This document summarizes a research paper on convolutional restricted Boltzmann machines (CRBMs) for feature learning. The paper proposes using CRBMs to learn hierarchical local feature detectors in an unsupervised and generative manner. CRBMs extend regular restricted Boltzmann machines to incorporate spatial locality. The learned features are evaluated on handwritten digit and human detection tasks, achieving results comparable to state-of-the-art. The paper contributes an approach to generative feature learning using CRBMs that can capture spatial relationships in images.

1. Convolutional Restricted
Boltzmann Machines for
Feature Learning
Mohammad Norouzi
Advisor: Dr. Greg Mori
CS @ Simon Fraser University
27 Nov 2009 1

2. CRBMs for
Feature Learning
Mohammad Norouzi
Advisor: Dr. Greg Mori
CS @ Simon Fraser University
27 Nov 2009 2

3. Problems
Human detection
Handwritten digit
classification
3

4. Sliding Window Approach
4

5. Sliding Window Approach (Cont’d)
5
[INRIA Person Dataset]

6. Success or Failure of an object recognition
algorithm hinges on the features used
Input
Feature
representation
Label
Our Focus Classifier
? Human
Background
0 / 1 / 2 / 3 / …
6
Learning

7. Local Feature Detector Hierarchies
7
Larger More complicated Less frequent

8. Generative & Layerwise Learning
8
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
Generative
CRBM
?
?
? ?
?
?
?
?
? ?
?
?

9. Visual Features: Filtering
9
1 0 -1
2 0 -2
1 0 -1
Filter Kernel (Feature)
-1 0 1
-2 0 2
-1 0 1
0 -1 -2
1 0 -1
2 1 0
Filter Response
1
W
V
2
W 2
W
)
,
( 1
W
V
Filter )
,
( 2
W
V
Filter )
,
( 3
W
V
Filter

10. Our approach to feature learning
is generative
?
?
?
1
H
2
H
3
H
V
Binary Hidden
Variables
10
1
W
2
W
3
W
(CRBM model)

11. Related Work
11

12. Related Work
• Convolutional Neural Network (CNN)
– Filtering layers are bundled with a classifier, and all
the layers are learned together using error
backpropagation.
– Does not perform well on natural images
• Biologically plausible models
– Hand-crafted first layer vs. Randomly selected
prototypes for second layer.
[Lecun et al. 98]
[Ranzato et al. CVPR'07]
[Serre et al., PAMI'07] [Mutch and Lowe, CVPR'06]
12

13. Related Work (cont’d)
• Deep Belief Net
– A two layer partially observed MRF, called RBM, is
the building block
– Learning is performed unsupervised and layer-by-
layer from bottom layer upwards
• Our contributions: We incorporate spatial
locality into RBMs and adapt the learning
algorithm accordingly
• We add more complicated components such
as pooling and sparsity into deep belief nets
[Hinton et al., NC'2006]
13

14. Why Generative &Unsupervised
• Discriminative learning of deep and large
neural networks has not been successful
– Requires large training sets
– Easily gets over-fitted for large models
– First layer gradients are relatively small
• Alternative hybrid approach
– Learn a large set of first layer features generatively
– Switch to a discriminative model to select the
discriminative features from those that are learned
– Discriminative fine-tuning is helpful

15. Details
15

16. CRBM
• Image is the visible layer
and hidden layer is
related to filter responses
• An energy based
probabilistic model
16
Dot product of vectorized matrices
   
 
)
,
(
)
;
,
(
)
;
,
(
)
;
,
(
,
exp
1
k
k
k
k
k k
k
H
W
V
Filter
H
W
H
V
E
W
H
V
E
W
H
V
E
H;W
V
E
Z
=
V;W
P








17. Training CRBMs
• Maximum likelihood learning of CRBMs is difficult
• Contrastive Divergence (CD) learning is applicable
• For CD learning we need to compute the
conditionals and .
data
17
sample
 
H
V
P |  
V
H
P |

18. CRBM (Backward)
• Nearby hidden variables
cooperate in reconstruction
• Conditional Probabilities
take the form
18
 
 
)
exp
1
(
1
*
)
(
)
,
(
)
|
(
)
,
(
)
|
(
x
k k
k
k
k
x
W
H
Filter
H
V
P
W
V
Filter
V
H
P










19. Learning the Hierarchy
• The structure is trained bottom up and layerwise
• The CRBM model for training filtering layers
• Filtering layers are followed by down-sampling
CRBM CRBM
Classifier
Pooling Pooling
19
Filtering
Non-linearity
Reduce the
dimensionality
layers

20. Input
1st
Filters 2nd
Filters
Responses
Responses
1 3
2 4

21. Experiments
21

22. Evaluation
MNIST digit dataset
• Training set: 60,000 image
of digits of size 28x28
• Test set: 10,000 images
INRIA person dataset
• Training set: 2416 person
windows of size 128 x 64
pixels and 4.5x106 negative
windows
• Test set: 1132 positive and
2x106 negative windows
22

23. First layer filters
• Gray-scale images of
INRIA positive set
• 15 filters of 7x7
23
• MNIST unlabeled digits
• 15 filters of 5x5

24. Second Layer Features (MNIST)
• Hard to visualize the filters
• We show patches highly responded to filters:
24
24

25. Second Layer Features (INRIA)
25

26. MNIST Results
• MNIST error rate when model is trained on
the full training set
26

27. Results
27
False Positive

28. 1st
28

29. 2nd
29

30. 3rd
30

31. 4th
31

32. 5th
32

33. INRIA Results
• Adding our large-scale features significantly
improves performance of the baseline (HOG)
33

34. Conclusion
• We extended the RBM model to Convolutional
RBM, useful for domains with spatial locality
• We exploited CRBMs to train local hierarchical
feature detectors one layer at a time and
generatively
• This method obtained results comparable to
state-of-the-art in digit classification and
human detection
34

35. Thank You 
35

36. Hierarchical Feature Detector
36
? ? ?
? ? ?
? ? ?

37. Contrastive Divergence Learning
37
 
data
1
k
data
0
k
k
k H
,
V
Filter
H
,
V
Filter
η
+
W
=
W )
(
)
( 1
0

   
k
k
H
V,
Filter
=
W
θ
H;
V,
E




38. Training CRBMs (Cont'd)
• The problem of reconstructing border region
becomes severe when number of Gibbs
sampling steps > 1.
– Partition visible units into middle and border
regions
• Instead of maximizing the
likelihood, we (approximately)
maximize  
 b
m
v
|
v
p

39. Enforcing Feature Sparsity
• The CRBM's representation is K (number of
filters) times overcomplete
• After a few CD learning iterations, V is
perfectly reconstructed
• Enforce sparsity to tackle this problem
– Hidden bias terms were frozen at large negative
values
• Having a single non-sparse hidden unit
improves the learned features
– Might be related to the ergodicity condition

40. Probabilistic Meaning of Max
1 2 3 4 5 6
1 2 3 4
Max
1 2 3 4 5 6
1 1 2 2
h
h'
v
 
6
4
5
3
4
2
3
1
:
T
4
:
T
3
:
T
2
:
T
1
v
w
h
+
v
w
h
+
v
w
h
+
v
w
h
=
h
v,
E

h'
v
   
 
6
4
5
3
4
2
3
1
:
T
2
:
T
2
:
T
1
:
T
1
v
w
h'
+
v
w
h'
max
+
v
w
h'
,
v
w
h'
max
=
h
v,
E


41. The Classifier Layer
• We used SVM as our final classifier
– RBF kernel for MNIST
– Linear kernel for INRIA
– For INRIA we combined our 4th layer outputs and
HOG features
• We experimentally observed that relaxing the
sparsity of CRBM's hidden units yields better
results
– This lets the discriminative model to set the
thresholds itself

42. Why HOG features are added?
• Because part-like features
are very sparse
• Having a template of the
human figure helps a lot
f

43. RBM
• Two layer pairwise MRF with a full set
of hidden-visible connections
• RBM Is an energy based model
• Hidden random variables are binary, Visible
variables can be binary or continuous
• Inference is straightforward: and
• Contrastive Divergence learning for training
h
v
w
 
 
 
 
θ
h;
v,
E
θ
Z
=
θ
h;
v,
p 
exp
1
  


 

 2
2
1
i
j
j
i
i
j
ij
i v
+
h
c
v
b
h
w
v
=
θ
h;
v,
E
 
v
|
h
p  
h
|
v
p

44. Why Unsupervised Bottom-Up
• Discriminative learning of deep structure has
not been successful
– Requires large training sets
– Easily is over-fitted for large models
– First layer gradients are relatively small
• Alternative hybrid approach
– Learn a large set of first layer features generatively
– Later, switch to a discriminative model to select
the discriminative features from those learned
– Fine-tune the features using

45. INRIA Results (Cont'd)
• Missrate at different FPPW rates
• FPPI is a better indicator of performance
• More experiments on size of features and
number of layers are desired