# Autograd¶

Autograd is now a core torch package for automatic differentiation. It uses a tape based system for automatic differentiation.

In the forward phase, the autograd tape will remember all the operations it executed, and in the backward phase, it will replay the operations.

## Variable¶

In autograd, we introduce a `Variable`

class, which is a very thin
wrapper around a `Tensor`

. You can access the raw tensor through the
`.data`

attribute, and after computing the backward pass, a gradient
w.r.t. this variable is accumulated into `.grad`

attribute.

There’s one more class which is very important for autograd
implementation - a `Function`

. `Variable`

and `Function`

are
interconnected and build up an acyclic graph, that encodes a complete
history of computation. Each variable has a `.grad_fn`

attribute that
references a function that has created a function (except for Variables
created by the user - these have `None`

as `.grad_fn`

).

If you want to compute the derivatives, you can call `.backward()`

on
a `Variable`

. If `Variable`

is a scalar (i.e. it holds a one element
tensor), you don’t need to specify any arguments to `backward()`

,
however if it has more elements, you need to specify a `grad_output`

argument that is a tensor of matching shape.

```
import torch
from torch.autograd import Variable
x = Variable(torch.ones(2, 2), requires_grad=True)
print(x) # notice the "Variable containing" line
```

Out:

```
Variable containing:
1 1
1 1
[torch.FloatTensor of size 2x2]
```

```
print(x.data)
```

Out:

```
1 1
1 1
[torch.FloatTensor of size 2x2]
```

```
print(x.grad)
```

Out:

```
None
```

```
print(x.grad_fn) # we've created x ourselves
```

Out:

```
None
```

Do an operation of x:

```
y = x + 2
print(y)
```

Out:

```
Variable containing:
3 3
3 3
[torch.FloatTensor of size 2x2]
```

y was created as a result of an operation, so it has a grad_fn

```
print(y.grad_fn)
```

Out:

```
<AddBackward0 object at 0x7f8e6cdc2f28>
```

More operations on y:

```
z = y * y * 3
out = z.mean()
print(z, out)
```

Out:

```
Variable containing:
27 27
27 27
[torch.FloatTensor of size 2x2]
Variable containing:
27
[torch.FloatTensor of size 1]
```

## Gradients¶

let’s backprop now and print gradients d(out)/dx

```
out.backward()
print(x.grad)
```

Out:

```
Variable containing:
4.5000 4.5000
4.5000 4.5000
[torch.FloatTensor of size 2x2]
```

By default, gradient computation flushes all the internal buffers
contained in the graph, so if you even want to do the backward on some
part of the graph twice, you need to pass in `retain_variables = True`

during the first pass.

```
x = Variable(torch.ones(2, 2), requires_grad=True)
y = x + 2
y.backward(torch.ones(2, 2), retain_graph=True)
# the retain_variables flag will prevent the internal buffers from being freed
print(x.grad)
```

Out:

```
Variable containing:
1 1
1 1
[torch.FloatTensor of size 2x2]
```

```
z = y * y
print(z)
```

Out:

```
Variable containing:
9 9
9 9
[torch.FloatTensor of size 2x2]
```

just backprop random gradients

```
gradient = torch.randn(2, 2)
# this would fail if we didn't specify
# that we want to retain variables
y.backward(gradient)
print(x.grad)
```

Out:

```
Variable containing:
0.6218 -0.5263
1.4369 1.2310
[torch.FloatTensor of size 2x2]
```

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