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反向传递法则是深度学习中最为重要的一部分，torch中的backward可以对计算图中的梯度进行计算和累积

这里通过一段程序来演示基本的backward操作以及需要注意的地方

>>> import torch
>>> from torch.autograd import Variable

>>> x = Variable(torch.ones(2,2), requires_grad=True)
>>> y = x + 2
>>> y.grad_fn
Out[6]: <torch.autograd.function.AddConstantBackward at 0x229e7068138>
>>> y.grad

>>> z = y*y*3
>>> z.grad_fn
Out[9]: <torch.autograd.function.MulConstantBackward at 0x229e86cc5e8>
>>> z
Out[10]: 
Variable containing:
 27 27
 27 27
[torch.FloatTensor of size 2x2]
>>> out = z.mean()
>>> out.grad_fn
Out[12]: <torch.autograd.function.MeanBackward at 0x229e86cc408>
>>> out.backward()   # 这里因为out为scalar标量，所以参数不需要填写
>>> x.grad
Out[19]: 
Variable containing:
 4.5000 4.5000
 4.5000 4.5000
[torch.FloatTensor of size 2x2]
>>> out  # out为标量
Out[20]: 
Variable containing:
 27
[torch.FloatTensor of size 1]

>>> x = Variable(torch.Tensor([2,2,2]), requires_grad=True)
>>> y = x*2
>>> y
Out[52]: 
Variable containing:
 4
 4
 4
[torch.FloatTensor of size 3]
>>> y.backward() # 因为y输出为非标量，求向量间元素的梯度需要对所求的元素进行标注，用相同长度的序列进行标注
Traceback (most recent call last):
 File "C:\Users\dell\Anaconda3\envs\my-pytorch\lib\site-packages\IPython\core\interactiveshell.py", line 2862, in run_code
  exec(code_obj, self.user_global_ns, self.user_ns)
 File "<ipython-input-53-95acac9c3254>", line 1, in <module>
  y.backward()
 File "C:\Users\dell\Anaconda3\envs\my-pytorch\lib\site-packages\torch\autograd\variable.py", line 156, in backward
  torch.autograd.backward(self, gradient, retain_graph, create_graph, retain_variables)
 File "C:\Users\dell\Anaconda3\envs\my-pytorch\lib\site-packages\torch\autograd\__init__.py", line 86, in backward
  grad_variables, create_graph = _make_grads(variables, grad_variables, create_graph)
 File "C:\Users\dell\Anaconda3\envs\my-pytorch\lib\site-packages\torch\autograd\__init__.py", line 34, in _make_grads
  raise RuntimeError("grad can be implicitly created only for scalar outputs")
RuntimeError: grad can be implicitly created only for scalar outputs

>>> y.backward(torch.FloatTensor([0.1, 1, 10]))
>>> x.grad        #注意这里的0.1,1.10为梯度求值比例
Out[55]: 
Variable containing:
 0.2000
 2.0000
 20.0000
[torch.FloatTensor of size 3]

>>> y.backward(torch.FloatTensor([0.1, 1, 10]))
>>> x.grad        # 梯度累积
Out[57]: 
Variable containing:
 0.4000
 4.0000
 40.0000
[torch.FloatTensor of size 3]

>>> x.grad.data.zero_() # 梯度累积进行清零
Out[60]: 
 0
 0
 0
[torch.FloatTensor of size 3]
>>> x.grad       # 累积为空
Out[61]: 
Variable containing:
 0
 0
 0
[torch.FloatTensor of size 3]
>>> y.backward(torch.FloatTensor([0.1, 1, 10]))
>>> x.grad
Out[63]: 
Variable containing:
 0.2000
 2.0000
 20.0000
[torch.FloatTensor of size 3]

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