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80 lines
3.1 KiB
Markdown
80 lines
3.1 KiB
Markdown
<!--
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Copyright (c) ONNX Project Contributors
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SPDX-License-Identifier: Apache-2.0
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-->
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# Broadcasting in ONNX
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In ONNX, element-wise operators can take inputs with different shape,
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as long as the input tensors are broadcastable to the same shape.
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ONNX supports two types of broadcasting: multidirectional broadcasting and
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unidirectional broadcasting. We will introduce these two types of broadcasting
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respectively in the following sections.
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## Multidirectional Broadcasting
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In ONNX, a set of tensors are multidirectional broadcastable to the same shape
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if one of the following is true:
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- The tensors all have exactly the same shape.
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- The tensors all have the same number of dimensions and the length of
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each dimensions is either a common length or 1.
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- The tensors that have too few dimensions can have their shapes prepended
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with a dimension of length 1 to satisfy property 2.
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For example, the following tensor shapes are supported by multidirectional broadcasting:
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- shape(A) = (2, 3, 4, 5), shape(B) = (,), i.e. B is a scalar ==> shape(result) = (2, 3, 4, 5)
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- shape(A) = (2, 3, 4, 5), shape(B) = (5,), ==> shape(result) = (2, 3, 4, 5)
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- shape(A) = (4, 5), shape(B) = (2, 3, 4, 5), ==> shape(result) = (2, 3, 4, 5)
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- shape(A) = (1, 4, 5), shape(B) = (2, 3, 1, 1), ==> shape(result) = (2, 3, 4, 5)
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- shape(A) = (3, 4, 5), shape(B) = (2, 1, 1, 1), ==> shape(result) = (2, 3, 4, 5)
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Multidirectional broadcasting is the same as [Numpy's broadcasting](https://docs.scipy.org/doc/numpy/user/basics.broadcasting.html#general-broadcasting-rules).
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Multidirectional broadcasting is supported by the following operators in ONNX:
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- [Add](Operators.md#Add)
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- [And](Operators.md#And)
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- [Div](Operators.md#Div)
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- [Equal](Operators.md#Equal)
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- [Greater](Operators.md#Greater)
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- [Less](Operators.md#Less)
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- [Max](Operators.md#Max)
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- [Mean](Operators.md#Mean)
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- [Min](Operators.md#Min)
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- [Mul](Operators.md#Mul)
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- [Or](Operators.md#Or)
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- [Pow](Operators.md#Pow)
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- [Sub](Operators.md#Sub)
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- [Sum](Operators.md#Sum)
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- [Where](Operators.md#Where)
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- [Xor](Operators.md#Xor)
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## Unidirectional Broadcasting
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In ONNX, tensor B is unidirectional broadcastable to tensor A
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if one of the following is true:
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- Tensor A and B both have exactly the same shape.
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- Tensor A and B all have the same number of dimensions and the length of
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each dimensions is either a common length or B's length is 1.
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- Tensor B has too few dimensions, and B can have its shapes prepended
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with a dimension of length 1 to satisfy property 2.
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When unidirectional broadcasting happens, the output's shape is the same as
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the shape of A (i.e., the larger shape of two input tensors).
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In the following examples, tensor B is unidirectional broadcastable to tensor A:
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- shape(A) = (2, 3, 4, 5), shape(B) = (,), i.e. B is a scalar ==> shape(result) = (2, 3, 4, 5)
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- shape(A) = (2, 3, 4, 5), shape(B) = (5,), ==> shape(result) = (2, 3, 4, 5)
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- shape(A) = (2, 3, 4, 5), shape(B) = (2, 1, 1, 5), ==> shape(result) = (2, 3, 4, 5)
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- shape(A) = (2, 3, 4, 5), shape(B) = (1, 3, 1, 5), ==> shape(result) = (2, 3, 4, 5)
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Unidirectional broadcasting is supported by the following operators in ONNX:
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- [Gemm](Operators.md#Gemm)
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- [PRelu](Operators.md#PRelu)
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