Keypoints on the paper 'Dynamic routing between capsules' . Some drawings are taken from sources on Medium. They are cited on the last slide.

1. DYNAMIC ROUTING BETWEEN
CAPSULES
AND OTHER CAPSULE THINGS

2. PART 1
WHY CNNs SUCK

3. The pooling operation used in
convolutional neural networks is a big
mistake and the fact that it works so
well is a disaster.
- Hinton

4. Max pooling loses the spatial information

5. Max pooling loses the spatial information
- We don’t use the relationship between objects. Is this a face?

6. Equivariance and invariance
- CNNs without max pooling are equivariant regarding translation.
- That’s something we want! But max pooling breaks it.

7. We work with frames of reference. CNNs do not.

8. PART 2
THE KEY CONCEPTS OF CAPSULES

9. VISION IS THE INVERSE OF GRAPHICS
The fundamental idea

10. Computer
Graphics
From a parameter
vector and a
projection matrix,
we generate a 3D
image.
This parameter
vector is viewpoint
invariant!

11. Can’t we go the
other way around
and achieve
viewpoint
invariance?
Computer
Vision?

12. CAPSULES ENCODE AN ENTITY
A capsule votes to say if a certain entity
is in the image.

13. Layer L Layer L+1
building
tea cup
face
nose
window
leaf
window nose leaf eye
face tea cup building
Correspondence
between network and
graph structure

14. Layer L Layer L+1
building
tea cup
face
nose
window
leaf
nose eye
face
Correspondence
between network and
graph structure
This graph has been carved out from
the full graph.

15. CAPSULES OUTPUT A VECTOR
A capsule encodes an entity (and its
properties) via its output vector.

16. Layer L Layer L+1
i
0.456
Fully
Connected
Net
The output of a
node (neuron) is a
scalar value.
0.456
0.456

17. Layer L Layer L+1
i
Capsules
Net
The output of a
node (capsule) is a
vector.

18. Layer L Layer L+1
digit 6
Capsules
Net:
an example
The first dimension
of the output vector
encodes for the
scale and thickness
of the digit.

19. Layer L Layer L+1
digit 6
Capsules
Net:
an example
The second
dimension of the
output vector
encodes for the
roundness of the
top part of the digit.

20. ROUTING MECHANISM
The information flows towards the
neurons that are the most adapted to
use this type of information.

21. Layer L Layer L+1
j+1
j
j-1
i
Wi,j-1
Wi,j
Wi,j+1
Fully
Connected
Net
The information is
distributed
uniformly to every
other node in the
next layer.

22. Layer L Layer L+1
j+1
j
j-1
i
ci,j-1
Wi,j-1
ci,j
Wi,j
ci,j+1
Wi,j+1
Capsules
Net
The information is
distributed to a
specific node in the
next layer.

23. Routing mechanism (bonus slide)
- In a CNN, this routing mechanism is ‘inverted’.
- In a CapsNet, the routing is learned.
0.2
0.1
0.6

24. Layer L Layer L+1
building
tea cup
face
nose
ci,j-1
Wi,j-1
ci,j
Wi,j
ci,j+1
Wi,j+1
Capsules
Net:
an example
window
leaf

25. HOW CAPSULES VOTE
How is the presence of an entity
encoded in the network?

26. Layer L Layer L+1
Norm of the
output
The norm of the
vector encodes the
probability that the
entity is in the image.
nose
window
leaf

27. Layer L Layer L+1
Learning
the routing
Capsules that detect
similar pose (via
scalar product)
estimations tend to
be coupled.
j+1
j
j-1
i

28. PART 3
FORMALISATION

29. Layer L Layer L+1
j+1
j
j-1
i
Computing
the output
vector
i-1
i+1
Weighted sum of
the inputs (before
activation function).

30. Layer L Layer L+1
j+1
j
j-1
i
Computing
the output
vector
Squashing the
output vector to
fallback on a
probability (non
linear activation
function).
i-1
i+1

32. How
routing is
achieved
How do we obtain
the ?
1 Start with log priors:
2 Initialise with
3 Make a forward pass to obtain the
4 Update the :

33. PART 4
RESULTS

34. MNIST
Error rate (%)
Number of
parameters
CNN baseline 0.39 35.4M
CapsNet 0.25 8.2M
MultiMNIST
Error rate
(%)
Number of
parameters
CNN baseline 8.1 24.56M
CapsNet 5.2 11.36M

35. affNIST
Accuracy (%) on... Original MNIST affNIST
CNN baseline 99.22 66.
CapsNet 99.23 79.

36. smallNORB
Error rate
(%)
Azimuth Elevation
CNN CapsNet CNN CapsNet
Familiar
Viewpoints
3.7 3.7 4.3 4.3
Novel
viewpoints
20. 13.5 17.8 12.3

37. FURTHER READING
- https://medium.com/mlreview/deep-neural-network-capsules-137be2877d44
- https://medium.com/@pechyonkin/understanding-hintons-capsule-networks-part
-i-intuition-b4b559d1159b
- https://hackernoon.com/what-is-a-capsnet-or-capsule-network-2bfbe48769cc
- https://hackernoon.com/capsule-networks-are-shaking-up-ai-heres-how-to-us
e-them-c233a0971952
- https://www.reddit.com/r/MachineLearning/comments/7bz5x9/d_eli5_capsule_ne
tworks_how_are_they_unique_and/
- https://kndrck.co/posts/capsule_networks_explained/