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Lecture 5 Smaller Network: CNN
 We know it is good to learn a small model.
 From this fully connected model, do we really need all
the edges?
 Can some of these be shared?
Consider learning an image:
Some patterns are much smaller than
the whole image
“beak” detector
Can represent a small region with fewer parameters
Same pattern appears in different places:
They can be compressed!
What about training a lot of such “small” detectors
and each detector must “move around”.
“upper-left
beak” detector
“middle beak”
detector
They can be compressed
to the same parameters.
A convolutional layer
A filter
A CNN is a neural network with some convolutional layers
(and some other layers). A convolutional layer has a number
of filters that does convolutional operation.
Beak detector
Convolution
1 0 0 0 0 1
0 1 0 0 1 0
0 0 1 1 0 0
1 0 0 0 1 0
0 1 0 0 1 0
0 0 1 0 1 0
6 x 6 image
1 -1 -1
-1 1 -1
-1 -1 1
Filter 1
-1 1 -1
-1 1 -1
-1 1 -1
Filter 2
…
…
These are the network
parameters to be learned.
Each filter detects a
small pattern (3 x 3).
Convolution
1 0 0 0 0 1
0 1 0 0 1 0
0 0 1 1 0 0
1 0 0 0 1 0
0 1 0 0 1 0
0 0 1 0 1 0
6 x 6 image
1 -1 -1
-1 1 -1
-1 -1 1
Filter 1
3 -1
stride=1
Dot
product
Convolution
1 0 0 0 0 1
0 1 0 0 1 0
0 0 1 1 0 0
1 0 0 0 1 0
0 1 0 0 1 0
0 0 1 0 1 0
6 x 6 image
1 -1 -1
-1 1 -1
-1 -1 1
Filter 1
3 -3
If stride=2
Convolution
1 0 0 0 0 1
0 1 0 0 1 0
0 0 1 1 0 0
1 0 0 0 1 0
0 1 0 0 1 0
0 0 1 0 1 0
6 x 6 image
1 -1 -1
-1 1 -1
-1 -1 1
Filter 1
3 -1 -3 -1
-3 1 0 -3
-3 -3 0 1
3 -2 -2 -1
stride=1
Convolution
1 0 0 0 0 1
0 1 0 0 1 0
0 0 1 1 0 0
1 0 0 0 1 0
0 1 0 0 1 0
0 0 1 0 1 0
6 x 6 image
3 -1 -3 -1
-3 1 0 -3
-3 -3 0 1
3 -2 -2 -1
-1 1 -1
-1 1 -1
-1 1 -1
Filter 2
-1 -1 -1 -1
-1 -1 -2 1
-1 -1 -2 1
-1 0 -4 3
Repeat this for each filter
stride=1
Two 4 x 4 images
Forming 2 x 4 x 4 matrix
Feature
Map
Color image: RGB 3 channels
1 0 0 0 0 1
0 1 0 0 1 0
0 0 1 1 0 0
1 0 0 0 1 0
0 1 0 0 1 0
0 0 1 0 1 0
1 0 0 0 0 1
0 1 0 0 1 0
0 0 1 1 0 0
1 0 0 0 1 0
0 1 0 0 1 0
0 0 1 0 1 0
1 0 0 0 0 1
0 1 0 0 1 0
0 0 1 1 0 0
1 0 0 0 1 0
0 1 0 0 1 0
0 0 1 0 1 0
1 -1 -1
-1 1 -1
-1 -1 1
Filter 1
-1 1 -1
-1 1 -1
-1 1 -1
Filter 2
1 -1 -1
-1 1 -1
-1 -1 1
1 -1 -1
-1 1 -1
-1 -1 1
-1 1 -1
-1 1 -1
-1 1 -1
-1 1 -1
-1 1 -1
-1 1 -1
Color image
1 0 0 0 0 1
0 1 0 0 1 0
0 0 1 1 0 0
1 0 0 0 1 0
0 1 0 0 1 0
0 0 1 0 1 0
image
convolution
-1 1 -1
-1 1 -1
-1 1 -1
1 -1 -1
-1 1 -1
-1 -1 1
1
x
2
x
…
…
36
x
…
…
1 0 0 0 0 1
0 1 0 0 1 0
0 0 1 1 0 0
1 0 0 0 1 0
0 1 0 0 1 0
0 0 1 0 1 0
Convolution v.s. Fully Connected
Fully-
connected
1 0 0 0 0 1
0 1 0 0 1 0
0 0 1 1 0 0
1 0 0 0 1 0
0 1 0 0 1 0
0 0 1 0 1 0
6 x 6 image
1 -1 -1
-1 1 -1
-1 -1 1
Filter 1
1
2
3
…
8
9
…
1
3
14
15
… Only connect to
9 inputs, not
fully connected
4:
10:
16
1
0
0
0
0
1
0
0
0
0
1
1
3
fewer parameters!
1 0 0 0 0 1
0 1 0 0 1 0
0 0 1 1 0 0
1 0 0 0 1 0
0 1 0 0 1 0
0 0 1 0 1 0
1 -1 -1
-1 1 -1
-1 -1 1
Filter 1
1:
2:
3:
…
7:
8:
9:
…
1
3:
14:
15:
…
4:
10:
16:
1
0
0
0
0
1
0
0
0
0
1
1
3
-1
Shared weights
6 x 6 image
Fewer parameters
Even fewer parameters
The whole CNN
Fully Connected
Feedforward network
cat dog ……
Convolution
Max Pooling
Convolution
Max Pooling
Flattened
Can
repeat
many
times
Max Pooling
3 -1 -3 -1
-3 1 0 -3
-3 -3 0 1
3 -2 -2 -1
-1 1 -1
-1 1 -1
-1 1 -1
Filter 2
-1 -1 -1 -1
-1 -1 -2 1
-1 -1 -2 1
-1 0 -4 3
1 -1 -1
-1 1 -1
-1 -1 1
Filter 1
Why Pooling
 Subsampling pixels will not change the object
Subsampling
bird
bird
We can subsample the pixels to make image
smaller fewer parameters to characterize the image
A CNN compresses a fully connected
network in two ways:
Reducing number of connections
Shared weights on the edges
Max pooling further reduces the complexity
Max Pooling
1 0 0 0 0 1
0 1 0 0 1 0
0 0 1 1 0 0
1 0 0 0 1 0
0 1 0 0 1 0
0 0 1 0 1 0
6 x 6 image
3 0
1
3
-1 1
3
0
2 x 2 image
Each filter
is a channel
New image
but smaller
Conv
Max
Pooling
The whole CNN
Convolution
Max Pooling
Convolution
Max Pooling
Can
repeat
many
times
A new image
The number of channels
is the number of filters
Smaller than the original
image
3 0
1
3
-1 1
3
0
The whole CNN
Fully Connected
Feedforward network
cat dog ……
Convolution
Max Pooling
Convolution
Max Pooling
Flattened
A new image
A new image
Flattening
3 0
1
3
-1 1
3
0 Flattened
3
0
1
3
-1
1
0
3
Fully Connected
Feedforward network
Only modified the network structure and
input format (vector -> 3-D tensor)
CNN in Keras
Convolution
Max Pooling
Convolution
Max Pooling
input
1 -1 -1
-1 1 -1
-1 -1 1
-1 1 -1
-1 1 -1
-1 1 -1
There are
25 3x3
filters.
…
…
Input_shape = ( 28 , 28 , 1)
1: black/white, 3: RGB
28 x 28 pixels
3 -1
-3 1
3
Only modified the network structure and
input format (vector -> 3-D array)
CNN in Keras
Convolution
Max Pooling
Convolution
Max Pooling
Input
1 x 28 x 28
25 x 26 x 26
25 x 13 x 13
50 x 11 x 11
50 x 5 x 5
How many parameters for
each filter?
How many parameters
for each filter?
9
225=
25x9
Only modified the network structure and
input format (vector -> 3-D array)
CNN in Keras
Convolution
Max Pooling
Convolution
Max Pooling
Input
1 x 28 x 28
25 x 26 x 26
25 x 13 x 13
50 x 11 x 11
50 x 5 x 5
Flattened
1250
Fully connected
feedforward network
Output
AlphaGo
Neural
Network
(19 x 19
positions)
Next move
19 x 19 matrix
Black: 1
white: -1
none: 0
Fully-connected feedforward
network can be used
But CNN performs much better
AlphaGo’s policy network
Note: AlphaGo does not use Max Pooling.
The following is quotation from their Nature article:
CNN in speech recognition
Time
Frequency
Spectrogram
CNN
Image
The filters move in the
frequency direction.
CNN in text classification
Source of image:
http://citeseerx.ist.psu.edu/viewdoc/downlo
ad?doi=10.1.1.703.6858&rep=rep1&type=p
df
?

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Deep-Learning-2017-Lecture5CNN.ppt

  • 1. Lecture 5 Smaller Network: CNN  We know it is good to learn a small model.  From this fully connected model, do we really need all the edges?  Can some of these be shared?
  • 2. Consider learning an image: Some patterns are much smaller than the whole image “beak” detector Can represent a small region with fewer parameters
  • 3. Same pattern appears in different places: They can be compressed! What about training a lot of such “small” detectors and each detector must “move around”. “upper-left beak” detector “middle beak” detector They can be compressed to the same parameters.
  • 4. A convolutional layer A filter A CNN is a neural network with some convolutional layers (and some other layers). A convolutional layer has a number of filters that does convolutional operation. Beak detector
  • 5. Convolution 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 0 1 0 1 0 6 x 6 image 1 -1 -1 -1 1 -1 -1 -1 1 Filter 1 -1 1 -1 -1 1 -1 -1 1 -1 Filter 2 … … These are the network parameters to be learned. Each filter detects a small pattern (3 x 3).
  • 6. Convolution 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 0 1 0 1 0 6 x 6 image 1 -1 -1 -1 1 -1 -1 -1 1 Filter 1 3 -1 stride=1 Dot product
  • 7. Convolution 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 0 1 0 1 0 6 x 6 image 1 -1 -1 -1 1 -1 -1 -1 1 Filter 1 3 -3 If stride=2
  • 8. Convolution 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 0 1 0 1 0 6 x 6 image 1 -1 -1 -1 1 -1 -1 -1 1 Filter 1 3 -1 -3 -1 -3 1 0 -3 -3 -3 0 1 3 -2 -2 -1 stride=1
  • 9. Convolution 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 0 1 0 1 0 6 x 6 image 3 -1 -3 -1 -3 1 0 -3 -3 -3 0 1 3 -2 -2 -1 -1 1 -1 -1 1 -1 -1 1 -1 Filter 2 -1 -1 -1 -1 -1 -1 -2 1 -1 -1 -2 1 -1 0 -4 3 Repeat this for each filter stride=1 Two 4 x 4 images Forming 2 x 4 x 4 matrix Feature Map
  • 10. Color image: RGB 3 channels 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 0 1 0 1 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 0 1 0 1 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 0 1 0 1 0 1 -1 -1 -1 1 -1 -1 -1 1 Filter 1 -1 1 -1 -1 1 -1 -1 1 -1 Filter 2 1 -1 -1 -1 1 -1 -1 -1 1 1 -1 -1 -1 1 -1 -1 -1 1 -1 1 -1 -1 1 -1 -1 1 -1 -1 1 -1 -1 1 -1 -1 1 -1 Color image
  • 11. 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 0 1 0 1 0 image convolution -1 1 -1 -1 1 -1 -1 1 -1 1 -1 -1 -1 1 -1 -1 -1 1 1 x 2 x … … 36 x … … 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 0 1 0 1 0 Convolution v.s. Fully Connected Fully- connected
  • 12. 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 0 1 0 1 0 6 x 6 image 1 -1 -1 -1 1 -1 -1 -1 1 Filter 1 1 2 3 … 8 9 … 1 3 14 15 … Only connect to 9 inputs, not fully connected 4: 10: 16 1 0 0 0 0 1 0 0 0 0 1 1 3 fewer parameters!
  • 13. 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 0 1 0 1 0 1 -1 -1 -1 1 -1 -1 -1 1 Filter 1 1: 2: 3: … 7: 8: 9: … 1 3: 14: 15: … 4: 10: 16: 1 0 0 0 0 1 0 0 0 0 1 1 3 -1 Shared weights 6 x 6 image Fewer parameters Even fewer parameters
  • 14. The whole CNN Fully Connected Feedforward network cat dog …… Convolution Max Pooling Convolution Max Pooling Flattened Can repeat many times
  • 15. Max Pooling 3 -1 -3 -1 -3 1 0 -3 -3 -3 0 1 3 -2 -2 -1 -1 1 -1 -1 1 -1 -1 1 -1 Filter 2 -1 -1 -1 -1 -1 -1 -2 1 -1 -1 -2 1 -1 0 -4 3 1 -1 -1 -1 1 -1 -1 -1 1 Filter 1
  • 16. Why Pooling  Subsampling pixels will not change the object Subsampling bird bird We can subsample the pixels to make image smaller fewer parameters to characterize the image
  • 17. A CNN compresses a fully connected network in two ways: Reducing number of connections Shared weights on the edges Max pooling further reduces the complexity
  • 18. Max Pooling 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 0 1 0 1 0 6 x 6 image 3 0 1 3 -1 1 3 0 2 x 2 image Each filter is a channel New image but smaller Conv Max Pooling
  • 19. The whole CNN Convolution Max Pooling Convolution Max Pooling Can repeat many times A new image The number of channels is the number of filters Smaller than the original image 3 0 1 3 -1 1 3 0
  • 20. The whole CNN Fully Connected Feedforward network cat dog …… Convolution Max Pooling Convolution Max Pooling Flattened A new image A new image
  • 21. Flattening 3 0 1 3 -1 1 3 0 Flattened 3 0 1 3 -1 1 0 3 Fully Connected Feedforward network
  • 22. Only modified the network structure and input format (vector -> 3-D tensor) CNN in Keras Convolution Max Pooling Convolution Max Pooling input 1 -1 -1 -1 1 -1 -1 -1 1 -1 1 -1 -1 1 -1 -1 1 -1 There are 25 3x3 filters. … … Input_shape = ( 28 , 28 , 1) 1: black/white, 3: RGB 28 x 28 pixels 3 -1 -3 1 3
  • 23. Only modified the network structure and input format (vector -> 3-D array) CNN in Keras Convolution Max Pooling Convolution Max Pooling Input 1 x 28 x 28 25 x 26 x 26 25 x 13 x 13 50 x 11 x 11 50 x 5 x 5 How many parameters for each filter? How many parameters for each filter? 9 225= 25x9
  • 24. Only modified the network structure and input format (vector -> 3-D array) CNN in Keras Convolution Max Pooling Convolution Max Pooling Input 1 x 28 x 28 25 x 26 x 26 25 x 13 x 13 50 x 11 x 11 50 x 5 x 5 Flattened 1250 Fully connected feedforward network Output
  • 25. AlphaGo Neural Network (19 x 19 positions) Next move 19 x 19 matrix Black: 1 white: -1 none: 0 Fully-connected feedforward network can be used But CNN performs much better
  • 26. AlphaGo’s policy network Note: AlphaGo does not use Max Pooling. The following is quotation from their Nature article:
  • 27. CNN in speech recognition Time Frequency Spectrogram CNN Image The filters move in the frequency direction.
  • 28. CNN in text classification Source of image: http://citeseerx.ist.psu.edu/viewdoc/downlo ad?doi=10.1.1.703.6858&rep=rep1&type=p df ?