%matplotlib inline
Central to all neural networks in PyTorch is the autograd package.
Let’s first briefly visit this, and we will then go to training our
first neural network.
The autograd package provides automatic differentiation for all operations
on Tensors. It is a define-by-run framework, which means that your backprop is
defined by how your code is run, and that every single iteration can be
different.
Let us see this in more simple terms with some examples.
torch.Tensor is the central class of the package. If you set its attribute
.requires_grad as True, it starts to track all operations on it. When
you finish your computation you can call .backward() and have all the
gradients computed automatically. The gradient for this tensor will be
accumulated into .grad attribute.
To stop a tensor from tracking history, you can call .detach() to detach
it from the computation history, and to prevent future computation from being
tracked.
To prevent tracking history (and using memory), you can also wrap the code block
in with torch.no_grad():. This can be particularly helpful when evaluating a
model because the model may have trainable parameters with requires_grad=True,
but we don't need the gradients.
There’s one more class which is very important for autograd
implementation - a Function.
Tensor 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
the Tensor (except for Tensors created by the user - their
grad_fn is None).
If you want to compute the derivatives, you can call .backward() on
a Tensor. If Tensor is a scalar (i.e. it holds a one element
data), you don’t need to specify any arguments to backward(),
however if it has more elements, you need to specify a gradient
argument that is a tensor of matching shape.
import torch
Create a tensor and set requires_grad=True to track computation with it
x = torch.ones(2, 2, requires_grad=True)
print(x)
Do an operation of tensor:
y = x + 2
print(y)
y was created as a result of an operation, so it has a grad_fn.
print(y.grad_fn)
Do more operations on y
z = y * y * 3
out = z.mean()
print(z, out)
.requires_grad_( ... ) changes an existing Tensor's requires_grad
flag in-place. The input flag defaults to True if not given.
a = torch.randn(2, 2)
a = ((a * 3) / (a - 1))
print(a.requires_grad)
a.requires_grad = True
print(a.requires_grad)
b = (a * a).sum()
print(a, a*a)
print(b.grad_fn)
Let's backprop now
Because out contains a single scalar, out.backward() is
equivalent to out.backward(torch.tensor(1)).
out.backward()
print gradients d(out)/dx
print(x.grad)
You should have got a matrix of 4.5. Let’s call the out
Tensor “$o$”.
We have that $o = \frac{1}{4}\sum_i z_i$,
$z_i = 3(x_i+2)^2$ and $z_i\bigr\rvert_{x_i=1} = 27$.
Therefore,
$\frac{\partial o}{\partial x_i} = \frac{3}{2}(x_i+2)$, hence
$\frac{\partial o}{\partial x_i}\bigr\rvert_{x_i=1} = \frac{9}{2} = 4.5$.
You can do many crazy things with autograd!
x = torch.randn(3, requires_grad=True)
y = x * 2
while y.data.norm() < 1000:
y = y * 2
print(y)
gradients = torch.tensor([0.1, 1.0, 0.0001], dtype=torch.float)
y.backward(gradients)
print(x.grad)
You can also stops autograd from tracking history on Tensors
with requires_grad=True by wrapping the code block in
with torch.no_grad():
print(x.requires_grad)
print((x ** 2).requires_grad)
with torch.no_grad():
print((x ** 2).requires_grad)
Read Later:
Documentation of autograd and Function is at
http://pytorch.org/docs/autograd