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_fnOut[6]: <torch.autograd.function.AddConstantBackward at 0x229e7068138>>>> y.grad>>> z = y*y*3>>> z.grad_fnOut[9]: <torch.autograd.function.MulConstantBackward at 0x229e86cc5e8>>>> zOut[10]: Variable containing: 27 27 27 27[torch.FloatTensor of size 2x2]>>> out = z.mean()>>> out.grad_fnOut[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.gradOut[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>>> yOut[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.gradOut[63]: Variable containing: 0.2000 2.0000 20.0000[torch.FloatTensor of size 3]

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