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Broadcasting in ONNX

In ONNX, element-wise operators can take inputs with different shape, as long as the input tensors are broadcastable to the same shape. ONNX supports two types of broadcasting: multidirectional broadcasting and unidirectional broadcasting. We will introduce these two types of broadcasting respectively in the following sections.

Multidirectional Broadcasting

In ONNX, a set of tensors are multidirectional broadcastable to the same shape if one of the following is true:

• The tensors all have exactly the same shape.
• The tensors all have the same number of dimensions and the length of each dimensions is either a common length or 1.
• The tensors that have too few dimensions can have their shapes prepended with a dimension of length 1 to satisfy property 2.

For example, the following tensor shapes are supported by multidirectional broadcasting:

• shape(A) = (2, 3, 4, 5), shape(B) = (,), i.e. B is a scalar ==> shape(result) = (2, 3, 4, 5)
• shape(A) = (2, 3, 4, 5), shape(B) = (5,), ==> shape(result) = (2, 3, 4, 5)
• shape(A) = (4, 5), shape(B) = (2, 3, 4, 5), ==> shape(result) = (2, 3, 4, 5)
• shape(A) = (1, 4, 5), shape(B) = (2, 3, 1, 1), ==> shape(result) = (2, 3, 4, 5)
• shape(A) = (3, 4, 5), shape(B) = (2, 1, 1, 1), ==> shape(result) = (2, 3, 4, 5)

Multidirectional broadcasting is the same as Numpy's broadcasting.

Multidirectional broadcasting is supported by the following operators in ONNX:

• Add
• And
• Div
• Equal
• Greater
• Less
• Max
• Mean
• Min
• Mul
• Or
• Pow
• Sub
• Sum
• Where
• Xor

Unidirectional Broadcasting

In ONNX, tensor B is unidirectional broadcastable to tensor A if one of the following is true:

• Tensor A and B both have exactly the same shape.
• Tensor A and B all have the same number of dimensions and the length of each dimensions is either a common length or B's length is 1.
• Tensor B has too few dimensions, and B can have its shapes prepended with a dimension of length 1 to satisfy property 2.

When unidirectional broadcasting happens, the output's shape is the same as the shape of A (i.e., the larger shape of two input tensors).

In the following examples, tensor B is unidirectional broadcastable to tensor A:

• shape(A) = (2, 3, 4, 5), shape(B) = (,), i.e. B is a scalar ==> shape(result) = (2, 3, 4, 5)
• shape(A) = (2, 3, 4, 5), shape(B) = (5,), ==> shape(result) = (2, 3, 4, 5)
• shape(A) = (2, 3, 4, 5), shape(B) = (2, 1, 1, 5), ==> shape(result) = (2, 3, 4, 5)
• shape(A) = (2, 3, 4, 5), shape(B) = (1, 3, 1, 5), ==> shape(result) = (2, 3, 4, 5)

Unidirectional broadcasting is supported by the following operators in ONNX:

• Gemm
• PRelu