Error: "One of the differentiated Tensors appears to not have been used in the graph"

Question

I am trying to compute a gradient of y_hat to x (y_hat is the sum of gradients of model output to x) but it gives me the error: One of the differentiated Tensors appears to not have been used in the graph. This is the code:

class Model(nn.Module):
    def __init__(self,):
        super(Model, self).__init__()
        self.weight1 = torch.nn.Parameter(torch.tensor([[.2,.5,.9],[1.0,.3,.5],[.3,.2,.7]]))
        self.weight2 = torch.nn.Parameter(torch.tensor([2.0,1.0,.4]))
   

    def forward(self, x):
        out =F.linear(x, self.weight1.T)
        out =F.linear(out, self.weight2.T)
        return out

model = Model() 
x = torch.tensor([[0.1,0.7,0.2]])
x = x.requires_grad_()
output = model(x)
y_hat = torch.sum(torch.autograd.grad(output, x, create_graph = True)[0])
torch.autograd.grad(y_hat, x)

I think x should be in the computational graph, so I don't know why it gives me this error? Any thoughts would be appreciated!

Answer 1

Cause this function is actually y = x@b so after the first derivative there is no x in the result and that's why we can't do the second derivative.