganizations like grokking exist. It is that our theory predicts the smooth loss, and not the jagged capability that the loss is supposed to stand for.