Broadcast

Broadcast  // Operation that produces a tensor based on arg's axes

Description

Operation whose output tensor ignores axes not in the arg tensor.

Inputs

Name

Element Type

Shape

arg

Any

Any

Attributes

Name

Type

Notes

shape

Shape

The shape of the output.

broadcast_axes

AxisSet

Axis positions in shape that are broadcast.

Outputs

Name

Element Type

Shape

output

Same as arg

Same as shape

The shape of arg must match shape with elements in broadcast_axes removed.

For example, if arg is \([a, b, c]\) then

\[\begin{split}\mathtt{Broadcast(arg, Shape{2, 3}, AxisSet{0})} &= \begin{bmatrix} a & b & c\\ a & b & c \end{bmatrix}\\ \mathtt{Broadcast(arg, Shape{3, 2}, AxisSet{1})} &= \begin{bmatrix} a & a\\ b & b\\ c & c \end{bmatrix}\end{split}\]

Mathematical Definition

For a coordinate \(C\), let \(p(C)\) be a coordinate with the axes in broadcast_axes removed. For example, if \(\mathtt{broadcast_axes}=\{1,3\}\) then \(p([d_0, d_1, d_2, d_3, d_4]) = [d_0, d_2, d_4]\). Then

\[\mathtt{output}_C = \mathtt{arg}_{p(C)}.\]

Backprop

\[\overline{\mathtt{arg}} \leftarrow \mathtt{Sum}(\Delta, \mathtt{broadcast_axes}).\]

C++ Interface

Warning

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