Equation 6 · Part 4 · Locality Is the Whole Game: The Memory Hierarchy and What a Kernel Does Not Read
=
=
What this part means
The expressions on both sides represent the same quantity under the stated assumptions.
Its job in the formula
The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.
Full expression→=→Article meaning
The passage around this formula
with the peak arithmetic rate, I the arithmetic intensity in operations per byte, and B the achievable bandwidth at the level that dominates. The two terms cross at a ridge point = /B . Below it a kernel is memory-bound and its runtime is set by traffic; above it the kernel is compute-bound and traffic is hidden.
Learn the underlying idea
An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.
Open the illustrated equality: what the equals sign claims guide →
Sources cited in the article section
- [5] Roofline: An Insightful Visual Performance Model for Floating-Point Programs and Multicore Architectures ↗
- [4] AI and Memory Wall ↗
- [1] FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness ↗
- [9] Data Movement Is All You Need: A Case Study on Optimizing Transformers ↗
These citations provide research context; check each source for the exact claim it supports.