Some operations do not support the Variables

There are some operations or function that do not support the variables, for example, the xor operation(^) which only support the tensor. What should I do if I want to use these operations on Variables. Thanks

Imagine you have c = xor(a, b).
What would be the gradient dc/da ?

Is that the reason why these operations do not support the variables?

If no gradients can be backpropagated, there is no reason to make them support Variables.
That is the main reason yes. That being said, there might be some operation that are (sub-)differentiable and don’t support Variables that are missing.

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