Equation 26 · Part 1 · The Network Is the Computer Again
Symbol α
What this part means
the writing.
Its job in the formula
α 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 α→Article meaning
Where the article explains it
Writing for latency per message, for transfer time per byte and for reduction time per byte, the cost of a collective over p participants on n bytes takes the shape T(n,p) = \,L(p) + \,W(n,p) + \,C(n,p), where L counts message steps, W counts bytes crossing each link and C counts arithmetic.
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.