Equation 6 · Part 9 · What an AI Accelerator Actually Is: Silicon, Packaging, and the Memory It Can Reach
subscript
subscript
What this part means
The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.
Its job in the formula
A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.
Full expression→subscript→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 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 →
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.