Equation 10 · Comparing the Main Approaches to AI Memory Systems and the Bandwidth Wall
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Symbol W
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The mechanism behind that number is the equation above, solved by moving W off the board entirely. Instead of a few hundred board-routed pins, HBM connects its DRAM dies to the compute die through a silicon interposer carrying thousands of short, low-speed, densely packed through-silicon vias and micro-bumps. The trade is explicit: enormous parallel width bought at the cost of an expensive, capacity-limited package. A stack’s capacity is fixed at manufacture — soldered in-package, not a field-upgradable component — and the interposer’s reticle-limited area caps how many stacks and how much logic can share one package. HBM is, in the vocabulary above, a high-bandwidth, high-cost,…
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The mechanism behind that number is the equation above, solved by moving W off the board entirely. Instead of a few hundred board-routed pins, HBM connects its DRAM dies to the compute die through a silicon interposer carrying thousands of short, low-speed, densely packed through-silicon vias and micro-bumps. The trade is explicit: enormous parallel width bought at the cost of an expensive, capacity-limited package. A stack’s capacity is fixed at manufacture — soldered in-package, not a field-upgradable component — and the interposer’s reticle-limited area caps how many stacks and how much logic can share one package. HBM is, in the vocabulary above, a high-bandwidth, high-cost, low-programmability-of-capacity answer: the accelerator that ships with it is stuck with whatever capacity was designed in, for the life of the part.
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