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

class Broadcast : public ngraph::op::Op

Operation which “adds” axes to an input tensor, replicating elements from the input as needed along the new axes.

Subclassed by ngraph::op::BroadcastLike

Public Functions

Broadcast(const std::shared_ptr<Node> &arg, const Shape &shape, const AxisSet &broadcast_axes)

Constructs a conversion operation.

Parameters
  • arg: Node that produces the input tensor to be broadcast.
  • shape: The shape of the output tensor.
  • broadcast_axes: The axis positions (0-based) in the result that are being broadcast. The remaining axes in shape must be the same as the shape of arg.

void validate_and_infer_types()

Throws if the node is invalid.

const AxisSet &get_broadcast_axes() const

Return
A set containing the indices of the broadcast axes (0-based).