Equation 6 · Part 1 · What an AI Accelerator Actually Is: Silicon, Packaging, and the Memory It Can Reach
Symbol I_gemm
What this part means
the ratio of work done to bytes moved.
Its job in the formula
emm is part of the quantity the equation computes from the expression on the right.
Full expression→Symbol I_gemm→Article meaning
Where the article explains it
If each element occupies s bytes, the ratio of work done to bytes moved is
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 subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.
Open the illustrated subscripts: which member of a family? guide →
See this notation across published equations →
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.