pytorch 广播是如何工作的?

问题描述

torch.add(torch.ones(4,1), torch.randn(4))

产生一个尺寸为:torch.Size([4,4]).

的张量

有人可以提供这背后的逻辑吗?

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示例 2::

T 和 F 分别代表 True 和 False 并指示我们允许广播的维度(来源:

torch.add(torch.ones(4,1), torch.randn(4))

produces a Tensor with size: torch.Size([4,4]).

Can someone provide a logic behind this?

PyTorch broadcasting is based on numpy broadcasting semantics which can be understood by reading numpy broadcasting rules or PyTorch broadcasting guide. Expounding the concept with an example would be intuitive to understand it better. So, please see the example below:

In [27]: t_rand
Out[27]: tensor([ 0.23451,  0.34562,  0.45673])

In [28]: t_ones
Out[28]: 
tensor([[ 1.],
        [ 1.],
        [ 1.],
        [ 1.]])

Now for torch.add(t_rand, t_ones), visualize it like:

               # shape of (3,)
               tensor([ 0.23451,      0.34562,       0.45673])
      # (4, 1)          | | | |       | | | |        | | | |
      tensor([[ 1.],____+ | | |   ____+ | | |    ____+ | | |
              [ 1.],______+ | |   ______+ | |    ______+ | |
              [ 1.],________+ |   ________+ |    ________+ |
              [ 1.]])_________+   __________+    __________+

which should give the output with tensor of shape (4,3) as:

# shape of (4,3)
In [33]: torch.add(t_rand, t_ones)
Out[33]: 
tensor([[ 1.23451,  1.34562,  1.45673],
        [ 1.23451,  1.34562,  1.45673],
        [ 1.23451,  1.34562,  1.45673],
        [ 1.23451,  1.34562,  1.45673]])

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Also, note that we get exactly the same result even if we pass the arguments in a reverse order as compared to the previous one:

# shape of (4, 3)
In [34]: torch.add(t_ones, t_rand)
Out[34]: 
tensor([[ 1.23451,  1.34562,  1.45673],
        [ 1.23451,  1.34562,  1.45673],
        [ 1.23451,  1.34562,  1.45673],
        [ 1.23451,  1.34562,  1.45673]])

Anyway, I prefer the former way of understanding for more straightforward intuitiveness.

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For pictorial understanding, I culled out more examples which are enumerated below:

Example-1:

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Example-2::

T and F stand for True and False respectively and indicate along which dimensions we allow broadcasting (source: Theano).

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Example-3:

Here are some shapes where the array b is broadcasted appropriately to match the shape of the array a.

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