Equation 27 · What an AI Accelerator Actually Is: Silicon, Packaging, and the Memory It Can Reach
What does this equation mean?
Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.
the number of bytes. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
Read it piece by piece
How to interpret it
Read this expression with the definitions, units, and assumptions supplied by the article.
What the article says around this equation
Their cost has a shape worth internalising. For the standard ring formulation of an all-reduce over p devices and N bytes, the operation decomposes into a reduce-scatter followed by an all-gather, each of p - 1 steps in which every device sends N/p bytes. Total time is approximately
Sources cited in the article section
- [11] NVIDIA Collective Communication Library (NCCL) Documentation ↗
- [9] NVIDIA Hopper Architecture In-Depth ↗
- [3] TPU v4: An Optically Reconfigurable Supercomputer for Machine Learning with Hardware Support for Embeddings ↗
These citations give research context. Read each source to check which claims it supports.
Return to What an AI Accelerator Actually Is: Silicon, Packaging, and the Memory It Can Reach