Chapter 35
Convolutional Neural Networks
NotebookPython 387 cells
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#hide
! [ -e /content ] && pip install -Uqq fastbook
import fastbook
fastbook.setup_book()In [ ]python · cell 2
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#hide
from fastai.vision.all import *
from fastbook import *
matplotlib.rc('image', cmap='Greys')Convolutional Neural Networks
The Magic of Convolutions
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top_edge = tensor([[-1,-1,-1],
[ 0, 0, 0],
[ 1, 1, 1]]).float()In [ ]python · cell 6
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path = untar_data(URLs.MNIST_SAMPLE)In [ ]python · cell 7
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#hide
Path.BASE_PATH = pathIn [ ]python · cell 8
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im3 = Image.open(path/'train'/'3'/'12.png')
show_image(im3);In [ ]python · cell 9
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im3_t = tensor(im3)
im3_t[0:3,0:3] * top_edgeIn [ ]python · cell 10
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(im3_t[0:3,0:3] * top_edge).sum()In [ ]python · cell 11
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df = pd.DataFrame(im3_t[:10,:20])
df.style.set_properties(**{'font-size':'6pt'}).background_gradient('Greys')In [ ]python · cell 12
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(im3_t[4:7,6:9] * top_edge).sum()In [ ]python · cell 13
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(im3_t[7:10,17:20] * top_edge).sum()In [ ]python · cell 14
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def apply_kernel(row, col, kernel):
return (im3_t[row-1:row+2,col-1:col+2] * kernel).sum()In [ ]python · cell 15
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apply_kernel(5,7,top_edge)Mapping a Convolution Kernel
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[[(i,j) for j in range(1,5)] for i in range(1,5)]In [ ]python · cell 18
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rng = range(1,27)
top_edge3 = tensor([[apply_kernel(i,j,top_edge) for j in rng] for i in rng])
show_image(top_edge3);In [ ]python · cell 19
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left_edge = tensor([[-1,1,0],
[-1,1,0],
[-1,1,0]]).float()
left_edge3 = tensor([[apply_kernel(i,j,left_edge) for j in rng] for i in rng])
show_image(left_edge3);Convolutions in PyTorch
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diag1_edge = tensor([[ 0,-1, 1],
[-1, 1, 0],
[ 1, 0, 0]]).float()
diag2_edge = tensor([[ 1,-1, 0],
[ 0, 1,-1],
[ 0, 0, 1]]).float()
edge_kernels = torch.stack([left_edge, top_edge, diag1_edge, diag2_edge])
edge_kernels.shapeIn [ ]python · cell 22
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mnist = DataBlock((ImageBlock(cls=PILImageBW), CategoryBlock),
get_items=get_image_files,
splitter=GrandparentSplitter(),
get_y=parent_label)
dls = mnist.dataloaders(path)
xb,yb = first(dls.valid)
xb.shapeIn [ ]python · cell 23
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xb,yb = to_cpu(xb),to_cpu(yb)In [ ]python · cell 24
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edge_kernels.shape,edge_kernels.unsqueeze(1).shapeIn [ ]python · cell 25
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edge_kernels = edge_kernels.unsqueeze(1)In [ ]python · cell 26
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batch_features = F.conv2d(xb, edge_kernels)
batch_features.shapeIn [ ]python · cell 27
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show_image(batch_features[0,0]);Strides and Padding
Understanding the Convolution Equations
Our First Convolutional Neural Network
Creating the CNN
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simple_net = nn.Sequential(
nn.Linear(28*28,30),
nn.ReLU(),
nn.Linear(30,1)
)In [ ]python · cell 33
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simple_netIn [ ]python · cell 34
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broken_cnn = sequential(
nn.Conv2d(1,30, kernel_size=3, padding=1),
nn.ReLU(),
nn.Conv2d(30,1, kernel_size=3, padding=1)
)In [ ]python · cell 35
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broken_cnn(xb).shapeIn [ ]python · cell 36
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def conv(ni, nf, ks=3, act=True):
res = nn.Conv2d(ni, nf, stride=2, kernel_size=ks, padding=ks//2)
if act: res = nn.Sequential(res, nn.ReLU())
return resIn [ ]python · cell 37
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simple_cnn = sequential(
conv(1 ,4), #14x14
conv(4 ,8), #7x7
conv(8 ,16), #4x4
conv(16,32), #2x2
conv(32,2, act=False), #1x1
Flatten(),
)In [ ]python · cell 38
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simple_cnn(xb).shapeIn [ ]python · cell 39
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learn = Learner(dls, simple_cnn, loss_func=F.cross_entropy, metrics=accuracy)In [ ]python · cell 40
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learn.summary()In [ ]python · cell 41
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learn.fit_one_cycle(2, 0.01)Understanding Convolution Arithmetic
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m = learn.model[0]
mIn [ ]python · cell 44
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m[0].weight.shapeIn [ ]python · cell 45
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m[0].bias.shapeReceptive Fields
A Note About Twitter
Color Images
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im = image2tensor(Image.open(image_bear()))
im.shapeIn [ ]python · cell 50
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show_image(im);In [ ]python · cell 51
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_,axs = subplots(1,3)
for bear,ax,color in zip(im,axs,('Reds','Greens','Blues')):
show_image(255-bear, ax=ax, cmap=color)Improving Training Stability
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path = untar_data(URLs.MNIST)In [ ]python · cell 54
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#hide
Path.BASE_PATH = pathIn [ ]python · cell 55
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path.ls()In [ ]python · cell 56
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def get_dls(bs=64):
return DataBlock(
blocks=(ImageBlock(cls=PILImageBW), CategoryBlock),
get_items=get_image_files,
splitter=GrandparentSplitter('training','testing'),
get_y=parent_label,
batch_tfms=Normalize()
).dataloaders(path, bs=bs)
dls = get_dls()In [ ]python · cell 57
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dls.show_batch(max_n=9, figsize=(4,4))A Simple Baseline
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def conv(ni, nf, ks=3, act=True):
res = nn.Conv2d(ni, nf, stride=2, kernel_size=ks, padding=ks//2)
if act: res = nn.Sequential(res, nn.ReLU())
return resIn [ ]python · cell 60
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def simple_cnn():
return sequential(
conv(1 ,8, ks=5), #14x14
conv(8 ,16), #7x7
conv(16,32), #4x4
conv(32,64), #2x2
conv(64,10, act=False), #1x1
Flatten(),
)In [ ]python · cell 61
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from fastai.callback.hook import *In [ ]python · cell 62
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def fit(epochs=1):
learn = Learner(dls, simple_cnn(), loss_func=F.cross_entropy,
metrics=accuracy, cbs=ActivationStats(with_hist=True))
learn.fit(epochs, 0.06)
return learnIn [ ]python · cell 63
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learn = fit()In [ ]python · cell 64
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learn.activation_stats.plot_layer_stats(0)In [ ]python · cell 65
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learn.activation_stats.plot_layer_stats(-2)Increase Batch Size
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dls = get_dls(512)In [ ]python · cell 68
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learn = fit()In [ ]python · cell 69
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learn.activation_stats.plot_layer_stats(-2)1cycle Training
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def fit(epochs=1, lr=0.06):
learn = Learner(dls, simple_cnn(), loss_func=F.cross_entropy,
metrics=accuracy, cbs=ActivationStats(with_hist=True))
learn.fit_one_cycle(epochs, lr)
return learnIn [ ]python · cell 72
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learn = fit()In [ ]python · cell 73
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learn.recorder.plot_sched()In [ ]python · cell 74
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learn.activation_stats.plot_layer_stats(-2)In [ ]python · cell 75
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learn.activation_stats.color_dim(-2)In [ ]python · cell 76
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learn.activation_stats.color_dim(-2)Batch Normalization
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def conv(ni, nf, ks=3, act=True):
layers = [nn.Conv2d(ni, nf, stride=2, kernel_size=ks, padding=ks//2)]
if act: layers.append(nn.ReLU())
layers.append(nn.BatchNorm2d(nf))
return nn.Sequential(*layers)In [ ]python · cell 79
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learn = fit()In [ ]python · cell 80
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learn.activation_stats.color_dim(-4)In [ ]python · cell 81
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learn = fit(5, lr=0.1)Conclusions
Questionnaire
- What is a "feature"?
- Write out the convolutional kernel matrix for a top edge detector.
- Write out the mathematical operation applied by a 3×3 kernel to a single pixel in an image.
- What is the value of a convolutional kernel apply to a 3×3 matrix of zeros?
- What is "padding"?
- What is "stride"?
- Create a nested list comprehension to complete any task that you choose.
- What are the shapes of the
inputandweightparameters to PyTorch's 2D convolution? - What is a "channel"?
- What is the relationship between a convolution and a matrix multiplication?
- What is a "convolutional neural network"?
- What is the benefit of refactoring parts of your neural network definition?
- What is
Flatten? Where does it need to be included in the MNIST CNN? Why? - What does "NCHW" mean?
- Why does the third layer of the MNIST CNN have
7*7*(1168-16)multiplications? - What is a "receptive field"?
- What is the size of the receptive field of an activation after two stride 2 convolutions? Why?
- Run conv-example.xlsx yourself and experiment with trace precedents.
- Have a look at Jeremy or Sylvain's list of recent Twitter "like"s, and see if you find any interesting resources or ideas there.
- How is a color image represented as a tensor?
- How does a convolution work with a color input?
- What method can we use to see that data in
DataLoaders? - Why do we double the number of filters after each stride-2 conv?
- Why do we use a larger kernel in the first conv with MNIST (with
simple_cnn)? - What information does
ActivationStatssave for each layer? - How can we access a learner's callback after training?
- What are the three statistics plotted by
plot_layer_stats? What does the x-axis represent? - Why are activations near zero problematic?
- What are the upsides and downsides of training with a larger batch size?
- Why should we avoid using a high learning rate at the start of training?
- What is 1cycle training?
- What are the benefits of training with a high learning rate?
- Why do we want to use a low learning rate at the end of training?
- What is "cyclical momentum"?
- What callback tracks hyperparameter values during training (along with other information)?
- What does one column of pixels in the
color_dimplot represent? - What does "bad training" look like in
color_dim? Why? - What trainable parameters does a batch normalization layer contain?
- What statistics are used to normalize in batch normalization during training? How about during validation?
- Why do models with batch normalization layers generalize better?
Further Research
- What features other than edge detectors have been used in computer vision (especially before deep learning became popular)?
- There are other normalization layers available in PyTorch. Try them out and see what works best. Learn about why other normalization layers have been developed, and how they differ from batch normalization.
- Try moving the activation function after the batch normalization layer in
conv. Does it make a difference? See what you can find out about what order is recommended, and why.
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