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# example from https://github.com/pytorch/examples/blob/master/vae/main.py
# commented and type annotated by Charl Botha <cpbotha@vxlabs.com>
import os
import torch
import torch.utils.data
from torch import nn, optim
from torch.autograd import Variable
from torch.nn import functional as F
from torchvision import datasets, transforms
from torchvision.utils import save_image
# changed configuration to this instead of argparse for easier interaction
CUDA = True
SEED = 1
BATCH_SIZE = 128
LOG_INTERVAL = 10
EPOCHS = 10
# connections through the autoencoder bottleneck
# in the pytorch VAE example, this is 20
ZDIMS = 20
# I do this so that the MNIST dataset is downloaded where I want it
os.chdir("/home/cpbotha/Downloads/pytorch-vae")
torch.manual_seed(SEED)
if CUDA:
torch.cuda.manual_seed(SEED)
# DataLoader instances will load tensors directly into GPU memory
kwargs = {'num_workers': 1, 'pin_memory': True} if CUDA else {}
# Download or load downloaded MNIST dataset
# shuffle data at every epoch
train_loader = torch.utils.data.DataLoader(
datasets.MNIST('data', train=True, download=True,
transform=transforms.ToTensor()),
batch_size=BATCH_SIZE, shuffle=True, **kwargs)
# Same for test data
test_loader = torch.utils.data.DataLoader(
datasets.MNIST('data', train=False, transform=transforms.ToTensor()),
batch_size=BATCH_SIZE, shuffle=True, **kwargs)
class VAE(nn.Module):
def __init__(self):
super(VAE, self).__init__()
# ENCODER
# 28 x 28 pixels = 784 input pixels, 400 outputs
self.fc1 = nn.Linear(784, 400)
# rectified linear unit layer from 400 to 400
# max(0, x)
self.relu = nn.ReLU()
self.fc21 = nn.Linear(400, ZDIMS) # mu layer
self.fc22 = nn.Linear(400, ZDIMS) # logvariance layer
# this last layer bottlenecks through ZDIMS connections
# DECODER
# from bottleneck to hidden 400
self.fc3 = nn.Linear(ZDIMS, 400)
# from hidden 400 to 784 outputs
self.fc4 = nn.Linear(400, 784)
self.sigmoid = nn.Sigmoid()
def encode(self, x: Variable) -> (Variable, Variable):
"""Input vector x -> fully connected 1 -> ReLU -> (fully connected
21, fully connected 22)
Parameters
----------
x : [128, 784] matrix; 128 digits of 28x28 pixels each
Returns
-------
(mu, logvar) : ZDIMS mean units one for each latent dimension, ZDIMS
variance units one for each latent dimension
"""
# h1 is [128, 400]
h1 = self.relu(self.fc1(x)) # type: Variable
return self.fc21(h1), self.fc22(h1)
def reparameterize(self, mu: Variable, logvar: Variable) -> Variable:
"""THE REPARAMETERIZATION IDEA:
For each training sample (we get 128 batched at a time)
- take the current learned mu, stddev for each of the ZDIMS
dimensions and draw a random sample from that distribution
- the whole network is trained so that these randomly drawn
samples decode to output that looks like the input
- which will mean that the std, mu will be learned
*distributions* that correctly encode the inputs
- due to the additional KLD term (see loss_function() below)
the distribution will tend to unit Gaussians
Parameters
----------
mu : [128, ZDIMS] mean matrix
logvar : [128, ZDIMS] variance matrix
Returns
-------
During training random sample from the learned ZDIMS-dimensional
normal distribution; during inference its mean.
"""
if self.training:
# multiply log variance with 0.5, then in-place exponent
# yielding the standard deviation
std = logvar.mul(0.5).exp_() # type: Variable
# - std.data is the [128,ZDIMS] tensor that is wrapped by std
# - so eps is [128,ZDIMS] with all elements drawn from a mean 0
# and stddev 1 normal distribution that is 128 samples
# of random ZDIMS-float vectors
eps = Variable(std.data.new(std.size()).normal_())
# - sample from a normal distribution with standard
# deviation = std and mean = mu by multiplying mean 0
# stddev 1 sample with desired std and mu, see
# https://stats.stackexchange.com/a/16338
# - so we have 128 sets (the batch) of random ZDIMS-float
# vectors sampled from normal distribution with learned
# std and mu for the current input
return eps.mul(std).add_(mu)
else:
# During inference, we simply spit out the mean of the
# learned distribution for the current input. We could
# use a random sample from the distribution, but mu of
# course has the highest probability.
return mu
def decode(self, z: Variable) -> Variable:
h3 = self.relu(self.fc3(z))
return self.sigmoid(self.fc4(h3))
def forward(self, x: Variable) -> (Variable, Variable, Variable):
mu, logvar = self.encode(x.view(-1, 784))
z = self.reparameterize(mu, logvar)
return self.decode(z), mu, logvar
model = VAE()
if CUDA:
model.cuda()
def loss_function(recon_x, x, mu, logvar) -> Variable:
# how well do input x and output recon_x agree?
BCE = F.binary_cross_entropy(recon_x, x.view(-1, 784))
# KLD is Kullback–Leibler divergence -- how much does one learned
# distribution deviate from another, in this specific case the
# learned distribution from the unit Gaussian
# see Appendix B from VAE paper:
# Kingma and Welling. Auto-Encoding Variational Bayes. ICLR, 2014
# https://arxiv.org/abs/1312.6114
# - D_{KL} = 0.5 * sum(1 + log(sigma^2) - mu^2 - sigma^2)
# note the negative D_{KL} in appendix B of the paper
KLD = -0.5 * torch.sum(1 + logvar - mu.pow(2) - logvar.exp())
# Normalise by same number of elements as in reconstruction
KLD /= BATCH_SIZE * 784
# BCE tries to make our reconstruction as accurate as possible
# KLD tries to push the distributions as close as possible to unit Gaussian
return BCE + KLD
# Dr Diederik Kingma: as if VAEs weren't enough, he also gave us Adam!
optimizer = optim.Adam(model.parameters(), lr=1e-3)
def train(epoch):
# toggle model to train mode
model.train()
train_loss = 0
# in the case of MNIST, len(train_loader.dataset) is 60000
# each `data` is of BATCH_SIZE samples and has shape [128, 1, 28, 28]
for batch_idx, (data, _) in enumerate(train_loader):
data = Variable(data)
if CUDA:
data = data.cuda()
optimizer.zero_grad()
# push whole batch of data through VAE.forward() to get recon_loss
recon_batch, mu, logvar = model(data)
# calculate scalar loss
loss = loss_function(recon_batch, data, mu, logvar)
# calculate the gradient of the loss w.r.t. the graph leaves
# i.e. input variables -- by the power of pytorch!
loss.backward()
train_loss += loss.data[0]
optimizer.step()
if batch_idx % LOG_INTERVAL == 0:
print('Train Epoch: {} [{}/{} ({:.0f}%)]\tLoss: {:.6f}'.format(
epoch, batch_idx * len(data), len(train_loader.dataset),
100. * batch_idx / len(train_loader),
loss.data[0] / len(data)))
print('====> Epoch: {} Average loss: {:.4f}'.format(
epoch, train_loss / len(train_loader.dataset)))
def test(epoch):
# toggle model to test / inference mode
model.eval()
test_loss = 0
# each data is of BATCH_SIZE (default 128) samples
for i, (data, _) in enumerate(test_loader):
if CUDA:
# make sure this lives on the GPU
data = data.cuda()
# we're only going to infer, so no autograd at all required: volatile=True
data = Variable(data, volatile=True)
recon_batch, mu, logvar = model(data)
test_loss += loss_function(recon_batch, data, mu, logvar).data[0]
if i == 0:
n = min(data.size(0), 8)
# for the first 128 batch of the epoch, show the first 8 input digits
# with right below them the reconstructed output digits
comparison = torch.cat([data[:n],
recon_batch.view(BATCH_SIZE, 1, 28, 28)[:n]])
save_image(comparison.data.cpu(),
'results/reconstruction_' + str(epoch) + '.png', nrow=n)
test_loss /= len(test_loader.dataset)
print('====> Test set loss: {:.4f}'.format(test_loss))
for epoch in range(1, EPOCHS + 1):
train(epoch)
test(epoch)
# 64 sets of random ZDIMS-float vectors, i.e. 64 locations / MNIST
# digits in latent space
sample = Variable(torch.randn(64, ZDIMS))
if CUDA:
sample = sample.cuda()
sample = model.decode(sample).cpu()
# save out as an 8x8 matrix of MNIST digits
# this will give you a visual idea of how well latent space can generate things
# that look like digits
save_image(sample.data.view(64, 1, 28, 28),
'results/sample_' + str(epoch) + '.png')
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