# Why do we need to pass the gradient parameter to the backward function in PyTorch?

**URL:** <https://discuss.pytorch.org/t/why-do-we-need-to-pass-the-gradient-parameter-to-the-backward-function-in-pytorch/116079>\
**Category:** autograd\
**Created:** [March 26, 2021, 1:47pm UTC](https://discuss.pytorch.org/t/why-do-we-need-to-pass-the-gradient-parameter-to-the-backward-function-in-pytorch/116079 "2021-03-26T13:47:01Z")\
**Posts on this page:** 5\
**Page:** 1

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**Author:** ![AbishekBashyal](https://discuss.pytorch.org/user_avatar/discuss.pytorch.org/abishekbashyal/32/36315_2.png) [@AbishekBashyal](https://discuss.pytorch.org/u/AbishekBashyal)\
**Post date:** [March 26, 2021, 1:47pm UTC](https://discuss.pytorch.org/t/why-do-we-need-to-pass-the-gradient-parameter-to-the-backward-function-in-pytorch/116079/1 "2021-03-26T13:47:01Z")

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According to the docs, when we call the backward function to the tensor if the tensor is non-scalar (i.e. its data has more than one element) and requires gradient, the function additionally requires specifying **gradient**.

```auto
import torch
a = torch.tensor([10.,10.],requires_grad=True)
b = torch.tensor([20.,20.],requires_grad=True)

F = a * b
F.backward(gradient=torch.tensor([1.,1.])) 

print(a.grad)

```

`Output: tensor([20., 20.])`

Now scaling the external gradient:

```auto
a = torch.tensor([10.,10.],requires_grad=True)
b = torch.tensor([20.,20.],requires_grad=True)

F = a * b
F.backward(gradient=torch.tensor([2.,2.])) #modified

print(a.grad)

```

`Output: tensor([40., 40.])`

So, passing the gradient argument to backward seems to scale the gradients.  
Also, by default `F.backward()` is `F.backward(gradient=torch.Tensor([1.]))`

Apart from scaling the grad value how does the `gradient` parameter passed to the backward function helps to compute the derivatives when we have a non-scalar tensor?  
Why can’t PyTorch calculate the derivative implicitly without asking explicit gradient parameter as it did for the scalar-tensor?

Also, In the case of scalar value, `.backward()` w/o parameters is equivalent to `.backward(torch.tensor(1.0))` then why can’t we use broadcasting of `torch.tensor(1.0)` so that it works for not-scalar inputs also instead of explicitly having to pass external `gradient` parameter while calculating the vector Jacobian product?

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**Author:** ![AlphaBetaGamma96](https://discuss.pytorch.org/letter_avatar_proxy/v4/letter/a/3da27b/32.png) [@AlphaBetaGamma96](https://discuss.pytorch.org/u/AlphaBetaGamma96)\
**Post date:** [March 26, 2021, 1:56pm UTC](https://discuss.pytorch.org/t/why-do-we-need-to-pass-the-gradient-parameter-to-the-backward-function-in-pytorch/116079/2 "2021-03-26T13:56:53Z")

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I’m pretty sure when you do something like `y.backward(torch.ones_like(y))` you’re just telling autograd to repeat `.backward()` for each element in `y` under the hood.

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**Author:** ![AbishekBashyal](https://discuss.pytorch.org/user_avatar/discuss.pytorch.org/abishekbashyal/32/36315_2.png) [@AbishekBashyal](https://discuss.pytorch.org/u/AbishekBashyal)\
**Post date:** [March 26, 2021, 2:13pm UTC](https://discuss.pytorch.org/t/why-do-we-need-to-pass-the-gradient-parameter-to-the-backward-function-in-pytorch/116079/3 "2021-03-26T14:13:17Z")

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@AlphaBetaGamma96 can you share some resources showing that describes:

> `y.backward(torch.ones_like(y))` is telling autograd to repeat `.backward()` for each element in `y` under the hood.

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**Author:** ![albanD](https://discuss.pytorch.org/user_avatar/discuss.pytorch.org/alband/32/215_2.png) [@albanD](https://discuss.pytorch.org/u/albanD)\
**Post date:** [March 26, 2021, 2:58pm UTC](https://discuss.pytorch.org/t/why-do-we-need-to-pass-the-gradient-parameter-to-the-backward-function-in-pytorch/116079/4 "2021-03-26T14:58:59Z")

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Hi,

If you consider a function f that has n\_input and n\_output. And a Jacobian matrix containing all its partial derivatives J\_f of size (n\_output x n\_input).  
Then what backpropagation (or AD whichever way you want to name it) does is to compute `v^T J_f` for a given `v`.  
If your function has a single output, then it makes sense to take `v = 1.` so that backprop will return `J_f`.  
But if you have multiple outputs, there is no good default and so we requirethe user to provide the `v` value they want.

If you want to reconstruct the full J\_f, you will have to do as many backwards as there are outputs in your function. You can use the autograd.functional.jacobian function if you need that.

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**Author:** ![AbishekBashyal](https://discuss.pytorch.org/user_avatar/discuss.pytorch.org/abishekbashyal/32/36315_2.png) [@AbishekBashyal](https://discuss.pytorch.org/u/AbishekBashyal)\
**Post date:** [March 26, 2021, 3:22pm UTC](https://discuss.pytorch.org/t/why-do-we-need-to-pass-the-gradient-parameter-to-the-backward-function-in-pytorch/116079/6 "2021-03-26T15:22:06Z")

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@albanD thanks, its clear now :D.