Equation 6 · Part 10 · What an AI Accelerator Actually Is: Silicon, Packaging, and the Memory It Can Reach
Numerator: 2mnk
What this part means
The complete quantity above the fraction bar.
Its job in the formula
2mnk occurs above the fraction bar. The numerator is divided by the entire denominator below it.
Full expression→Numerator: 2mnk→Article meaning
The passage around this formula
Multiplying an m k matrix by a k n matrix performs 2mnk floating-point operations while touching mk + kn + mn elements. If each element occupies s bytes, the ratio of work done to bytes moved is . which for large square matrices grows in proportion to the dimension. Double the matrix size and you roughly double the work performed per byte fetched. Almost nothing else in general-purpose computing behaves this way, and it is the entire economic basis for building a machine around one operation.
Learn the underlying idea
A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.
Open the illustrated fractions: division written vertically guide →
Sources cited in the article section
- [1] In-Datacenter Performance Analysis of a Tensor Processing Unit ↗
- [3] TPU v4: An Optically Reconfigurable Supercomputer for Machine Learning with Hardware Support for Embeddings ↗
- [10] NVIDIA Hopper Tuning Guide ↗
These citations provide research context; check each source for the exact claim it supports.