Equation 7 · Part 8 · From n-Grams to Reasoning Models: A Technical History of the Language Model
superscript
superscript
What this part means
A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.
Its job in the formula
A raised mark can be a power or an index. Its position and the surrounding notation determine which.
Full expression→superscript→Article meaning
The passage around this formula
By this point compute had become the binding constraint, and the field did not know how to spend it. Kaplan and colleagues characterised the relationship empirically, finding that cross-entropy loss scales as a power law in model size, dataset size and compute, with trends spanning more than seven orders of magnitude, and concluding that compute-efficient training meant very large models on relatively modest data, stopped well short of convergence [ 16 ] . The functional form is the important part: . Hoffmann and colleagues then trained over four hundred models and reached a different allocation: model size and training tokens should scale in roughly equal proportion, and…
Learn the underlying idea
An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.
Open the illustrated exponents: repeated multiplication and powers guide →
Sources cited in the surrounding passage
These citations provide research context; check each source for the exact claim it supports.