rcalix
August 23, 2022, 8:49am
#1
Hello,

I want to do a sensitivity analysis of a torch nn regression model. I understand how it works like this:

x1 = torch.randn(1, requires_grad=True)
x2 = torch.randn(1, requires_grad=True)

u = u(x1,x2)
u = 3 * x1 ** 3 - x2 ** 2
print(u)

1st derivatives
dx1 = torch.autograd.grad(u, x1)[0]
dx2 = torch.autograd.grad(u, x2)[0]
print(dx1)
print(dx2)
print(dx1 > dx2)

But how do I reference the input features (x1, x2) and the u (model), if I am using an NN module like this:

Linear Regression
class LinRegNet_SIO(nn.Module):
## initialize the layers
def init (self, x_means, x_deviations, y_means, y_deviations):
super().init ()
self.x_means = x_means
self.x_deviations = x_deviations
self.y_means = y_means
self.y_deviations = y_deviations
self.linear1 = nn.Linear(4, 2)

```
## perform inference
def forward(self, x):
x = (x - self.x_means) / self.x_deviations
y_scaled = self.linear1(x)
y_descaled = y_scaled * self.y_deviations + self.y_means
return y_descaled, y_scaled
```

is it something like this?

u = model()

1st derivatives
dx1 = torch.autograd.grad(u, u.layers.input.x1)[0]
dx2 = torch.autograd.grad(u, u.layers.inout.x2)[0]
print(dx1)

Thanks!

rcalix
August 25, 2022, 6:59pm
#2
Hello,

Can someone help me with this?

Thanks

ptrblck
August 25, 2022, 11:06pm
#3
PyTorch modules do not store an `.input`

attribute and I assume `x1`

and `x2`

are treated as trainable parameters in the first example? If so, they would correspond to e.g. `u.linear1.weight`

.

rcalix
August 26, 2022, 3:55pm
#4
Thanks for your reply. I need the derivatives in terms of each feature such as:

du/dx1 and du/x2

so I need to access the input tensor from the computational graph. Is there another way to do that?

u.linear1.weight is a reference to the weights but I need the layer before that (i.e. the input)

Thanks

I’m unsure what your exact use case is, but maybe `torch.autograd.grad`

is what you are looking for.

rcalix
August 27, 2022, 3:03am
#6
Thank you. Yes, torch.autograd is what I have been using. The use case is feature ranking. In theory, you can use the derivatives of the function with respect to each input. In a classic linear regression it is called sensitivity analysis. I just have not seen this done for neural nets and PyTorch.

The goal is to know which features are most important for the regression model prediction.

Thank you.

Would this approach of looping through the inputs to calculate the gradients (or using `jacobian`

) work for your use case?