Autograd

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.

Tensors that track history

In autograd, if any input Tensor of an operation has requires_grad=True, the computation will be tracked. After computing the backward pass, a gradient w.r.t. this tensor is accumulated into .gradattribute.

There’s one more class which is very important for autograd implementation - a Function. Tensorand 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 Tensors created by the user - these have None as .grad_fn).

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 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

Create a tensor and set requires_grad=True to track computation with it

x = torch.ones(2, 2, requires_grad=True)
print(x)

Out:

tensor([[1., 1.],
        [1., 1.]], requires_grad=True)

print(x.data)

Out:

tensor([[1., 1.],
        [1., 1.]])

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:

tensor([[3., 3.],
        [3., 3.]], grad_fn=)

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

print(y.grad_fn)

Out:

More operations on y:

z = y * y * 3
out = z.mean()

print(z, out)

Out:

tensor([[27., 27.],
        [27., 27.]], grad_fn=) tensor(27., grad_fn=)

.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(b.grad_fn)

Out:

False
True

Gradients

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

out.backward()
print(x.grad)

Out:

tensor([[4.5000, 4.5000],
        [4.5000, 4.5000]])

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 = 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:

tensor([[1., 1.],
        [1., 1.]])

z = y * y
print(z)

Out:

tensor([[9., 9.],
        [9., 9.]], grad_fn=)

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:

tensor([[ 0.8181,  1.6773],
        [ 1.6309, -0.5167]])

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)

Out:

True
True
False

 

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