So PyTorch is the new popular framework for deep learners and many new papers release code in PyTorch that one might want to inspect. Here is my understanding of it narrowed down to the most basics to help read PyTorch code. This is based on Justin Johnson’s great tutorial. If you want to learn more or have more than 10 minutes for a PyTorch starter go read that!
PyTorch consists of 4 main packages:
- torch: a general purpose array library similar to Numpy that can do computations on GPU when the tensor type is cast to (torch.cuda.TensorFloat)
- torch.autograd: a package for building a computational graph and automatically obtaining gradients
- torch.nn: a neural net library with common layers and cost functions
- torch.optim: an optimization package with common optimization algorithms like SGD,Adam, etc
0. import stuff
You can import PyTorch stuff like this:
import torch # arrays on GPU import torch.autograd as autograd #build a computational graph import torch.nn as nn ## neural net library import torch.nn.functional as F ## most non-linearities are here import torch.optim as optim # optimization package
1. the torch array replaces numpy ndarray ->provides linear algebra on GPU support
PyTorch provides a multi-dimensional array like Numpy array that can be processed on GPU when it’s data type is cast as (torch.cuda.TensorFloat). This array and it’s associated functions are general scientific computing tool.
confer Torch for numpy users for how it relates to numpy.
# 2 matrices of size 2x3 into a 3d tensor 2x2x3 d = [ [[1., 2.,3.], [4.,5.,6.]], [[7.,8.,9.], [11.,12.,13.]] ] d = torch.Tensor(d) # array from python list print "shape of the tensor:", d.size() # the first index is the depth z = d + d print "adding up the two matrices of the 3d tensor:",z
shape of the tensor: torch.Size([2, 2, 3]) adding up the two matrices of the 3d tensor: 8 10 12 15 17 19 [torch.FloatTensor of size 2x3]
# a heavily used operation is reshaping of tensors using .view() print d.view(2,-1) #-1 makes torch infer the second dim
1 2 3 4 5 6 7 8 9 11 12 13 [torch.FloatTensor of size 2x6]
2. torch.autograd can make a computational graph -> auto-compute gradients
The second feature is the autograd package that provides the ability to define a computational graph so that we can automatically compute gradients. In the computational graph, a node is an array and an edge is an operation on the array. To make a computational graph, we make a node by wrapping an array inside the torch.aurograd.Variable() function. All operations that we do on this node from then on will be defined as edges in the computational graph. The edges of the graph also result in new nodes in the computational graph. Each node in the graph has a .data property which is a multi-dimensional array and a .grad property which is it’s gradient with respect to some scalar value (.grad is also a .Variable() itself). After defining the computational graph, we can calculate gradients of the loss with respect to all nodes in the graph with a single command i.e. loss.backward().
- Convert a Tensor to a node in the computational graph using torch.autograd.Variable()
- access its value using x.data
- access its gradient using x.grad
- Do operations on the .Variable() to make edges of the graph
# d is a tensor not a node, to create a node based on it: x = autograd.Variable(d, requires_grad=True) print "the node's data is the tensor:", x.data.size() print "the node's gradient is empty at creation:", x.grad # the grad is empty right now
the node's data is the tensor: torch.Size([2, 2, 3]) the node's gradient is empty at creation: None
# do operation on the node to make a computational graph y = x + 1 z = x + y s = z.sum() print s.creator
<torch.autograd._functions.reduce.Sum object at 0x7f1e59988790>
# calculate gradients s.backward() print "the variable now has gradients:",x.grad
the variable now has gradients: Variable containing: (0 ,.,.) = 2 2 2 2 2 2 (1 ,.,.) = 2 2 2 2 2 2 [torch.FloatTensor of size 2x2x3]
3. torch.nn contains various NN layers (linear mappings of rows of a tensor) + (nonlinearities ) -> helps build a neural net computational graph without the hassle of manipulating tensors and parameters manually
The third feature is a high-level neural networks library torch.nn that abstracts away all parameter handling in layers of neural networks to make it easy to define a NN in a few commands (e.g. torch.nn.conv). This package also comes with a set of popular loss functions (e.g. torch.nn.MSEloss). We start with defining a model container, for example, a model with a sequence of layers using torch.nn.Sequential and then list the layers that we desire in a sequence. The library handles every thing else; we can access the parameter nodes Variable() using model.parameters()
# linear transformation of a 2x5 matrix into a 2x3 matrix linear_map = nn.Linear(5,3) print "using randomly initialized params:", linear_map.parameters
using randomly initialized params: <bound method Linear.parameters of Linear (5 -> 3)>
# data has 2 examples with 5 features and 3 target data = torch.randn(2,5) # training y = autograd.Variable(torch.randn(2,3)) # target # make a node x = autograd.Variable(data, requires_grad=True) # apply transformation to a node creates a computational graph a = linear_map(x) z = F.relu(a) o = F.softmax(z) print "output of softmax as a probability distribution:", o.data.view(1,-1) # loss function loss_func = nn.MSELoss() #instantiate loss function L=loss_func(z,y) # calculateMSE loss between output and target print "Loss:", L
output of softmax as a probability distribution: 0.2092 0.1979 0.5929 0.4343 0.3038 0.2619 [torch.FloatTensor of size 1x6] Loss: Variable containing: 2.9838 [torch.FloatTensor of size 1]
We can also define custom layers by sub-classing torch.nn.Module and implementing a forward() function that accepts a Variable() as input and produces a Variable() as output. We can even make a dynamic network by defining a layer that morphs in time!
- When defining a custom layer, 2 functions need to be implemented:
- __init__ function has to always be inherited first, then define parameters of the layer here as the class variables i.e. self.x
- forward funtion is where we pass an input through the layer, perform operations on inputs using parameters and return the output. The input needs to be an autograd.Variable() so that pytorch can build the computational graph of the layer.
class Log_reg_classifier(nn.Module): def __init__(self, in_size,out_size): super(Log_reg_classifier,self).__init__() #always call parent's init self.linear = nn.Linear(in_size, out_size) #layer parameters def forward(self,vect): return F.log_softmax(self.linear(vect)) #
4. torch.optim can do optimization -> we build a nn computational graph using torch.nn, compute gradients using torch.autograd, and then feed them into torch.optim to update network parameters
The forth feature is an optimization package torch.optim that works in tandem with the NN library. This library contains sophisticated optimizers like Adam, RMSprop, etc. We define an optimizer and pass network parameters and learning rate to it (i.e. opt=torch.optim.Adam(model.parameters(), lr=learning_rate)) and then we just call opt.step() to do a one-step update on our parameters.
optimizer = optim.SGD(linear_map.parameters(), lr = 1e-2) # instantiate optimizer with model params + learning rate # epoch loop: we run following until convergence optimizer.zero_grad() # make gradients zero L.backward(retain_variables = True) optimizer.step() print L
Variable containing: 2.9838 [torch.FloatTensor of size 1]
Building a neural net is easy. Here is an example showing how things work together:
# define model model = Log_reg_classifier(10,2) # define loss function loss_func = nn.MSELoss() # define optimizer optimizer = optim.SGD(model.parameters(),lr=1e-1) # send data through model in minibatches for 10 epochs for epoch in range(10): for minibatch, target in data: model.zero_grad() # pytorch accumulates gradients, making them zero for each minibatch #forward pass out = model(autograd.Variable(minibatch)) #backward pass L = loss_func(out,target) #calculate loss L.backward() # calculate gradients optimizer.step() # make an update step