Test loss falls as a power law in each of parameters \(N\), data \(D\) and compute \(C\), with the others held non-limiting:
The practical consequence is that training runs became predictable: the loss of a model too expensive to train twice can be forecast from a series of small ones. That predictability is why frontier-scale training is a planned engineering activity rather than a gamble, and it is the mechanism behind the generality observed in P-0004.
Limits of the framing
Scaling laws describe loss, not capability. The mapping from loss to downstream competence is not itself a power law and is not smooth — which is what discussions of emergent ability are really about. They also say nothing about data exhaustion, and nothing at all about continual learning, where the i.i.d. assumption underpinning them does not hold.