19.3 One table divided into parts

Content and key concepts

On the previous page, the same models see different examples.
The different devices calculate the different columns of the result. The columns are then assembled in the correct order.
You can divide data, tables, or steps. Partial results need to be linked. Different patterns first turn into vectors of appropriate width, and experts are selected along a limited route.
Для изменения рисунка включитеJavaScript; расчёт и теория доступны далее.
One matrix operation is distributed between declarations
When layer is not placed on the same line, weight matrix is divided.
W=[W_1|W_2]
Each development calculates
xW_i
When row partition, local partial sumes need to be combined in a coordinated operation.Megatron-LM uses harmonized column/row splits within Transformer layers. F16.
x
[
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x[W_1|W_2]=[xW_1|xW_2],
\qquad
\begin{bmatrix}x_1&x_2\end{bmatrix}
\begin{bmatrix}W_1\\W_2\end{bmatrix}=x_1W_1+x_2W_2.
x
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.
Sharding is obliged to maintain axis semantics, bias, and the order of events. Collective communication is on the critic path of each layer, so the topology interconnect has a significant impact on the latincy.
That's what the model shows.
The visual model changes column/row split and shows where concat is needed, and where sum. Shape ledger signs global and local testors.
Scope of applicability.
Fixture calculates local slices in advance without a network and does not measure speedup. Tensor parallel degree is limited to shapes, kernel sises and interconnect. Too small shards reduce arifttic intensity; more devises can slow down one request.
x_19c=[2,3]; W_19c=[[1,0,1,2],[0,1,3,4]]
dense_19c=[sum(x_19c[r_19c]*W_19c[r_19c][c_19c] for r_19c in range(2)) for c_19c in range(4)]
left_19c=dense_19c[:2]; right_19c=dense_19c[2:]; gathered_19c=left_19c+right_19c
assert gathered_19c==dense_19c==[2,3,11,16]
The code repeats the operations just taken care of.
Completely checked Python-example Chapter
Available with a separate file; the short piece shown does not replace its implementation.
The Column partition gives different output columns of the same dense operation.
The calculation stages on different devices. How does this question continue the result?
Python examples of Chapter 19
Academic base