Second derivative with respect to input

autograd
1

Hi, I’m trying to implement the second derivative with respect to input. However, the returned error confused me. The following are the sample code.

import torch
import torch.nn as nn

class Net(nn.Module):
    def __init__(self):
        super(Net, self).__init__()
        self.fc1 = nn.Linear(2, 1)

    def forward(self, x):
        x = self.fc1(x)
        return x

dat = torch.tensor([[1.2,3.4], [5.6,1.6]], requires_grad=True)
model = Net()
out = model(dat)
tmp,  = torch.autograd.grad(outputs = out, inputs = dat, grad_outputs = torch.ones_like(out), retain_graph=True, create_graph=True)
second = torch.autograd.grad(outputs = tmp, inputs = dat, grad_outputs =torch.ones_like(tmp), retain_graph=True, create_graph=True)

The error message are the following

--------------------------------------------------------------------------
RuntimeError                              Traceback (most recent call last)
<ipython-input-66-8ad432f34bca> in <module>
----> 1 torch.autograd.grad(outputs = tmp, inputs = dat, grad_outputs =torch.ones_like(tmp), retain_graph=True)

~/.local/lib/python3.8/site-packages/torch/autograd/__init__.py in grad(outputs, inputs, grad_outputs, retain_graph, create_graph, only_inputs, allow_unused)
    221         retain_graph = create_graph
    222 
--> 223     return Variable._execution_engine.run_backward(
    224         outputs, grad_outputs_, retain_graph, create_graph,
    225         inputs, allow_unused, accumulate_grad=False)

RuntimeError: One of the differentiated Tensors appears to not have been used in the graph. Set allow_unused=True if this is the desired behavior.

I tried “Set allow_unused=True if this is the desired behavior.” But it returns a empty tensor

Can anyone help me to fix this?

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