Equation 5 · Locality Is the Whole Game: The Memory Hierarchy and What a Kernel Does Not Read
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the achievable bandwidth at the level that dominates. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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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.
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 give research context. Read each source to check which claims it supports.
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