Equation 11 · Part 1 · OpenAI Model Systems from First Principles: Weights, Post-Training, and Inference Compute
Symbol L
What this part means
L is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Its job in the formula
L is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Full expression→Symbol L→Article meaning
The passage around this formula
with N parameters and D training tokens, the factor of six counting the forward and backward passes. Empirically, test loss falls as a power law in each of parameters, data, and compute over many orders of magnitude, a relationship first characterised systematically by Kaplan and colleagues [ 5 ] . The important structural feature is the functional form: a term of the shape . has an irreducible floor and diminishing returns above it. Doubling N buys a fixed decrement in loss, not a fixed multiple of capability.
Learn the underlying idea
A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.
Open the illustrated functions: inputs become outputs guide →
See this notation across published equations →
Sources cited in the surrounding passage
These citations provide research context; check each source for the exact claim it supports.