Scaling Laws

Layer 4 · Foundations

Scaling Laws

The full parametric loss surface, the Lagrangian derivation of the compute-optimal split, and why loss extrapolation has hard limits.

10 min read180 XP

Training compute is approximated as FLOPs (2 for the forward pass per parameter per token, doubled again for backward, i.e. roughly 6 total — a standard estimate for dense transformers, ignoring attention's quadratic term which is usually small relative to the linear projections at typical context lengths). The compute-optimal problem is: