1. Analysis of Trained CNN (Receptive Field & Weights of Network)
Bukweon Kim

2. Basic Example:Mnist Data
Mnist data is data of 28 by 28 sized handwritten digit images, all labeled which is which.
Let us observe the structural characteristics with this Mnist data using simple CNN.

3. Example CNN structure Input Image 24 X 24 28 X 28 5 X 5 X 4 5 X 5 X 4
First Convolution Weights
24 X 24
12 X 12
Convolution
Pooling
X 8
5 X 5 X 4
Second Convolution Weights
8 X 8
4 X 4
Fully Connected
Classify
4 X 4 X 8
X 16
Fully Connected Layer Weights
Classify Dictionary
16 X 1
16 X 10
ReLU
Softmax
ReLU
ReLU

4. Receptive Field
Receptive field is the area that this value is determined from.
The green box is determined by red red boxes and green box affects cyan box or values.
Any value that is not inside red box does not affect the value of the green box.

5. Classification
Similar (high inner product value) 1 2 3 4 5 6 7 8 9
Inner product and softmax
Result achieved by applying softmax on inner-product result of signal and library
This feature strongly suggest input is either 0, 4, 5, 6, or 8
Signals of 16 features extracted from previous steps of CNN
Library of 16 features for each digit

6. Outputs of several 6s 6
We will focus on this 13th signal and analysis what it means.
Library of 16 features for 6

7. 6 6 like image examples for explanation
We will focus on this 13th signal and analysis what it means.
Library of 16 features for 6
14th Mnist Data
Confuses between 6 and 0
Classified as 6
Classified as 6
Classified as 1

8. What is the meaning of this 13th features?
0.2 +
0.1
0.4
0.7
Inner Product
ReLU
1.7
For the convenience of understanding I will focus on the strongest signal
Output of previous pooling layer
Weights for 13th signal of next layer

9. Weight and signal analysis : Weight value
Receptive field of each values.
positive
negative
Main signal given from previous layer
0.22
0.18
0.04
0.05
2.22
2.97
0.07
0.66
0.83
0.61
-1.04
0.15
4.27
-1.18
-1.19
-0.21
-1.22
-1.33
-0.55
-0.67
0.07
0.05
0.12
0.22
0.18
0.04
Value translated as image moved 8 pixels below.
Inner Product
Inner Product
0.7
-0.7

10. Weight and signal analysis : Pooling
0.22
0.18
0.04
0.05
The max pooling made signal a bit local translation invariant.
Even though we moved the image 2 pixels, the signal of selected pixel did not change
0.14
0.22
0.05
2 pixels
0.22
0.18
0.04
2 pixels
2×2 max pooling with stride 2

11. Weight and signal analysis : Weight value deeper understanding 1
Increased value of input corresponding to positive weight enhances the signal.
Increased value of input corresponding to negative weight suppress the signal.
0.03
-0.01
-0.26
-0.09
-0.12
-0.03
-0.85
-0.04
-0.02
0.15
-0.43
0.11
0.14
0.06
0.04
-0.21
0.02
-0.05
0.05
Value change of input corresponding to weight near 0 does not effect the signal much.

12. Weight and signal analysis : Pooling deeper understanding
Strongest signal output from one of this inner product or

13. + Weight and signal analysis : Weight value deeper understanding 2
Map of the pattern determined from 2 previous filters
Convolution
&
pooling
Convolution
Map of the signal of combination of any of 4 patterns we looked for
ReLU +
Weights of first convolution layer
Outputs of first pooling layer
8th Weight in second convolutional layer

14. Weight and signal analysis : Weight value deeper understanding 3
ReLU +
Each maps are looking for the patterns somewhat similar to these
(these are not exact because it is not linear)
the final output may be considered as the value derived from taking many combination of patterns in account.
These accounted patterns may not only enhance the value, but also suppress the value.
ReLU( + + + )=
suppress
enhance
ReLU( + + + )=
Input for fully connected layer!!
suppress
enhance

15. Why was CNN fooled/not fooled for examples?
The strong 13th signal usually tells if input is 6 or not because of what it looks for.
The strong 13th signal usually tells if input is 6 or not because of what it looks for.
ignored
Library of 16 features for 6
Existence of / pattern on middle fooled them to think it is 1.
Confuses between 6 and 0
14th Mnist Data
Classified as 6
Classified as 6
Classified as 1

16. The CNN with ReLU looks for combination of patterns as it gets deeper.
Conclusion
The CNN with ReLU looks for combination of patterns as it gets deeper.
The pooling layer tells CNN that we are looking for local translation invariant features.
Deeper layers of CNN allow the network to look for more complex combination of patterns. Also, it allow wider invariance for local patterns.
With knowing what exactly CNN looks for, we can tell have deeper understanding of how the CNN works, and what can or can’t it do.

17. Semantic Segmentation Using Image Classification
Pixelwise Classification
Amniotic Fluid
Umbilical Vein
Stomach Bubble
Shadowing Artifact
Bone
Other white region
Classification CNN
Stomach Bubble
Repeat for every pixel
Extract Patch centered at pixel
Classify pixel

18. Comparison for Segmentation Result with and without spine position
With some change of CNN structure, we could give the spine position information into the CNN structure where we wanted them to be applied