Broadcast

Versioned name: Broadcast-3

Category: Data movement

Short description: Broadcast replicates data on the first input to fit a given shape on the second input.

Detailed description:

Broadcast takes the first tensor data and, following broadcasting rules that are specified by mode attribute and the 3rd input axes_mapping, builds a new tensor with shape matching the 2nd input tensor target_shape. target_shape input is a 1D integer tensor that represents required shape of the output.

Attribute mode and the 3rd input axes_mapping are relevant for cases when rank of the input data tensor doesn't match the size of the target_shape input. They both define how axes from data shape are mapped to the output axes. If mode is set to numpy, it means that the standard one-directional numpy broadcasting rules are applied. They are similar to rules that applied in all binary element-wise operations in case when auto_broadcasting attribute is set to numpy, and are similar to rules described at here, when only one-directional broadcasting is applied: input tensor data is broadcasted to target_shape but not vice-versa.

In case if mode is set to bidirectional, then the broadcast rule is similar to numpy.array(input) * numpy.ones(target_shape). Dimensions are right alignment. Two corresponding dimension must have the same value, or one of them is equal to 1. If this attribute value is used, then the 3rd input for the operation shouldn't be provided. The behaviour of such kind of broadcasting is equivalent to ONNX operation Expand.

In case if mode is set to explicit, then 3rd input axes_mapping comes to play. It contains a list of axis indices, each index maps an axis from the 1st input tensor data to axis in the output. The size of axis_mapping should match the rank of input data tensor, so all axes from data tensor should be mapped to axes of the output.

For example, axes_mapping = [1] enables broadcasting of a tensor with shape [C] to shape [N,C,H,W] by replication of initial tensor along dimensions 0, 2 and 3. Another example is broadcasting of tensor with shape [H,W] to shape [N,H,W,C] with axes_mapping = [1, 2]. Both examples requires mode set to explicit and providing mentioned axes_mapping input, because such operations cannot be expressed with axes_mapping set to numpy.

Attributes:

• mode
  • Description: specifies rules used for mapping of input tensor axes to output shape axes.
  • Range of values:
    • numpy - numpy broadcasting rules, aligned with ONNX Broadcasting. Description is available in ONNX docs.; only one-directional broadcasting is applied from data to target_shape. If this attribute value is used, then the 3rd input for the operation shouldn't be provided.
    • explicit - mapping of the input data shape axes to output shape is provided as an explicit 3rd input.
    • bidirectional - the broadcast rule is similar to numpy.array(input) * numpy.ones(target_shape). Dimensions are right alignment. Two corresponding dimension must have the same value, or one of them is equal to 1. If this attribute value is used, then the 3rd input for the operation shouldn't be provided.
  • Type: string
  • Default value: "numpy"
  • Required: no

Inputs:

• 1: data - source tensor of type T and shape that is being broadcasted. Required.
• 2: target_shape - 1D tensor of type T_SHAPE describing output shape. Required.
• 3: axes_mapping - 1D tensor of type T_SHAPE describing a list of axis indices, each index maps an axis from the 1st input tensor data to axis in the output. The index values in this tensor should be sorted, that disables on-the-fly transpositions of input data tensor while the broadcasting. axes_mapping input is needed for mode equal to explicit only.

Outputs:

• 1: Output tensor of data tensor type with replicated content from the 1st tensor data and with shape matched target_shape.

Types

• T: any numeric type.
• T_SHAPE: any integer type.

Example

<layer ... type="Broadcast" ...>
    <data mode="numpy"/>
    <input>
        <port id="0">
            <dim>16</dim>
            <dim>1</dim>
            <dim>1</dim>
       </port>
        <port id="1">
            <dim>4</dim>   
        </port>
        
    </input>
    <output>
        <port id="2">
            <dim>1</dim>
            <dim>16</dim>
            <dim>50</dim>
            <dim>50</dim>
        </port>
    </output>
</layer>

<layer ... type="Broadcast" ...>
    <data mode="explicit"/>
    <input>
        <port id="0">
            <dim>16</dim>
       </port>
        <port id="1">
            <dim>4</dim>   
        </port>
        <port id="1">
            <dim>1</dim>   
        </port>
    </input>
    <output>
        <port id="2">
            <dim>1</dim>
            <dim>16</dim>
            <dim>50</dim>
            <dim>50</dim>
        </port>
    </output>
</layer>

<layer ... type="Broadcast" ...>
    <data mode="explicit"/>
    <input>
        <port id="0">
            <dim>50</dim>
            <dim>50</dim>
       </port>
        <port id="1">
            <dim>4</dim>   
        </port>
        <port id="1">
            <dim>2</dim>   
        </port>
    </input>
    <output>
        <port id="2">
            <dim>1</dim>
            <dim>50</dim>
            <dim>50</dim>
            <dim>16</dim>
        </port>
    </output>
</layer>

<layer ... type="Broadcast" ...>
    <data mode="bidirectional"/>
    <input>
        <port id="0">
            <dim>16</dim>
            <dim>1</dim>
            <dim>1</dim>
       </port>
        <port id="1">
            <dim>4</dim>   
        </port>
        
    </input>
    <output>
        <port id="2">
            <dim>1</dim>
            <dim>16</dim>
            <dim>50</dim>
            <dim>50</dim>
        </port>
    </output>
</layer>