Symbol L
L is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Read this term in its guide →Published equation contexts
Why this formula appears here
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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Symbol N
N is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Read this term in its guide →Symbol N_c
occurs above the fraction bar. The numerator is divided by the entire denominator below it.
Read this term in its guide →Symbol alpha_N
alph is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Read this term in its guide →How to interpret it
With a fixed numerator, increasing a nonzero denominator reduces the fraction. Its accuracy depends on the assumptions and range of use described in the article.
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Published contexts (1)
A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.
Equation 11 · Foundation Models
OpenAI Model Systems from First Principles: Weights, Post-Training, and Inference Compute
This equation gives an approximation: it relates the quantities while allowing an approximation.
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.