Introduction to PyTorch¶
Introduction to Torch’s tensor library¶
All of deep learning is computations on tensors, which are generalizations of a matrix that can be indexed in more than 2 dimensions. We will see exactly what this means in-depth later. First, lets look what we can do with tensors.
# Author: Robert Guthrie import torch import torch.autograd as autograd import torch.nn as nn import torch.nn.functional as F import torch.optim as optim torch.manual_seed(1)
Tensors can be created from Python lists with the torch.Tensor() function.
# Create a torch.Tensor object with the given data. It is a 1D vector V_data = [1., 2., 3.] V = torch.Tensor(V_data) print(V) # Creates a matrix M_data = [[1., 2., 3.], [4., 5., 6]] M = torch.Tensor(M_data) print(M) # Create a 3D tensor of size 2x2x2. T_data = [[[1., 2.], [3., 4.]], [[5., 6.], [7., 8.]]] T = torch.Tensor(T_data) print(T)
1 2 3 [torch.FloatTensor of size 3] 1 2 3 4 5 6 [torch.FloatTensor of size 2x3] (0 ,.,.) = 1 2 3 4 (1 ,.,.) = 5 6 7 8 [torch.FloatTensor of size 2x2x2]
What is a 3D tensor anyway? Think about it like this. If you have a vector, indexing into the vector gives you a scalar. If you have a matrix, indexing into the matrix gives you a vector. If you have a 3D tensor, then indexing into the tensor gives you a matrix!
A note on terminology: when I say “tensor” in this tutorial, it refers to any torch.Tensor object. Matrices and vectors are special cases of torch.Tensors, where their dimension is 1 and 2 respectively. When I am talking about 3D tensors, I will explicitly use the term “3D tensor”.
# Index into V and get a scalar print(V) # Index into M and get a vector print(M) # Index into T and get a matrix print(T)
1.0 1 2 3 [torch.FloatTensor of size 3] 1 2 3 4 [torch.FloatTensor of size 2x2]
You can also create tensors of other datatypes. The default, as you can see, is Float. To create a tensor of integer types, try torch.LongTensor(). Check the documentation for more data types, but Float and Long will be the most common.
You can create a tensor with random data and the supplied dimensionality with torch.randn()
x = torch.randn((3, 4, 5)) print(x)
(0 ,.,.) = 0.6614 0.2669 0.0617 0.6213 -0.4519 -0.1661 -1.5228 0.3817 -1.0276 -0.5631 -0.8923 -0.0583 -0.1955 -0.9656 0.4224 0.2673 -0.4212 -0.5107 -1.5727 -0.1232 (1 ,.,.) = 3.5870 -1.8313 1.5987 -1.2770 0.3255 -0.4791 1.3790 2.5286 0.4107 -0.9880 -0.9081 0.5423 0.1103 -2.2590 0.6067 -0.1383 0.8310 -0.2477 -0.8029 0.2366 (2 ,.,.) = 0.2857 0.6898 -0.6331 0.8795 -0.6842 0.4533 0.2912 -0.8317 -0.5525 0.6355 -0.3968 -0.6571 -1.6428 0.9803 -0.0421 -0.8206 0.3133 -1.1352 0.3773 -0.2824 [torch.FloatTensor of size 3x4x5]
Operations with Tensors¶
You can operate on tensors in the ways you would expect.
x = torch.Tensor([1., 2., 3.]) y = torch.Tensor([4., 5., 6.]) z = x + y print(z)
5 7 9 [torch.FloatTensor of size 3]
See the documentation for a complete list of the massive number of operations available to you. They expand beyond just mathematical operations.
One helpful operation that we will make use of later is concatenation.
# By default, it concatenates along the first axis (concatenates rows) x_1 = torch.randn(2, 5) y_1 = torch.randn(3, 5) z_1 = torch.cat([x_1, y_1]) print(z_1) # Concatenate columns: x_2 = torch.randn(2, 3) y_2 = torch.randn(2, 5) # second arg specifies which axis to concat along z_2 = torch.cat([x_2, y_2], 1) print(z_2) # If your tensors are not compatible, torch will complain. Uncomment to see the error # torch.cat([x_1, x_2])
-2.5667 -1.4303 0.5009 0.5438 -0.4057 1.1341 -1.1115 0.3501 -0.7703 -0.1473 0.6272 1.0935 0.0939 1.2381 -1.3459 0.5119 -0.6933 -0.1668 -0.9999 -1.6476 0.8098 0.0554 1.1340 -0.5326 0.6592 [torch.FloatTensor of size 5x5] -1.5964 -0.3769 -3.1020 -0.0020 -1.0952 0.6016 0.6984 -0.8005 -0.0995 -0.7213 1.2708 1.5381 1.4673 1.5951 -1.5279 1.0156 [torch.FloatTensor of size 2x8]
Use the .view() method to reshape a tensor. This method receives heavy use, because many neural network components expect their inputs to have a certain shape. Often you will need to reshape before passing your data to the component.
x = torch.randn(2, 3, 4) print(x) print(x.view(2, 12)) # Reshape to 2 rows, 12 columns # Same as above. If one of the dimensions is -1, its size can be inferred print(x.view(2, -1))
(0 ,.,.) = -0.2020 -1.2865 0.8231 -0.6101 -1.2960 -0.9434 0.6684 1.1628 -0.3229 1.8782 -0.5666 0.4016 (1 ,.,.) = -0.1153 0.3170 0.5629 0.8662 -0.3528 0.3482 1.1371 -0.3339 -1.4724 0.7296 -0.1312 -0.6368 [torch.FloatTensor of size 2x3x4] Columns 0 to 9 -0.2020 -1.2865 0.8231 -0.6101 -1.2960 -0.9434 0.6684 1.1628 -0.3229 1.8782 -0.1153 0.3170 0.5629 0.8662 -0.3528 0.3482 1.1371 -0.3339 -1.4724 0.7296 Columns 10 to 11 -0.5666 0.4016 -0.1312 -0.6368 [torch.FloatTensor of size 2x12] Columns 0 to 9 -0.2020 -1.2865 0.8231 -0.6101 -1.2960 -0.9434 0.6684 1.1628 -0.3229 1.8782 -0.1153 0.3170 0.5629 0.8662 -0.3528 0.3482 1.1371 -0.3339 -1.4724 0.7296 Columns 10 to 11 -0.5666 0.4016 -0.1312 -0.6368 [torch.FloatTensor of size 2x12]
Computation Graphs and Automatic Differentiation¶
The concept of a computation graph is essential to efficient deep learning programming, because it allows you to not have to write the back propagation gradients yourself. A computation graph is simply a specification of how your data is combined to give you the output. Since the graph totally specifies what parameters were involved with which operations, it contains enough information to compute derivatives. This probably sounds vague, so lets see what is going on using the fundamental class of Pytorch: autograd.Variable.
First, think from a programmers perspective. What is stored in the torch.Tensor objects we were creating above? Obviously the data and the shape, and maybe a few other things. But when we added two tensors together, we got an output tensor. All this output tensor knows is its data and shape. It has no idea that it was the sum of two other tensors (it could have been read in from a file, it could be the result of some other operation, etc.)
The Variable class keeps track of how it was created. Lets see it in action.
# Variables wrap tensor objects x = autograd.Variable(torch.Tensor([1., 2., 3]), requires_grad=True) # You can access the data with the .data attribute print(x.data) # You can also do all the same operations you did with tensors with Variables. y = autograd.Variable(torch.Tensor([4., 5., 6]), requires_grad=True) z = x + y print(z.data) # BUT z knows something extra. print(z.grad_fn)
1 2 3 [torch.FloatTensor of size 3] 5 7 9 [torch.FloatTensor of size 3] <AddBackward1 object at 0x7f8e6ccb1080>
So Variables know what created them. z knows that it wasn’t read in from a file, it wasn’t the result of a multiplication or exponential or whatever. And if you keep following z.grad_fn, you will find yourself at x and y.
But how does that help us compute a gradient?
# Lets sum up all the entries in z s = z.sum() print(s) print(s.grad_fn)
Variable containing: 21 [torch.FloatTensor of size 1] <SumBackward0 object at 0x7f8e6cc96780>
So now, what is the derivative of this sum with respect to the first component of x? In math, we want
Well, s knows that it was created as a sum of the tensor z. z knows that it was the sum x + y. So
And so s contains enough information to determine that the derivative we want is 1!
Of course this glosses over the challenge of how to actually compute that derivative. The point here is that s is carrying along enough information that it is possible to compute it. In reality, the developers of Pytorch program the sum() and + operations to know how to compute their gradients, and run the back propagation algorithm. An in-depth discussion of that algorithm is beyond the scope of this tutorial.
Lets have Pytorch compute the gradient, and see that we were right: (note if you run this block multiple times, the gradient will increment. That is because Pytorch accumulates the gradient into the .grad property, since for many models this is very convenient.)
# calling .backward() on any variable will run backprop, starting from it. s.backward() print(x.grad)
Variable containing: 1 1 1 [torch.FloatTensor of size 3]
Understanding what is going on in the block below is crucial for being a successful programmer in deep learning.
x = torch.randn((2, 2)) y = torch.randn((2, 2)) z = x + y # These are Tensor types, and backprop would not be possible var_x = autograd.Variable(x, requires_grad=True) var_y = autograd.Variable(y, requires_grad=True) # var_z contains enough information to compute gradients, as we saw above var_z = var_x + var_y print(var_z.grad_fn) var_z_data = var_z.data # Get the wrapped Tensor object out of var_z... # Re-wrap the tensor in a new variable new_var_z = autograd.Variable(var_z_data) # ... does new_var_z have information to backprop to x and y? # NO! print(new_var_z.grad_fn) # And how could it? We yanked the tensor out of var_z (that is # what var_z.data is). This tensor doesn't know anything about # how it was computed. We pass it into new_var_z, and this is all the # information new_var_z gets. If var_z_data doesn't know how it was # computed, theres no way new_var_z will. # In essence, we have broken the variable away from its past history
<AddBackward1 object at 0x7f8e6cd28320> None
Here is the basic, extremely important rule for computing with autograd.Variables (note this is more general than Pytorch. There is an equivalent object in every major deep learning toolkit):
If you want the error from your loss function to backpropagate to a component of your network, you MUST NOT break the Variable chain from that component to your loss Variable. If you do, the loss will have no idea your component exists, and its parameters can’t be updated.
I say this in bold, because this error can creep up on you in very subtle ways (I will show some such ways below), and it will not cause your code to crash or complain, so you must be careful.
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