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Is column selection in Pytorch differentiable? for eg if I want to select a single column from each row to make a new row X 1 array and then backdrop using this new array, will the backdrop work properly? 

qvalues = qvalues[range(5),[0,1,0,1,0]]

if element selection is done as shown above from a 5*2 tensor?

Manuel Lagunas
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patrick
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1 Answers1

23

I think it is. Let me make an example with code.

First we create the qvalues tensor and we say we want to compute its gradients

qvalues = torch.rand((5, 5), requires_grad=True)

Now we create the tensor to index it and obtain a 5x2 tensor as its result (I think this is the same selection you wanted to perform with qvalues[range(5),[0,1,0,1,0]]):

y = torch.LongTensor([1, 3])
new_qvalues = qvalues[:, y]

We see that the slice new_qvalues of the original qvalues will compute the gradient

print(new_qvalues.requires_grad) # True

Now we perform our mathematical operations. In this example code, I am doing the square of new_qvalues because we know that its gradient (derivative) will be 2 * new_qvalues.

qvalues_a = new_qvalues ** 2

Now, we have to compute the gradients of qvalues_a. We set retain_graph=True to store the .grad of each tensor and avoid freeing the buffers on the backward pass.

qvalues_a.backward(torch.ones(new_qvalues.shape), retain_graph=True)

Now, we can go back to the original qvalues and see if the gradients have been calculated

print(qvalues)
print(qvalues.grad)

# result of the print statemets

#tensor([[ 0.9677,  0.4303,  0.2036,  0.3870,  0.6085],
#    [ 0.8876,  0.8695,  0.2028,  0.3283,  0.1560],
#    [ 0.1764,  0.4718,  0.5418,  0.5167,  0.6200],
#    [ 0.7610,  0.9322,  0.5584,  0.5589,  0.8901],
#    [ 0.8146,  0.7296,  0.8036,  0.5277,  0.5754]])

#tensor([[ 0.0000,  0.8606,  0.0000,  0.7739,  0.0000],
#    [ 0.0000,  1.7390,  0.0000,  0.6567,  0.0000],
#    [ 0.0000,  0.9435,  0.0000,  1.0334,  0.0000],
#    [ 0.0000,  1.8645,  0.0000,  1.1178,  0.0000],
#    [ 0.0000,  1.4592,  0.0000,  1.0554,  0.0000]])

We can observe how the gradients have been computed only in the selected indexes. To be sure about it we create some fast test by comparing that the value of qvalues.grad for the selected slice is equal to the derivate 2 * new_qvalues.

assert torch.equal(qvalues.grad[:, y], 2 * new_qvalues)

And it does not throw any error, so I would assume that you can get the gradient of the slice.

Manuel Lagunas
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  • Thanks for this insightful answer. I was wondering if it is possible to use different disjoint slices of a tensor as input in different batches. The problem I am facing is that since the gradients are associated with the original tensor only (and not the slices), after the first slice is used in a batch, the results are freed and I get the error of doing backward twice: `RuntimeError: Trying to backward through the graph a second time, but the buffers have already been freed. Specify retain_graph=True when calling backward the first time.` – NotNotLogic Sep 27 '21 at 16:46
  • If I set the `retain_graph=True` as mentioned in the error, then I get another error: `RuntimeError: one of the variables needed for gradient computation has been modified by an inplace operation...` which is also due to different slices being used in different batches and backward being called. I don't know what is the proper way to do this. Please let me know if you have a solution/suggestion. I posted a question but it was closed, so I am not sure where to seek help. – NotNotLogic Sep 27 '21 at 16:54