Equation 11 · Part 3 · OpenAI Model Systems from First Principles: Weights, Post-Training, and Inference Compute
Symbol L_infty
What this part means
the irreducible floor.
Its job in the formula
nfty 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_infty→Article meaning
Where the article explains it
has an irreducible floor and diminishing returns above it.
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.
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Sources cited in the surrounding passage
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