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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