Equation 3 · Part 2 · Locality Is the Whole Game: The Memory Hierarchy and What a Kernel Does Not Read
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
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
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
- [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.