Equation 34 · What an AI Accelerator Actually Is: Silicon, Packaging, and the Memory It Can Reach
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the latency term grows linearly in. 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 per-step latency and the per-link bandwidth. The bandwidth term approaches 2N/ and stops growing with p ; the latency term grows linearly in p . Small, frequent collectives are therefore latency bound and scale badly, while large ones are bandwidth bound and scale well — which is precisely why gradient bucketing and overlapping communication with backward computation are standard practice rather than optimisations.
Sources cited in the article section
- [11] NVIDIA Collective Communication Library (NCCL) Documentation ↗
- [9] NVIDIA Hopper Architecture In-Depth ↗
- [3] TPU v4: An Optically Reconfigurable Supercomputer for Machine Learning with Hardware Support for Embeddings ↗
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