Equation 2 · How AI Memory Systems and the Bandwidth Wall Actually Work
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the peak arithmetic rate of the device. 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 of the device, B the achievable bandwidth of the memory tier supplying the operands, and P the attainable performance [ 11 ] . The two terms cross at a ridge point = /B : below it, runtime is set by how many bytes must move, whatever the peak arithmetic rate promises; above it, the arithmetic units are the limit and the memory system is idle capacity. Because peak compute has grown roughly twice as fast as memory bandwidth for two decades running [ 12 ] , that ridge point has been climbing — a kernel that was comfortably compute-bound on one generation of hardware can become memory-bound on the next without a single line of its code…
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with the peak arithmetic rate of the device, B the achievable bandwidth of the memory tier supplying the operands, and P the attainable performance [ 11 ] . The two terms cross at a ridge point = /B : below it, runtime is set by how many bytes must move, whatever the peak arithmetic rate promises; above it, the arithmetic units are the limit and the memory system is idle capacity. Because peak compute has grown roughly twice as fast as memory bandwidth for two decades running [ 12 ] , that ridge point has been climbing — a kernel that was comfortably compute-bound on one generation of hardware can become memory-bound on the next without a single line of its code changing.
Sources cited in the surrounding passage
- [11] Roofline: An Insightful Visual Performance Model for Floating-Point Programs and Multicore Architectures ↗
- [12] AI and Memory Wall ↗
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