Equation 27 · Part 1 · The Network Is the Computer Again
Symbol β
What this part means
β is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Its job in the formula
β is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Full expression→Symbol β→Article meaning
The passage around this formula
The consequence for model work is direct. Tensor parallelism produces small, frequent messages, so it lives in the latency-dominated regime where and participant count decide everything. Data parallelism produces one enormous message, so it lives in the bandwidth-dominated regime where decides everything. A fabric optimised for one is not optimised for the other, and a partitioning plan that ignores which regime each of its collectives falls into will be wrong in a way no amount of kernel tuning recovers.
Learn the underlying idea
A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.
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Sources cited in the article section
- [2] Collective communication: theory, practice, and experience ↗
- [3] NCCL Tests — Performance Reporting and Bus Bandwidth ↗
- [1] Optimization of Collective Communication Operations in MPICH ↗
These citations provide research context; check each source for the exact claim it supports.