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Equation 11 · Part 1 · OpenAI Model Systems from First Principles: Weights, Post-Training, and Inference Compute

Symbol L

L(N)≈L∞+(NcN)αNL(N) \approx L_\infty + \left(\frac{N_c}{N}\right)^{\alpha_N}
LL

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.

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 L(N)≈L∞+(NcN)αNL(N) \approx L_\infty + \left(\frac{N_c}{N}\right)^{\alpha_N}. has an irreducible floor L∞L_\infty and diminishing returns above it. Doubling N buys a fixed decrement in loss, not a fixed multiple of capability.

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A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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