Lecture 06 marco aurelio ranzato - deep learning

Deep Learning
Marc'Aurelio Ranzato
Facebook A.I. Research
ICVSS – 15 July 2014www.cs.toronto.edu/~ranzato

https://sites.google.com/site/deeplearningcvpr2014/

6
fixed unsupervised supervised
classifier
Mixture of
Gaussians
MFCC
ˈd ē p
classifier
K-Means/
pooling
SIFT/HOG
“car”
classifiern-grams
Parse Tree
Syntactic “+”
This burrito place
is yummy and fun!
Traditional Pattern Recognition
VISION
SPEECH
NLP
Ranzato

7
Hierarchical Compositionality (DEEP)
VISION
SPEECH
NLP
pixels edge texton motif part object
sample spectral
band
formant motif phone word
character NP/VP/.. clause sentence storyword
Ranzato

8
classifier
Mixture of
Gaussians
MFCC
ˈd ē p
classifier
K-Means/
pooling
SIFT/HOG
“car”
classifiern-grams
Parse Tree
Syntactic “+”
This burrito place
is yummy and fun!
Traditional Pattern Recognition
VISION
SPEECH
NLP
Ranzato

9
Deep Learning
“car”
Cascade of non-linear transformations
End to end learning
General framework (any hierarchical model is deep)
What is Deep Learning
Ranzato

10
Ranzato
THE SPACE OF
MACHINE LEARNING METHODS

11
PerceptronNeural Net
Boosting
SVM
GMMΣΠ
BayesNP
Convolutional
Neural Net
Recurrent
Neural Net
Autoencoder
Neural Net
Sparse Coding
Restricted BMDeep Belief Net
Deep (sparse/denoising)
Autoencoder
Disclaimer: showing only a
subset of the known methods

12
Boosting
SVM
GMMΣΠ
BayesNP
Convolutional
Neural Net
Recurrent
Neural Net
Autoencoder
Neural Net
Sparse Coding
Autoencoder
SHALLOW
DEEP

13
Boosting
SVM
GMMΣΠ
BayesNP
Convolutional
Neural Net
Recurrent
Neural Net
Autoencoder
Neural Net
Sparse Coding
Autoencoder
UNSUPERVISED
SUPERVISED
DEEP
SHALLOW

14
Boosting
SVM
Convolutional
Neural Net
Recurrent
Neural Net
Autoencoder
Neural Net
Autoencoder
UNSUPERVISED
SUPERVISED
DEEP
SHALLOWΣΠ
BayesNP
Deep Belief Net
GMM
Sparse Coding
Restricted BM
PROBABILISTIC

15
Main types of deep architectures
Ranzato
Deep Learning is B I G
input input
input
feed-forward
Feed-back
Bi-directional
Neural nets
Conv Nets
Hierar. Sparse Coding
Deconv Nets
Stacked
Auto-encoders
DBM
input
Recurrent
Recurrent Neural nets
Recursive Nets
LISTA

16
Ranzato
input input
input
feed-forward
Feed-back
Bi-directional
Neural nets
Conv Nets
Hierar. Sparse Coding
Deconv Nets
Stacked
Auto-encoders
DBM
input
Recurrent
Recurrent Neural nets
Recursive Nets
LISTA
Main types of deep architectures

17
Ranzato
Main types of learning protocols
Purely supervised
Backprop + SGD
Good when there is lots of labeled data.
Layer-wise unsupervised + superv. linear classifier
Train each layer in sequence using regularized auto-encoders or
RBMs
Hold fix the feature extractor, train linear classifier on features
Good when labeled data is scarce but there is lots of unlabeled
data.
Layer-wise unsupervised + supervised backprop
Train each layer in sequence
Backprop through the whole system
Good when learning problem is very difficult.

18
Ranzato
Main types of learning protocols
Purely supervised
Backprop + SGD
Good when there is lots of labeled data.
Layer-wise unsupervised + superv. linear classifier
Train each layer in sequence using regularized auto-encoders or
RBMs
Hold fix the feature extractor, train linear classifier on features
Good when labeled data is scarce but there is lots of unlabeled
data.
Layer-wise unsupervised + supervised backprop
Train each layer in sequence
Backprop through the whole system
Good when learning problem is very difficult.

19
Outline Part I
Ranzato
Supervised Neural Networks
Convolutional Neural Networks
Examples
Tips

20
Neural Networks
Ranzato
Assumptions (for the next few slides):
The input image is vectorized (disregard the spatial layout of pixels)
The target label is discrete (classification)
Question: what class of functions shall we consider to map the input
into the output?
Answer: composition of simpler functions.
Follow-up questions: Why not a linear combination? What are the
“simpler” functions? What is the interpretation?
Answer: later...

21
Neural Networks: example
h2
h1
x
max 0,W
1
x max0,W
2
h
1
 W
3
h
2
Ranzato
input
1-st layer hidden units
2-nd layer hidden units
output
Example of a 2 hidden layer neural network (or 4 layer network,
counting also input and output).
x
h1
h2
o
o

22
Forward Propagation
Ranzato
Def.: Forward propagation is the process of computing the
output of the network given its input.

23
Forward Propagation
Ranzato
h1
=max0,W 1
xb1

x∈ RD
W 1
∈R
N 1
×D
b1
∈R
N 1
h
1
∈R
N 1
x
1-st layer weight matrix or weightsW 1
1-st layer biasesb1
o
The non-linearity is called ReLU in the DL literature.
Each output hidden unit takes as input all the units at the previous
layer: each such layer is called “fully connected”.
u=max 0,v
h2
h1
max 0,W
1
x max0,W
2
h
1
 W
3
h
2

24
Forward Propagation
Ranzato
h2
=max 0,W 2
h1
b2

h1
∈R
N 1
W 2
∈R
N 2
×N 1
b2
∈R
N 2
h
2
∈R
N 2
x o
2-nd layer weight matrix or weightsW 2
2-nd layer biasesb2
h2
h1
max 0,W
1
x max0,W
2
h
1
 W
3
h
2

25
Forward Propagation
Ranzato
o=max 0,W 3
h2
b3

h2
∈R
N 2
W 3
∈R
N 3
×N 2
b3
∈R
N 3
o∈R
N 3
x o
3-rd layer weight matrix or weightsW 3
3-rd layer biasesb3
h2
h1
max 0,W
1
x max0,W
2
h
1
 W
3
h
2

26
Alternative Graphical Representation
Ranzato
h
k1
h
k
max 0,W
k1
h
k

hk1
h
k
W k 1
h1
k
h2
k
h3
k
h4
k
h1
k 1
h2
k 1
h3
k 1
w1,1
k1
w3,4
k1
h
k
hk1
W k 1

27
Interpretation
Ranzato
Question: Why can't the mapping between layers be linear?
Answer: Because composition of linear functions is a linear function.
Neural network would reduce to (1 layer) logistic regression.
Question: What do ReLU layers accomplish?
Answer: Piece-wise linear tiling: mapping is locally linear.
Montufar et al. “On the number of linear regions of DNNs” arXiv 2014

28
Ranzato
[0/1]
[0/1]
[0/1]
[0/1] [0/1]
[0/1]
[0/1]
[0/1]
ReLU layers do local linear approximation. Number of planes grows
exponentially with number of hidden units. Multiple layers yeild
exponential savings in number of parameters (parameter sharing).
Montufar et al. “On the number of linear regions of DNNs” arXiv 2014

29
Interpretation
Ranzato
Question: Why do we need many layers?
Answer: When input has hierarchical structure, the use of a
hierarchical architecture is potentially more efficient because
intermediate computations can be re-used. DL architectures are
efficient also because they use distributed representations which
are shared across classes.
[0 0 1 0 0 0 0 1 0 0 1 1 0 0 1 0 … ]
Exponentially more efficient than a
1-of-N representation (a la k-means)
truck feature

30
Interpretation
Ranzato
[0 0 1 0 0 0 0 1 0 0 1 1 0 0 1 0 … ]
[1 1 0 0 0 1 0 1 0 0 0 0 1 1 0 1… ] motorbike
truck

31
Interpretation
Ranzato
Input image
low level
parts
prediction of class
mid-level
parts
high-level
parts
distributed representations
feature sharing
compositionality
...
Lee et al. “Convolutional DBN's ...” ICML 2009

32
Interpretation
Ranzato
Question: How many layers? How many hidden units?
Answer: Cross-validation or hyper-parameter search methods are
the answer. In general, the wider and the deeper the network the
more complicated the mapping.
Question: What does a hidden unit do?
Answer: It can be thought of as a classifier or feature detector.
Question: How do I set the weight matrices?
Answer: Weight matrices and biases are learned.
First, we need to define a measure of quality of the current mapping.
Then, we need to define a procedure to adjust the parameters.

33
h
2
h
1
x o
Loss
max 0,W
1
x max0,W
2
h
1
 W
3
h
2
Lx , y ; =−∑j
y j log pc j∣x
pck =1∣x=
e
ok
∑j=1
C
eo j
Probability of class k given input (softmax):
(Per-sample) Loss; e.g., negative log-likelihood (good for classification
of small number of classes):
Ranzato
How Good is a Network?
y=[00..010..0]
k1 C

34
Training
∗
=arg min ∑n=1
P
Lxn
, yn
; 
Learning consists of minimizing the loss (plus some
regularization term) w.r.t. parameters over the whole training set.
Question: How to minimize a complicated function of the
parameters?
Answer: Chain rule, a.k.a. Backpropagation! That is the procedure
to compute gradients of the loss w.r.t. parameters in a multi-layer
neural network.
Rumelhart et al. “Learning internal representations by back-propagating..” Nature 1986

35
Derivative w.r.t. Input of Softmax
Lx , y ; =−∑j
y j log pc j∣x
pck =1∣x=
e
ok
∑j
e
o j
By substituting the fist formula in the second, and taking the
derivative w.r.t. we get:o
∂ L
∂o
= pc∣x− y
HOMEWORK: prove it!
Ranzato
y=[00..010..0]
k1 C

36
Backward Propagation
h
2
h
1
x
Loss
y
Given and assuming we can easily compute the
Jacobian of each module, we have:
∂ L/∂ o
∂ L
∂ o
max 0,W
1
x max0,W
2
h
1
 W
3
h
2
∂ L
∂W
3
=
∂ L
∂ o
∂ o
∂W
3

37
h
2
h
1
x
Loss
y
∂ L/∂ o
∂ L
∂W
3
=
∂ L
∂ o
∂ o
∂W
3
∂ L
∂ o
max 0,W
1
x max0,W
2
h
1
 W
3
h
2
∂ L
∂W
3
=  pc∣x−y h
2 T

38
h
2
h
1
x
Loss
y
∂ L/∂ o
∂ L
∂ h
2
=
∂ L
∂ o
∂ o
∂ h
2
∂ L
∂W
3
=
∂ L
∂ o
∂ o
∂W
3
∂ L
∂ o
max 0,W
1
x max0,W
2
h
1
 W
3
h
2
∂ L
∂W
3
=  pc∣x−y h
2 T

39
h
2
h
1
x
Loss
y
∂ L/∂ o
∂ L
∂ h
2
=
∂ L
∂ o
∂ o
∂ h
2
∂ L
∂W
3
=
∂ L
∂ o
∂ o
∂W
3
∂ L
∂ o
max 0,W
1
x max0,W
2
h
1
 W
3
h
2
∂ L
∂W
3
=  pc∣x−y h
2 T ∂ L
∂ h
2
= W
3 T
 pc∣x−y

40
h
1
x
Loss
y
Given we can compute now:
∂ L
∂ h
2
∂ L
∂ h
1
=
∂ L
∂ h
2
∂ h2
∂ h
1
∂ L
∂W
2
=
∂ L
∂ h
2
∂ h
2
∂ W
2
∂ L
∂ o
∂ L
∂ h2
Ranzato
max 0,W
1
x max0,W
2
h
1
 W 3
h2

41
x
Loss
y
Given we can compute now:
∂ L
∂ h
1
∂ L
∂W
1
=
∂ L
∂ h
1
∂ h1
∂ W
1
∂ L
∂ h
1
Ranzato
max 0,W
1
x max0,W
2
h
1

∂ L
∂ o
∂ L
∂ h
2
W 3
h2

42
Ranzato
Question: Does BPROP work with ReLU layers only?
Answer: Nope, any a.e. differentiable transformation works.
Question: What's the computational cost of BPROP?
Answer: About twice FPROP (need to compute gradients w.r.t. input
and parameters at every layer).
Note: FPROP and BPROP are dual of each other. E.g.,:
+
+
FPROP BPROP
SUMCOPY

43
Optimization
Stochastic Gradient Descent (on mini-batches):
  −
∂ L
∂
,∈0,1
Stochastic Gradient Descent with Momentum:
 0.9 
∂ L
∂
  −
Ranzato
Note: there are many other variants...

44
Outline
Ranzato
Examples
Tips

45
Example: 200x200 image
40K hidden units
~2B parameters!!!
- Spatial correlation is local
- Waste of resources + we have not enough
training samples anyway..
Fully Connected Layer
Ranzato

46
Locally Connected Layer
40K hidden units
Filter size: 10x10
4M parameters
Ranzato
Note: This parameterization is good
when input image is registered (e.g.,
face recognition).

47
STATIONARITY? Statistics is similar at
different locations
Ranzato
Note: This parameterization is good
when input image is registered (e.g.,
face recognition).
Locally Connected Layer
40K hidden units
Filter size: 10x10
4M parameters

48
Convolutional Layer
Share the same parameters across
different locations (assuming input is
stationary):
Convolutions with learned kernels
Ranzato

Convolutional Layer
RanzatoMathieu et al. “Fast training of CNNs through FFTs” ICLR 2014

Convolutional Layer
*
-1 0 1
-1 0 1
-1 0 1
Ranzato
=

66
Learn multiple filters.
E.g.: 200x200 image
100 Filters
Filter size: 10x10
10K parameters
Ranzato
Convolutional Layer

67
h j
n
=max 0,∑k =1
K
hk
n−1
∗wkj
n

Ranzato
Conv.
layer
h1
n−1
h2
n−1
h3
n−1
h1
n
h2
n
output
feature map
input feature
map
kernel
Convolutional Layer

68
h j
n
=max 0,∑k =1
K
hk
n−1
∗wkj
n

Ranzato
h1
n−1
h2
n−1
h3
n−1
h1
n
h2
n
output
feature map
input feature
map
kernel
Convolutional Layer

69
h j
n
=max 0,∑k =1
K
hk
n−1
∗wkj
n

Ranzato
h1
n−1
h2
n−1
h3
n−1
h1
n
h2
n
output
feature map
input feature
map
kernel
Convolutional Layer

70
Ranzato
Question: What is the size of the output? What's the computational
cost?
Answer: It is proportional to the number of filters and depends on the
stride. If kernels have size KxK, input has size DxD, stride is 1, and
there are M input feature maps and N output feature maps then:
- the input has size M@DxD
- the output has size N@(D-K+1)x(D-K+1)
- the kernels have MxNxKxK coefficients (which have to be learned)
- cost: M*K*K*N*(D-K+1)*(D-K+1)
Question: How many feature maps? What's the size of the filters?
Answer: Usually, there are more output feature maps than input
feature maps. Convolutional layers can increase the number of
hidden units by big factors (and are expensive to compute).
The size of the filters has to match the size/scale of the patterns we
want to detect (task dependent).
Convolutional Layer

71
A standard neural net applied to images:
- scales quadratically with the size of the input
- does not leverage stationarity
Solution:
- connect each hidden unit to a small patch of the input
- share the weight across space
This is called: convolutional layer.
A network with convolutional layers is called convolutional network.
LeCun et al. “Gradient-based learning applied to document recognition” IEEE 1998
Key Ideas

72
Let us assume filter is an “eye” detector.
Q.: how can we make the detection robust to
the exact location of the eye?
Pooling Layer
Ranzato

73
By “pooling” (e.g., taking max) filter
responses at different locations we gain
robustness to the exact spatial location
of features.
Ranzato
Pooling Layer

74
Ranzato
Pooling Layer: Examples
h j
n
 x , y=maxx∈N x , y∈N y  hj
n−1
x ,y
Max-pooling:
h j
n
 x , y=1/ K ∑x∈N  x , y ∈N  y
hj
n−1
x ,y
Average-pooling:
h j
n
 x , y=∑x ∈N  x, y∈N  y
hj
n−1
x ,y2
L2-pooling:
h j
n
 x , y=∑k ∈N  j
hk
n−1
 x , y2
L2-pooling over features:

75
Ranzato
Pooling Layer
Question: What is the size of the output? What's the computational
cost?
Answer: The size of the output depends on the stride between the
pools. For instance, if pools do not overlap and have size KxK, and
the input has size DxD with M input feature maps, then:
- output is M@(D/K)x(D/K)
- the computational cost is proportional to the size of the input
(negligible compared to a convolutional layer)
Question: How should I set the size of the pools?
Answer: It depends on how much “invariant” or robust to distortions
we want the representation to be. It is best to pool slowly (via a few
stacks of conv-pooling layers).

76
Ranzato
Pooling Layer: Interpretation
Task: detect orientation L/R
Conv layer:
linearizes manifold

77
Ranzato
Pooling Layer: Interpretation
Conv layer:
linearizes manifold
Pooling layer:
collapses manifold
Task: detect orientation L/R

78
Ranzato
Pooling Layer: Receptive Field Size
Conv.
layer
hn−1 h
n
Pool.
layer
h
n1
If convolutional filters have size KxK and stride 1, and pooling layer
has pools of size PxP, then each unit in the pooling layer depends
upon a patch (at the input of the preceding conv. layer) of size:
(P+K-1)x(P+K-1)

79
Ranzato
Pooling Layer: Receptive Field Size
Conv.
layer
hn−1 h
n
Pool.
layer
h
n1
If convolutional filters have size KxK and stride 1, and pooling layer
has pools of size PxP, then each unit in the pooling layer depends
upon a patch (at the input of the preceding conv. layer) of size:
(P+K-1)x(P+K-1)

80
Local Contrast Normalization
h
i1
 x , y=
hi
x , y−mi
N x , y
max  ,
i
N x , y
Ranzato

81
We want the same response.
Ranzato
h
i1
 x , y=
hi
x , y−mi
N x , y
max  ,
i
N x , y

82
Performed also across features
and in the higher layers..
Effects:
– improves invariance
– improves optimization
– increases sparsity
Note: computational cost is
negligible w.r.t. conv. layer.
Ranzato
h
i1
 x , y=
hi
x , y−mi
N x , y
max  ,
i
N x , y

83
ConvNets: Typical Stage
Convol. LCN Pooling
One stage (zoom)
courtesy of
K. Kavukcuoglu Ranzato

84
Convol. LCN Pooling
One stage (zoom)
Conceptually similar to: SIFT, HoG, etc.
Ranzato
ConvNets: Typical Stage

85courtesy of
K. Kavukcuoglu Ranzato
Note: after one stage the number of feature maps is usually increased
(conv. layer) and the spatial resolution is usually decreased (stride in
conv. and pooling layers). Receptive field gets bigger.
Reasons:
- gain invariance to spatial translation (pooling layer)
- increase specificity of features (approaching object specific units)

86
Convol. LCN Pooling
One stage (zoom)
Fully Conn.
Layers
Whole system
1st
stage 2nd
stage 3rd
stage
Input
Image
Class
Labels
Ranzato
ConvNets: Typical Architecture

87
SIFT → K-Means → Pyramid Pooling → SVM
SIFT → Fisher Vect. → Pooling → SVM
Lazebnik et al. “...Spatial Pyramid Matching...” CVPR 2006
Sanchez et al. “Image classifcation with F.V.: Theory and practice” IJCV 2012
Conceptually similar to:
Ranzato
Fully Conn.
Layers
Whole system
1st
stage 2nd
stage 3rd
stage
Input
Image
Class
Labels
ConvNets: Typical Architecture

88
ConvNets: Training
Algorithm:
Given a small mini-batch
- F-PROP
- B-PROP
- PARAMETER UPDATE
All layers are differentiable (a.e.).
We can use standard back-propagation.
Ranzato

89
Ranzato
Note: After several stages of convolution-pooling, the spatial resolution
is greatly reduced (usually to about 5x5) and the number of feature
maps is large (several hundreds depending on the application).
It would not make sense to convolve again (there is no translation
invariance and support is too small). Everything is vectorized and fed
into several fully connected layers.
If the input of the fully connected layers is of size Nx5x5, the first fully
connected layer can be seen as a conv. layer with 5x5 kernels.
The next fully connected layer can be seen as a conv. layer with 1x1
kernels.

90
Ranzato
NxMxM, M small
H hidden units /
Hx1x1 feature maps
Fully conn. layer /
Conv. layer (H kernels of size NxMxM)

91
NxMxM, M small
H hidden units /
Hx1x1 feature maps
Fully conn. layer /
Conv. layer (H kernels of size NxMxM)
K hidden units /
Kx1x1 feature maps
Fully conn. layer /
Conv. layer (K kernels of size Hx1x1)

92
Viewing fully connected layers as convolutional layers enables efficient
use of convnets on bigger images (no need to slide windows but unroll
network over space as needed to re-use computation).
CNNInput
Image
CNN
Input
Image
Input
Image
TRAINING TIME
TEST TIME
x
y

93
Viewing fully connected layers as convolutional layers enables efficient
use of convnets on bigger images (no need to slide windows but unroll
network over space as needed to re-use computation).
CNNInput
Image
CNN
Input
Image
TRAINING TIME
TEST TIME
x
y
Unrolling is order of magnitudes more eficient than sliding windows!
CNNs work on any image size!

94
ConvNets: Test
At test time, run only is forward mode (FPROP).
Ranzato

95
Fancier Architectures: Multi-Scale
Farabet et al. “Learning hierarchical features for scene labeling” PAMI 2013

96
Fancier Architectures: Multi-Modal
Frome et al. “Devise: a deep visual semantic embedding model” NIPS 2013
CNN
Text
Embedding
tiger
Matching
shared representation

97
Fancier Architectures: Multi-Task
Zhang et al. “PANDA..” CVPR 2014
Conv
Norm
Pool
Conv
Norm
Pool
Conv
Norm
Pool
Conv
Norm
Pool
Fully
Conn.
Fully
Conn.
Fully
Conn.
Fully
Conn.
...
Attr. 1
Attr. 2
Attr. N
image

98
Fancier Architectures: Multi-Task
Osadchy et al. “Synergistic face detection and pose estimation..” JMLR 2007

99
Fancier Architectures: Generic DAG
Any DAG of differentialble
modules is allowed!

100
Fancier Architectures: Generic DAG
If there are cycles (RNN), one needs to un-roll it.
Graves “Offline Arabic handwriting recognition..” Springer 2012

101
Outline
Ranzato
Examples
Tips

102
CONV NETS: EXAMPLES
- OCR / House number & Traffic sign classification
Ciresan et al. “MCDNN for image classification” CVPR 2012
Wan et al. “Regularization of neural networks using dropconnect” ICML 2013
Goodfellow et al. “Multi-digit nuber recognition from StreetView...” ICLR 2014
Jaderberg et al. “Synthetic data and ANN for natural scene text recognition” arXiv 2014

103
CONV NETS: EXAMPLES
- Texture classification
Sifre et al. “Rotation, scaling and deformation invariant scattering...” CVPR 2013

104
CONV NETS: EXAMPLES
- Pedestrian detection
Sermanet et al. “Pedestrian detection with unsupervised multi-stage..” CVPR 2013

105
CONV NETS: EXAMPLES
- Scene Parsing
Farabet et al. “Learning hierarchical features for scene labeling” PAMI 2013
RanzatoPinheiro et al. “Recurrent CNN for scene parsing” arxiv 2013

106
CONV NETS: EXAMPLES
- Segmentation 3D volumetric images
Ciresan et al. “DNN segment neuronal membranes...” NIPS 2012
Turaga et al. “Maximin learning of image segmentation” NIPS 2009 Ranzato

107
CONV NETS: EXAMPLES
- Action recognition from videos
Taylor et al. “Convolutional learning of spatio-temporal features” ECCV 2010
Karpathy et al. “Large-scale video classification with CNNs” CVPR 2014
Simonyan et al. “Two-stream CNNs for action recognition in videos” arXiv 2014

108
CONV NETS: EXAMPLES
- Robotics
Sermanet et al. “Mapping and planning ...with long range perception” IROS 2008

109
CONV NETS: EXAMPLES
- Denoising
Burger et al. “Can plain NNs compete with BM3D?” CVPR 2012
original noised denoised
Ranzato

110
CONV NETS: EXAMPLES
- Dimensionality reduction / learning embeddings
Hadsell et al. “Dimensionality reduction by learning an invariant mapping” CVPR 2006

111
CONV NETS: EXAMPLES
- Object detection
Sermanet et al. “OverFeat: Integrated recognition, localization, ...” arxiv 2013
Szegedy et al. “DNN for object detection” NIPS 2013 Ranzato
Girshick et al. “Rich feature hierarchies for accurate object detection...” arxiv 2013

Dataset: ImageNet 2012
Deng et al. “Imagenet: a large scale hierarchical image database” CVPR 2009

114
Architecture for Classification
CONV
LOCAL CONTRAST NORM
MAX POOLING
FULLY CONNECTED
LINEAR
CONV
LOCAL CONTRAST NORM
MAX POOLING
CONV
CONV
CONV
MAX POOLING
FULLY CONNECTED
Krizhevsky et al. “ImageNet Classification with deep CNNs” NIPS 2012
category
prediction
input
Ranzato

115CONV
LOCAL CONTRAST NORM
MAX POOLING
FULLY CONNECTED
LINEAR
CONV
LOCAL CONTRAST NORM
MAX POOLING
CONV
CONV
CONV
MAX POOLING
FULLY CONNECTED
Total nr. params: 60M
4M
16M
37M
442K
1.3M
884K
307K
35K
Total nr. flops: 832M
4M
16M
37M
74M
224M
149M
223M
105M
Krizhevsky et al. “ImageNet Classification with deep CNNs” NIPS 2012
category
prediction
input
Ranzato
Architecture for Classification

116
Optimization
SGD with momentum:
Learning rate = 0.01
Momentum = 0.9
Improving generalization by:
Weight sharing (convolution)
Input distortions
Dropout = 0.5
Weight decay = 0.0005
Ranzato

117
Results: ILSVRC 2012
RanzatoKrizhevsky et al. “ImageNet Classification with deep CNNs” NIPS 2012

119
TEST
IMAGE
RETRIEVED IMAGES

120
Outline
Ranzato
Examples
Tips

121
Choosing The Architecture
Task dependent
Cross-validation
[Convolution → LCN → pooling]* + fully connected layer
The more data: the more layers and the more kernels
Look at the number of parameters at each layer
Look at the number of flops at each layer
Computational resources
Be creative :)
Ranzato

122
How To Optimize
SGD (with momentum) usually works very well
Pick learning rate by running on a subset of the data
Bottou “Stochastic Gradient Tricks” Neural Networks 2012
Start with large learning rate and divide by 2 until loss does not diverge
Decay learning rate by a factor of ~1000 or more by the end of training
Use non-linearity
Initialize parameters so that each feature across layers has
similar variance. Avoid units in saturation.
Ranzato

123
Improving Generalization
Weight sharing (greatly reduce the number of parameters)
Data augmentation (e.g., jittering, noise injection, etc.)
Dropout
Hinton et al. “Improving Nns by preventing co-adaptation of feature detectors”
arxiv 2012
Weight decay (L2, L1)
Sparsity in the hidden units
Multi-task (unsupervised learning)
Ranzato

124
ConvNets: till 2012
Loss
parameter
Common wisdom: training does not work
because we “get stuck in local minima”

125
ConvNets: today
Loss
parameter
Local minima are all similar, there are long plateaus,
it can take long time to break symmetries.
w w
input/output invariant to permutations
breaking ties
between parameters
W T
X
1
Saturating units
Dauphin et al. “Identifying and attacking the saddle point problem..” arXiv 2014

126
Like walking on a ridge between valleys
Neural Net Optimization is...

127
ConvNets: today
Loss
parameter
Local minima are all similar, there are long
plateaus, it can take long to break symmetries.
Optimization is not the real problem when:
– dataset is large
– unit do not saturate too much
– normalization layer

128
ConvNets: today
Loss
parameter
Today's belief is that the challenge is about:
– generalization
How many training samples to fit 1B parameters?
How many parameters/samples to model spaces with 1M dim.?
– scalability

129
data
flops/s
capacity
T
IM
E
ConvNets: Why so successful today?
TIME
As time goes by, we get more data and more
flops/s. The capacity of ML models should grow
accordingly.
1K 1M 1B
1M
100M
10T
Ranzato

130
data
capacity
T
IM
E
ConvNets: Why so successful today?
CNN were in many ways
premature, we did not have
enough data and flops/s to
train them.
They would overfit and be
too slow to tran (apparent
local minima).
flops/s
1B
NOTE: methods have to
be easily scalable!
Ranzato

131
Good To Know
Check gradients numerically by finite differences
Visualize features (feature maps need to be uncorrelated)
and have high variance.
samples
hidden unit
Good training: hidden units are sparse across samples
and across features. Ranzato

132
samples
hidden unit
Bad training: many hidden units ignore the input and/or
exhibit strong correlations. Ranzato
Good To Know

133
Visualize parameters
Good training: learned filters exhibit structure and are uncorrelated.
GOOD BADBAD BAD
too noisy too correlated lack structure
Ranzato
Good To Know
Zeiler, Fergus “Visualizing and understanding CNNs” arXiv 2013
Simonyan, Vedaldi, Zisserman “Deep inside CNNs: visualizing image classification models..” ICLR 2014

134
Visualize parameters
Measure error on both training and validation set.
Test on a small subset of the data and check the error → 0.
Ranzato
Good To Know

135
What If It Does Not Work?
Training diverges:
Learning rate may be too large → decrease learning rate
BPROP is buggy → numerical gradient checking
Parameters collapse / loss is minimized but accuracy is low
Check loss function:
Is it appropriate for the task you want to solve?
Does it have degenerate solutions? Check “pull-up” term.
Network is underperforming
Compute flops and nr. params. → if too small, make net larger
Visualize hidden units/params → fix optmization
Network is too slow
Compute flops and nr. params. → GPU,distrib. framework, make
net smaller
Ranzato

136
Summary Part I
Deep Learning = learning hierarhical models. ConvNets are the
most successful example. Leverage large labeled datasets.
Optimization
Don't we get stuck in local minima? No, they are all the same!
In large scale applications, local minima are even less of an issue.
Scaling
GPUs
Distributed framework (Google)
Better optimization techniques
Generalization on small datasets (curse of dimensionality):
data augmentation
weight decay
dropout
unsupervised learning
multi-task learning
Ranzato

137
SOFTWARE
Torch7: learning library that supports neural net training
http://www.torch.ch
http://code.cogbits.com/wiki/doku.php (tutorial with demos by C. Farabet)
https://github.com/sermanet/OverFeat
Python-based learning library (U. Montreal)
- http://deeplearning.net/software/theano/ (does automatic differentiation)
Caffe (Yangqing Jia)
– http://caffe.berkeleyvision.org
Efficient CUDA kernels for ConvNets (Krizhevsky)
– code.google.com/p/cuda-convnet
Ranzato

138
REFERENCES
Convolutional Nets
– LeCun, Bottou, Bengio and Haffner: Gradient-Based Learning Applied to Document
Recognition, Proceedings of the IEEE, 86(11):2278-2324, November 1998
- Krizhevsky, Sutskever, Hinton “ImageNet Classification with deep convolutional
neural networks” NIPS 2012
– Jarrett, Kavukcuoglu, Ranzato, LeCun: What is the Best Multi-Stage Architecture for
Object Recognition?, Proc. International Conference on Computer Vision (ICCV'09),
IEEE, 2009
- Kavukcuoglu, Sermanet, Boureau, Gregor, Mathieu, LeCun: Learning Convolutional
Feature Hierachies for Visual Recognition, Advances in Neural Information
Processing Systems (NIPS 2010), 23, 2010
– see yann.lecun.com/exdb/publis for references on many different kinds of
convnets.
– see http://www.cmap.polytechnique.fr/scattering/ for scattering networks (similar to
convnets but with less learning and stronger mathematical foundations)
– see http://www.idsia.ch/~juergen/ for other references to ConvNets and LSTMs.
Ranzato

139
REFERENCES
Applications of Convolutional Nets
– Farabet, Couprie, Najman, LeCun. Scene Parsing with Multiscale Feature Learning,
Purity Trees, and Optimal Covers”, ICML 2012
– Pierre Sermanet, Koray Kavukcuoglu, Soumith Chintala and Yann LeCun:
Pedestrian Detection with Unsupervised Multi-Stage Feature Learning, CVPR 2013
- D. Ciresan, A. Giusti, L. Gambardella, J. Schmidhuber. Deep Neural Networks
Segment Neuronal Membranes in Electron Microscopy Images. NIPS 2012
- Raia Hadsell, Pierre Sermanet, Marco Scoffier, Ayse Erkan, Koray Kavackuoglu, Urs
Muller and Yann LeCun. Learning Long-Range Vision for Autonomous Off-Road
Driving, Journal of Field Robotics, 26(2):120-144, 2009
– Burger, Schuler, Harmeling. Image Denoisng: Can Plain Neural Networks Compete
with BM3D?, CVPR 2012
– Hadsell, Chopra, LeCun. Dimensionality reduction by learning an invariant mapping,
CVPR 2006
– Bergstra et al. Making a science of model search: hyperparameter optimization in
hundred of dimensions for vision architectures, ICML 2013
Ranzato

140
REFERENCES
Latest and Greatest Convolutional Nets
– Girshick, Donahue, Darrell, Malick. “Rich feature hierarchies for accurate object
detection and semantic segmentation”, arXiv 2014
– Simonyan, Zisserman “Two-stream CNNs for action recognition in videos” arXiv
2014
- Cadieu, Hong, Yamins, Pinto, Ardila, Solomon, Majaj, DiCarlo. “DNN rival in
representation of primate IT cortex for core visual object recognition”. arXiv 2014
- Erhan, Szegedy, Toshev, Anguelov “Scalable object detection using DNN” CVPR
2014
- Razavian, Azizpour, Sullivan, Carlsson “CNN features off-the-shelf: and astounding
baseline for recognition” arXiv 2014
- Krizhevsky “One weird trick for parallelizing CNNs” arXiv 2014
Ranzato

141
REFERENCES
Deep Learning in general
– deep learning tutorial @ CVPR 2014 https://sites.google.com/site/deeplearningcvpr2014/
– deep learning tutorial slides at ICML 2013: icml.cc/2013/?page_id=39
– Yoshua Bengio, Learning Deep Architectures for AI, Foundations and Trends in
Machine Learning, 2(1), pp.1-127, 2009.
– LeCun, Chopra, Hadsell, Ranzato, Huang: A Tutorial on Energy-Based Learning, in
Bakir, G. and Hofman, T. and Schölkopf, B. and Smola, A. and Taskar, B. (Eds),
Predicting Structured Data, MIT Press, 2006
Ranzato
“Theory” of Deep Learning
– Mallat: Group Invariant Scattering, Comm. In Pure and Applied Math. 2012
– Pascanu, Montufar, Bengio: On the number of inference regions of DNNs with piece
wise linear activations, ICLR 2014
– Pascanu, Dauphin, Ganguli, Bengio: On the saddle-point problem for non-convex
optimization, arXiv 2014
- Delalleau, Bengio: Shallow vs deep Sum-Product Networks, NIPS 2011

143
Outline Part II
Theory: Energy-Based Models
Energy function
Loss function
Examples:
Supervised learning: neural nets
Unsupervised learning: sparse coding
Unsupervised learning: gated MRF
Conclusions
Ranzato

144
Energy:
LeCun et al. “Tutorial on Energy-based learning ...” Predicting Structure Data 2006
Ranzato et al. “A unified energy-based framework for unsup. learning” AISTATS 2007
Energy-Based Models: Energy Function
E y ; E y ; x ,or
unsupervised supervised

145
Energy:
E y ; E y ; x ,or
y can be
discrete
continuous
{

146
Energy:
E y ; E y ; x ,or
y can be
discrete
continuous
{
We will refer to the
unsupervised/continous case, but
much of the following applies to
the other cases as well.

147
Energy should be lower for desired output
E
y
Ranzato

148
Make energy lower at the desired output
E
yy∗
BEFORE TRAINING
Ranzato

149
Make energy lower at the desired output
E
yy∗
AFTER TRAINING
Ranzato

150
Examples of energy function:
PCA
Linear binary classifier
Neural net binary classifier
E y=∥y−W W
T
y∥2
2
E y ; x=−yW T
x
y∈{−1,1}
E y ; x=−yW 2
T
f x ;W 1

151
Energy-Based Models: Loss Function
Loss is a function of the energy
Minimizing the loss over the training set yields
the desired energy landscape.

∗
=min∑p
LE y
p
;
Examples of loss function:
PCA
Logistic regression classifier
E y=∥y−W W T
y∥2
2
E y ; x=−yW
T
x
LE y=E y
LE y ; x=log 1expE  y ; x

152

∗
=min∑p
LE y
p
;
How to design loss good functions?
Ranzato

153

∗
=min∑p
LE y
p
;
E
y
L=E  y

154

∗
=min∑p
LE y
p
;
E
y
L=E  y

155

∗
=min∑p
LE y
p
;
E
y
L=E  y
BAD LOSS
Energy is degenerate:
low everywhere!

156

∗
=min∑p
LE y
p
;
L=E  ylog∑y
exp−Ey
E
y

157

∗
=min∑p
LE y
p
;
exp−Ey
E
y
GOOD LOSS
but potentially
very expensive

158
Strategies to Shape E: #1
Pull down the correct answer and pull up
everywhere else.
E
y
exp−E y
PROS
It produces calibrated probabilities.
CONS
Expensive to compute when y is discrete and high dimensional.
Generally intractable when y is continuous.
Negative
Log-Likelihood
p y=
e
−E  y
∑u
e
−Eu

159
carefully chosen points.
L=max0,m−E y−E y, e.g. y=miny≠ y E  y
E
yy
E.g.: Contrastive Divergence, Ratio Matching, Noise Contrastive
Estimation, Minimum Probability Flow...
Hinton et al. “A fast learning algorithm for DBNs” Neural Comp. 2008
Gutmann et al. “Noise contrastive estimation of unnormalized...” JMLR 2012
Hyvarinen “Some extensions of score matchine” Comp Stats 2007
Sohl-Dickstein et al. “Minimum probability flow learning” ICML 2011

160
carefully chosen points.
PROS
Efficient.
CONS
The criterion to pick where to pull up is tricky (overall in high
dimensional spaces): trades-off computational and statistical efficiency.
L=max0,m−E y−E y, e.g. y=miny≠ y E  y
E
yy

161
Pull down the correct answer and increase local
curvature.
E
y
Score Matching
L=∂ E  y
∂ y 
2

∂2
E  y
∂ y2
Hyvarinen “Estimation of non-normalized statistical models using score matching”
JMLR 2005

162
curvature.
E Score Matching
y
Hyvarinen “Estimation of non-normalized statistical models using score matching”
JMLR 2005
L=∂ E  y
∂ y 
2

∂2
E  y
∂ y2

163
curvature.
PROS
Efficient in continuous but not too high dimensional spaces.
CONS
Very complicated to compute and not practical in very high
dimensional spaces. Not applicable in discrete spaces.
E Score Matching
y
L=∂ E  y
∂ y 
2

∂2
E  y
∂ y2

164
Pull down correct answer and have global
constrain on the energy: only few minima exist
E
y
PCA, ICA,
sparse coding,...
PROS
Efficient in continuous, high dimensional spaces.
L=E  y
CONS
Need to design good global constraints. Used in unsup. learning only.

165
E
y
PCA, ICA,
sparse coding,...
L=E  y
PROS
Efficient in continuous, high dimensional spaces.
CONS
Need to design good global constraints. Used in unsup. learning only.

166
Typical methods (unsup. learning):
Use compact internal representation (PCA)
Have finite number of internal states (K-Means)
Use sparse codes (ICA, sparse coding)
Ranzato

167
INPUT SPACE: FEATURE SPACE:
f  x ,h
g x ,h
hx
Ranzato
training sample
input data point which is not a training sample
feature (code)

168
Wh
f  x ,h
hxINPUT SPACE: FEATURE SPACE:
E.g. K-means: is 1-of-N.h
Since there are very few “codes” available and the
energy (MSE) is minimized on the training set, the
energy must be higher elsewhere.
Ranzato

169
F Denoising AE
L=E  y
Make the observed an attractor state of some
energy function. Need only to define a dynamics.
y
E.g.:
L=
1
2
∥y−y∥
2
y=W 2 W 1 yn, n∈N 0, I 
y
Vincent et al. “Extracting and composing robust features with denoising autoencoders”
ICML 2008
Training samples must be
stable points (local minima)
and attractors.

170
Denoising AE
E.g.:
yn
and attractors.
F
Kamyshanska et al. “On autoencoder scoring” ICML 2013
y
L=E  y
y
y=W 2 W 1 yn, n∈N 0, I 
L=
1
2
∥y−y∥
2
Ranzato

171
Denoising AE
E.g.:
F
and attractors.
y
L=E  y
y yn
y=W 2 W 1 yn, n∈N 0, I 
L=
1
2
∥y−y∥
2
Ranzato

172
PROS
Efficient in high dimensional spaces.
CONS
Need to pick noise distribution. May need to pick many noisy points.
Denoising AEF
y
L=E  y
y yn

173
Loss: summary
Goal of loss: make energy lower for correct answer.
Different losses choose differently how to “pull-up”
Pull-up all points
Pull up one or a few points only
Make observations minima & increase curvature
Add global constraints/penalties on internal states
Define a dynamics with observations at the minima
Choice of loss depends on desired landscape,
computational budget, domain of input
(discrete/continouus), task, etc.
Ranzato

174
Final Notes on EBMs
EBMs apply to any predictor (shallow & deep).
EBMs subsume graphical models (e.g., use
strategy #1 or #2 to “pull-up”).
EBM is general framework to design good loss
functions.
Ranzato

175
Outline
Ranzato
Energy function
Loss function
Examples:
Conclusions

176
Perceptron
Neural Net
Boosting
SVM
GMM
ΣΠ
BayesNP
CNN
Recurrent
Neural Net
Autoencoder
Neural Net
Sparse Coding
Restricted BMDBN
Autoencoder
UNSUPERVISED
SUPERVISED
DEEP
SHALLOWPROBABILISTIC
Loss: type #1

177
Neural Nets for Classification
h2h1x h3
Loss
y
max 0,W 1 x max 0,W 2 h1 W 3 h2
LE y ; x=log 1expE  y ; x
E y ; x=−y h3
{W 1,
∗
W 2,
∗
W 3
∗
}=arg minW 1,W 2,W 3
LE y ; x
Loss: type #1
Ranzato

178
Perceptron
Neural Net
Boosting
SVM
GMM
ΣΠ
BayesNP
CNN
Recurrent
Neural Net
Autoencoder
Neural Net
Sparse Coding
Restricted BMDBN
Autoencoder
UNSUPERVISED
SUPERVISED
DEEP
SHALLOWPROBABILISTIC Loss: type #4

179
Energy & latent variables
Energy may have latent variables.
Two major approaches:
Marginalization (intractable if space is large)
Minimization
E y=minh E y ,h
E y=−log ∑h
exp−E y ,h
Ranzato

180
Sparse Coding
L= E x ;W 
E x ,h;W =
1
2
∥x−W h∥2
2
∥h∥1
E x ;W =minh E x ,h;W  Loss type #4: energy loss
with (sparsity) constraints.
Ranzato et al. NIPS 2006Olshausen & Field, Nature 1996

181
Inference
Prediction of latent variables
h∗
=arg minh E x ,h;W 
Inference is an iterative process.
E x ,h;W =
1
2
∥x−W h∥2
2
∥h∥1
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182
Inference
Prediction of latent variables
h∗
=arg minh E x ,h;W 
Inference is an iterative process.
E x ,h;W =
1
2
∥x−W h∥2
2
∥h∥1
Q.: Is it possible to make inference more efficient?
A.: Yes, by training another module to directly predict
Kavukcuoglu et al. “Predictive Sparse Decomposition” ArXiv 2008

183
Inference in Sparse Coding
E x ,h=
1
2
∥x−W 2 h∥2
2
∥h∥1
x
h
x
h
W
arg minh E
Ranzato

184
E x ,h=
1
2
∥x−W 2 h∥2
2
∥h∥1
W 2 h
∥x−W 2 h∥2
2
∥h∥1
h
x
Inference in Sparse Coding
Ranzato

185
Learning To Perform Fast Inference
E x ,h=
1
2
∥x−W 2 h∥2
2
∥h∥1
1
2
∥h−g x ;W 1∥2
2
g x ;W 1
∥h−g x ;W 1∥2
2
h
x
Ranzato

186
Predictive Sparse Decomposition
E x ,h=
1
2
∥x−W 2 h∥2
2
∥h∥1
1
2
∥h−g x ;W 1∥2
2
g x ;W 1
W 2 h
∥x−W 2 h∥2
2
∥h−g x ;W 1∥2
2
∥h∥1
h
x
Ranzato

187
Sparse Auto-Encoders
Example: Predictive Sparse Decomposition
E x ,h=
1
2
∥x−W 2 h∥2
2
∥h∥1
1
2
∥h−g x ;W 1∥2
2
TRAINING:
For every sample:
Initialize
(E) Infer optimal latent variables:
(M) Update parameters
h=g  x ;W 1
h∗
=minh E x ,h;W 
W 1 ,W 2
Inference at test time (fast):
h∗
≈g x ;W 1
Ranzato

188
E x ,h=
1
2
∥x−W 2 h∥2
2
∥h∥1
1
2
∥h−g x ;W 1∥2
2
x
h
W x h
alternative graphical representations
Predictive Sparse Decomposition
Ranzato

189
Gregor et al. “Learning fast approximations of sparse coding” ICML 2010
LISTA
W 1
W 2
∥x−W 2 h∥2
2
∥h−g x ;W 1∥2
2
∥h∥1
h
x
++W 3 W 3 W 3
Ranzato

190
KEY IDEAS
Inference can require expensive optimization
We may approximate exact inference well by using a non-
linear function (learn optimal approximation to perform fast
inference)
The original model and the fast predictor can be trained
jointly
Rolfe et al. “Discriminative Recurrent Sparse Autoencoders” ICLR 2013
Szlam et al. “Fast approximations to structured sparse coding...” ECCV 2012
Gregor et al. “Structured sparse coding via lateral inhibition” NIPS 2011
Kavukcuoglu et al. “Learning convolutonal feature hierarchies..” NIPS 2010
Ranzato

191
Outline
Energy function
Loss function
Examples:
Supervised learning: convnets
Other examples
Practical tricks
Ranzato

192
Perceptron
Neural Net
Boosting
SVM
GMM
ΣΠ
BayesNP
CNN
Recurrent
Neural Net
Autoencoder
Neural Net
Sparse Coding
Restricted BMDBN
Autoencoder
UNSUPERVISED
SUPERVISED
DEEP
SHALLOWPROBABILISTIC
Loss: type #2

193
Probabilistic Models of Natural Images
INPUT SPACE LATENT SPACE
Training sample Latent vector
p x∣h=N meanh ,D 
- examples: PPCA, Factor Analysis, ICA, Gaussian RBM
p x∣h
Ranzato

194
input image
model does not represent well dependecies, only mean intensity
ph∣x p x∣h
generated image
latent variables
p x∣h=N meanh ,D 
- examples: PPCA, Factor Analysis, ICA, Gaussian RBM
Ranzato

195
p x∣h=N 0,Covarianceh
- examples: PoT, cRBM
p x∣h
Welling et al. NIPS 2003, Ranzato et al. AISTATS 10
Ranzato

196
Welling et al. NIPS 2003, Ranzato et al. AISTATS 10
model does not represent well mean intensity, only dependencies
Andy Warhol 1960
input image
ph∣x p x∣h
generated image
latent variables
p x∣h=N 0,Covarianceh
- examples: PoT, cRBM

197
p x∣h=N meanh ,Covariance h
- this is what we propose: mcRBM, mPoT
Ranzato et al. CVPR 10, Ranzato et al. NIPS 2010, Ranzato et al. CVPR 11
p x∣h
Ranzato

198
Ranzato et al. CVPR 10, Ranzato et al. NIPS 2010, Ranzato et al. CVPR 11
p x∣h
p x∣h=N meanh ,Covariance h
- this is what we propose: mcRBM, mPoT
Ranzato

199
PoT PPCA
Our model
N(0,Σ) N(m,I)
N(m,Σ)
Ranzato

200
Deep Gated MRF
Layer 1:
E x ,h
c
,h
m
=
1
2
x ' 
−1
x
pair-wise MRF
x p xq
Ranzato et al. “Modeling natural images with gated MRFs” PAMI 2013
p x ,hc
,hm
e−E x , h
c
,h
m

Ranzato

201
Deep Gated MRF
Layer 1:
E x ,h
c
,h
m
=
1
2
x ' C C ' x
pair-wise MRF
x p xq
F
Ranzato et al. “Modeling natural images with gated MRFs” PAMI 2013 Ranzato

202
Deep Gated MRF
Layer 1:
E x ,h
c
,h
m
=
1
2
x ' C [diag h
c
]C ' x
gated MRF
x p xq
hk
c
CC
F
F
Ranzato et al. “Modeling natural images with gated MRFs” PAMI 2013 Ranzato

203
Deep Gated MRF
Layer 1:
E x ,h
c
,h
m
=
1
2
x ' C [diag h
c
]C ' x
1
2
x' x−x' W h
m
x p xq
h j
m
W
CC
F
M
hk
c
N
gated MRF
p x∫h
c ∫h
m e−E x ,h
c
, h
m


204
Deep Gated MRF
Layer 1:
E x ,h
c
,h
m
=
1
2
x ' C [diag h
c
]C ' x
1
2
x' x−x' W h
m
Inference of latent variables: just a forward pass
Generation: sampling from multi-variate Gaussian
p x∣hc
,hm
=N Whm
, 

−1
=C diag [h
c
]C 'I
phk
c
=1∣x=−
1
2
Pk C ' x
2
bk 
phj
m
=1∣x= W j ' xb j

205
Deep Gated MRF: Training
Layer 1:
E x ,h
c
,h
m
=
1
2
x ' C [diag h
c
]C ' x
1
2
x' x−x' W h
m
Training by maximum likelihood (PCD):
p x=
∫h
m
, h
c e
−E x , h
m
, h
c

∫x ,h
m
, h
c e
−Ex ,h
m
,h
c

Loss type #2
Since integrating over the input space is intractable we use:

206
∂ F
∂ w
training sample
F= - log(p(x)) + K
p x=
e−F x
∫x
e−F  x
F x=−log∫h
m
, h
c e−E x , h
m
, h
c

free energy

207
HMC dynamics
∂ F
∂ w
training sample
F= - log(p(x)) + K
p x=
e−F x
∫x
e−F  x
m
, h
c e−E x , h
m
, h
c

free energy

208
∂ F
∂ w
training sample
F= - log(p(x)) + K HMC dynamics
p x=
e−F x
∫x
e−F  x
m
, h
c e−E x , h
m
, h
c

free energy

209
∂ F
∂ w
training sample
p x=
e−F x
∫x
e−F  x
m
, h
c e−E x , h
m
, h
c

free energy

210
∂ F
∂ w
training sample
p x=
e−F x
∫x
e−F  x
m
, h
c e−E x , h
m
, h
c

free energy

211
∂ F
∂ w
training sample
p x=
e−F x
∫x
e−F  x
m
, h
c e−E x , h
m
, h
c

free energy

212
∂ F
∂ w
p x=
e−F x
∫x
e−F  x
m
, h
c e−E x , h
m
, h
c

free energy

213
∂ F
∂ w
weight update
∂ F
∂ w
sampledata
point
w  w− − 
∂ F
∂ w
∣sample
∂ F
∂ w
∣data
F= - log(p(x)) + K
p x=
e−F x
∫x
e−F  x
m
, h
c e−E x , h
m
, h
c

free energy

214
∂ F
∂ w
∂ F
∂ w
sampledata
point
w  w− − 
∂ F
∂ w
∣sample
∂ F
∂ w
∣data
F= - log(p(x)) + K weight update
p x=
e−F x
∫x
e−F  x
m
, h
c e−E x , h
m
, h
c

free energy

215
w  w− − 
∂ F
∂ w
∣sample
∂ F
∂ w
∣data
Start dynamics from previous point
data
point
sample
F= - log(p(x)) + K
p x=
e−F x
∫x
e−F  x
m
, h
c e−E x , h
m
, h
c

free energy

216
Deep Gated MRF
Layer 1
Layer 2
input
h2
Ranzato

217
Deep Gated MRF
Layer 1
h2
Layer 2
input
h3
Layer 3
Ranzato

218
Gaussian model marginal wavelet
from Simoncelli 2005
Pair-wise MRF FoE
from Schmidt, Gao, Roth CVPR 2010
Sampling High-Resolution Images

219
Pair-wise MRF FoE
gMRF: 1 layer
Ranzato et al. PAMI 2013

220
Pair-wise MRF FoE
gMRF: 1 layer

221
Pair-wise MRF FoE
gMRF: 1 layer

222
Pair-wise MRF FoE
gMRF: 3 layer

223
Pair-wise MRF FoE
gMRF: 3 layer

224
Pair-wise MRF FoE
gMRF: 3 layer

225
Pair-wise MRF FoE
gMRF: 3 layer

226
Sampling After Training on Face Images
Original Input 1st
layer 2nd
layer 3rd
layer 4th
layer 10 times
unconstrained samples
conditional (on the left part of the face) samples
Ranzato et al. PAMI 2013 Ranzato

227
Expression Recognition Under Occlusion
Ranzato et al. PAMI 2013 Ranzato

228
Tang et al. Robust BM for decognition and denoising CVPR 2012 Ranzato

229
Pros Cons
Feature extraction is fast
Unprecedented generation
quality
Advances models of natural
images
Trains without labeled data
Training is inefficient
Slow
Tricky
Sampling scales badly with
dimensionality
What's the use case of
generative models?
Conclusion
If generation is not required, other feature learning methods are
more efficient (e.g., sparse auto-encoders).
What's the use case of generative models?
Given enough labeled data, unsup. learning methods have
not produced more useful features.

230
Modeling Sequences: RNNs
http://www.cs.toronto.edu/~graves/handwriting.html

231
Structured Prediction: GTN
LeCun et al. “Gradient-based learning applied to document recognition” IEEE 1998

232
Summary Part II
Energy-based model: framework to understand and design loss
functions
Training is about shaping the energy. Dealing with high-
dimensional (continuous) spaces: explicit pull-up VS global
constraints (e.g., sparsity).
Unsupervised learning: a field in its infancy
Humas use it a lot
How to discover good compositional feature hierarchies?
How to scale to large dimensional spaces (curse of dimensionality)?
Hot research topic:
Scaling up to even larger datasets
Unsupervised learning
Multi-modal & multi-task learning
Video
Structure prediction
Ranzato

233
Questions
A ReLU layer computes: h = max(0, W x + b), where x is a D dimensional vector, h
and b are N dimensional vectors and W is a matrix of size NxD. If dL/dh is the
derivative of the loss w.r.t. h, then backpropagation computes (in matlab notation):
a) the derivatives dL/dx = W' (dL/dh .* 1(h)), where 1(h) = 1 if h>0 o/w it is 0
b) the derivatives dL/dW = (dL/dh .* 1(h)) x' and dL/db = dL/dh .* 1(h)
c) both the derivatives in a) and b)
Ranzato
A convolutional network:
a) is well defined only when layers are everywhere differentiable
b) requires unsupervised learning even if the labeled dataset is very large
c) has usually many convolution/pooling/normalization layers followed by fully
connected layers
Sparse coding:
a) aims at extracting sparse features that are good at reconstructing the input
and it does not need labels for training; the dimensionality of the feature vector is
usually higher than the input.
b) requires to have lots of images with their corresponding labels
c) can be interpreted as a graphical model, and inference of the latent variables
(sparse codes) is done by marginalization.

Lecture 06 marco aurelio ranzato - deep learning

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Lecture 06 marco aurelio ranzato - deep learning