Introduction to deep learning

Outline
• Introduction
• Supervised Learning
– Convolutional Neural Network
– Sequence Modelling: RNN and its extensions
• Unsupervised Learning
– Autoencoder
– Stacked Denoising Autoencoder
• Reinforcement Learning
– Deep Reinforcement Learning
– Two applications: Playing Atari & AlphaGo

Introduction
• Traditional pattern recognition models use hand-
crafted features and relatively simple trainable
classifier.
• This approach has the following limitations:
– It is very tedious and costly to develop hand-
crafted features
– The hand-crafted features are usually highly
dependents on one application, and cannot be
transferred easily to other applications
hand-crafted
feature
extractor
“Simple”
Trainable
Classifier
output

Deep Learning
• Deep learning (a.k.a. representation learning) seeks to
learn rich hierarchical representations (i.e. features)
automatically through multiple stage of feature
learning process.
Low-level
features
output
Mid-level
features
High-level
features
Trainable
classifier
Feature visualization of convolutional net trained on ImageNet
(Zeiler and Fergus, 2013)

Learning Hierarchical
Representations
• Hierarchy of representations with increasing level of
abstraction. Each stage is a kind of trainable nonlinear
feature transform
• Image recognition
– Pixel → edge → texton → motif → part → object
• Text
– Character → word → word group → clause → sentence →
story
Low-
level
features
output
Mid-
level
features
High-level
features
Trainable
classifier
Increasing level of abstraction

The Mammalian Visual
Cortex is Hierarchical
• It is good to be inspired
by nature, but not too
much.
• We need to understand
which details are
important, and which
details are merely the
result of evolution.
• Each module in Deep
Learning transforms its
input representation into
a higher-level one, in a
way similar to human
cortex.(van Essen and Gallant, 1994)

Supervised Learning
• Convolutional Neural Network
• Sequence Modelling
– Why do we need RNN?
– What are RNNs?
– RNN Extensions
– What can RNNs can do?

Convolutional Neural Network
• Input can have very high dimension. Using a fully-connected
neural network would need a large amount of parameters.
• Inspired by the neurophysiological experiments conducted by
[Hubel & Wiesel 1962], CNNs are a special type of neural
network whose hidden units are only connected to local receptive
field. The number of parameters needed by CNNs is much
smaller.
Example: 200x200 image
a) fully connected: 40,000
hidden units => 1.6 billion
parameters
b) CNN: 5x5 kernel, 100
feature maps => 2,500
parameters

Three Stages of a
Convolutional Layer
1. Convolution stage
2. Nonlinearity: a
nonlinear transform
such as rectified
linear or tanh
3. Pooling: output a
summary statistics
of local input, such
as max pooling and
average pooling

Convolution Operation in CNN
• Input: an image (2-D array) x
• Convolution kernel/operator(2-D array of learnable parameters): w
• Feature map (2-D array of processed data): s
• Convolution operation in 2-D domains:

Multiple Convolutions
Usually there are multiple feature maps,
one for each convolution operator.

Non-linearity
Tanh(x) ReLU
tanh x =
ex
− e−x
ex + e−x
𝑓 𝑥 = max(0, 𝑥)

Pooling
• Common pooling operations:
– Max pooling: reports the maximum output within a rectangular
neighborhood.
– Average pooling: reports the average output of a rectangular
neighborhood (possibly weighted by the distance from the
central pixel).

Deep CNN: winner
of ImageNet 2012
• Multiple feature maps per convolutional layer.
• Multiple convolutional layers for extracting
features at different levels.
• Higher-level layers take the feature maps in
lower-level layers as input.
(Alex et al., 2012)

Deep CNN for Image
Classification
Try out a live demo at
http://demo.caffe.berkeleyvision.org/

Deep CNN in AlphaGO
Policy network:
• Input: 19x19, 48
input channels
• Layer 1: 5x5 kernel,
192 filters
• Layer 2 to 12: 3x3
kernel, 192 filters
• Layer 13: 1x1 kernel,
1 filter
Value network has
similar architecture to
policy network
(Silver et al, 2016)

Sequence Modelling
• Why do we need RNN?
• What are RNNs?
• RNN Extensions
• What can RNNs can do?

Why do we need RNNs?
The limitations of the Neural network (CNNs)
• Rely on the assumption of independence among the
(training and test) examples.
– After each data point is processed, the entire state of the
network is lost
• Rely on examples being vectors of fixed length
We need to model the data with temporal or sequential
structures and varying length of inputs and outputs
– Frames from video
– Snippets of audio
– Words pulled from sentences

Recurrent neural networks (RNNs) are connectionist models with the
ability to selectively pass information across sequence steps, while
processing sequential data one element at a time.
The simplest form of fully recurrent
neural network is an MLP with the
previous set of hidden unit activations
feeding back into the network along
with the inputs
ℎ 𝑡 = 𝑓𝐻 𝑊𝐼𝐻 𝑥 𝑡 + 𝑊𝐻𝐻ℎ(𝑡 − 1)
𝑦 𝑡 = 𝑓𝑂(𝑊𝐻𝑂ℎ(𝑡))
𝑓𝐻 and 𝑓𝑂 are the activation function for
hidden and output unit; 𝑊𝐼𝐻, 𝑊𝐻𝐻, and
𝑊𝐻𝑂 are connection weight matrices which
are learnt by training
Allow a ‘memory’ of previous inputs to persist in
the network’s internal state, and thereby
influence the network output
What are RNNs?

An unfolded recurrent network. Each node represents a layer of network units at a single time
step. The weighted connections from the input layer to hidden layer are labelled ‘w1’, those from
the hidden layer to itself (i.e. the recurrent weights) are labelled ‘w2’ and the hidden to output
weights are labelled‘w3’. Note that the same weights are reused at every time step. Bias weights
are omitted for clarity.
What are RNNs?
• The recurrent network can be converted into a
feed-forward network by unfolding over time

What are RNNs?
• Training RNNs (determine the parameters)
Back Propagation Through Time (BPTT) is often used to learn the RNN
BPTT is an extension of the back-propagation (BP)
𝑠𝑡 = tanh 𝑈𝑥 𝑡 + 𝑊𝑠𝑡−1
𝑦𝑡 = 𝑠𝑜𝑓𝑡𝑚𝑎𝑥(𝑉𝑠𝑡)
 The loss/error function of this network is
 The output of this RNN is 𝑦𝑡
𝐸𝑡 𝑦𝑡, 𝑦𝑡 = −𝑦𝑡log 𝑦𝑡
𝐸 𝑦, 𝑦 =
𝑡
𝐸𝑡(𝑦𝑡, 𝑦𝑡)
The error at
each time step
the total loss is
the sum of the
errors at each
time step

What are RNNs?
• Training RNNs (determine the parameters)
 The gradients of the error with respect to our parameters
Just like we sum up the errors, we also sum up the gradients at each
time step for one training example. For parameter 𝑊, the gradient is
𝜕𝐸
𝜕𝑊
=
𝑡
𝜕𝐸𝑡
𝜕𝑊
 The gradient at each time step
we use time 3 as an example
𝜕𝐸3
𝜕𝑊
=
𝜕𝐸3
𝜕 𝑦3
𝜕 𝑦3
𝜕𝑠3
𝜕𝑠3
𝜕𝑊
Chain Rule
𝑠3 = tanh(𝑈𝑥1 + 𝑊𝑠2)
𝑠3 depends on 𝑊and 𝑠1, we cannot simply
treat 𝑠2 a constant
𝜕𝐸3
𝜕𝑊
=
𝑘=0
3
𝜕𝐸3
𝜕 𝑦3
𝜕 𝑦3
𝜕𝑠3
𝜕𝑠3
𝜕𝑠 𝑘
𝜕𝑠 𝑘
𝜕𝑊
Apply Chain Rule again on 𝑠 𝑘

What are RNNs?
 Training RNNs (determine the parameters)
Becaise 𝑊 is used in every step up to the output we care about, we need to
back-propagate gradients from 𝑡 = 3 through the network all the way to 𝑡 = 0
𝜕𝐸3
𝜕𝑊
=
𝑘=0
3
𝜕𝐸3
𝜕 𝑦3
𝜕 𝑦3
𝜕𝑠3
𝜕𝑠3
𝜕𝑠 𝑘
𝜕𝑠 𝑘
𝜕𝑊

What are RNNs?
 The vanishing gradient problem
To understand why, let’s take a closer look at the gradient we calculated above:
𝜕𝐸3
𝜕𝑊
=
𝑘=0
3
𝜕𝐸3
𝜕 𝑦3
𝜕 𝑦3
𝜕𝑠3
𝜕𝑠3
𝜕𝑠 𝑘
𝜕𝑠 𝑘
𝜕𝑊
𝜕𝐸3
𝜕𝑊
=
𝑘=0
3
𝜕𝐸3
𝜕 𝑦3
𝜕 𝑦3
𝜕𝑠3
𝑗=𝑘+1
3
𝜕𝑠𝑗
𝜕𝑠𝑗−1
𝜕𝑠 𝑘
𝜕𝑊
Because the layers and time steps of deep neural
networks relate to each other through multiplication,
derivatives are susceptible to vanishing
Gradient contributions from “far away” steps become zero, and the
state at those steps doesn’t contribute to what you are learning: You
end up not learning long-range dependencies.

What are RNNs?
 How to sole the vanishing gradient problem?
Proper initialization of the matrix can reduce the effect of vanishing gradient
 Proper initialization of the 𝑊 matrix can reduce the effect of vanishing
gradients
 Use ReLU instead of tanh or sigmoid activation function
ReLU derivate is a constant of either 0 or 1, so it isn’t likely to suffer
from vanishing gradients
 Use Long Short-Term Memory or Gated Recurrent unit architectures
LSTM will be introduced later

ℎ 𝑡 = 𝑓(𝑊 𝑥ℎ 𝑥 𝑡 + 𝑊ℎℎℎ 𝑡−1 + 𝑏ℎ)
ℎ 𝑡 = 𝑓(𝑊 𝑥ℎ 𝑥 𝑡 + 𝑊ℎℎℎ 𝑡−1 + 𝑏ℎ)
𝑦𝑡 = 𝑊ℎ𝑦ℎ 𝑡 + 𝑊ℎ𝑦ℎ 𝑡 + 𝑏 𝑦
training
sequence
forwards and
backwards to
two separate
recurrent
hidden layers
past and future context
determines the output
An unfolded BRNN
RNN Extensions: Bidirectional
Recurrent Neural Networks
Traditional RNNs only model the dependence of the current state on
the previous state, BRNNs (Schuster and Paliwal, 1997) extend to
model dependence on both past states and future states.
For example: predicting a missing word in a sequence you want to
look at both the left and the right context.

A gating mechanism of the LSTM , which
generates the current hidden state by the paste
hidden state and current input ..It contains five
modules: input gate, new memory cell, forget
gate, final memory generation, and output gate.
RNN Extensions: Long
Short-term Memory
The vanishing gradient problem prevents standard RNNs from learning
long-term dependencies. LSTMs (Hochreiter and Schmidhuber, 1997)
were designed to combat vanishing gradients through a gating mechanism.

New memory cell
use the input word and the past hidden
state to generate a new memory which
includes aspects of the new input
𝑐𝑡 = tanh(𝑊 𝑐 𝑥𝑡 + 𝑈 𝑐ℎ 𝑡−1)
New memory
Short-term Memory
A gating mechanism of the LSTM

Forget gate
The forget gate looks at the input
word and the past hidden state and
makes an assessment on whether
the past memory cell is useful for
the computation of the current
memory cell
𝑓𝑡 = σ( 𝑊 𝑓 𝑥𝑡 + 𝑈 𝑓ℎ 𝑡−1)
Short-term Memory

Final memory cell
𝑖 𝑡
𝑓𝑡
𝑐𝑡−1
𝑐𝑡
𝑐𝑡 = 𝑓𝑡 ∘ 𝑐𝑡−1 + 𝑖 𝑡 ∘ 𝑐𝑡
This stage first takes the advice of
the forget gate ft and accordingly
forgets the past memory
ct−1. Similarly, it takes the advice
of the input gate 𝑖 𝑡 and accordingly
gates the new memory. It then
sums these two results to produce
the final memory
Short-term Memory

Output gate
𝑜𝑡 = 𝜎(𝑊𝑜 𝑥𝑡 + 𝑈 𝑜ℎ 𝑡−1)
This gate makes the
assessment regarding what
parts of the memory 𝑐𝑡 needs to
be exposed/present in the
hidden state ℎ 𝑡.
Short-term Memory

The hidden state
ℎ 𝑡 = 𝑜𝑡 ∘ tanh(𝑐𝑡)
Short-term Memory

RNN extensions: Long
Short-term memory
LSTMs contain information outside the normal flow of the
recurrent network in a gated cell. Information can be stored in,
written to, or read from a cell, much like data in a computer’s
memory. The cells learn when to allow data to enter, leave or be
deleted through the iterative process of making guesses, back-
propagating error, and adjusting weights via gradient descent.
Conclusions on LSTM

RNN extensions: Long
Short-term Memory
Why LSTM can combat the vanish gradient problem?
LSTMs help preserve the error that can be back-propagated
through time and layers. By maintaining a more constant error,
they allow recurrent nets to continue to learn over many time steps
(over 1000), thereby opening a channel to link causes and effects
remotely

What can RNNs can do?
Machine Translation Visual Question Answering

In machine translation, the input is a sequence of
words in source language, and the output is a
sequence of words in target language.
Encoder-decoder architecture for machine translation
Encoder: An RNN to encode
the input sentence into a
hidden state (feature)
Decoder: An RNN
with the hidden state
of the sentence in
source language as
the input and output
the translated
sentence
Machine Translation

Demo Website
VQA: Given an image and a natural language
question about the image, the task is to provide an
accurate natural language answer
Visual Question Answering
(VQA)
Picture from (Antol et al., 2015)

The output is to be conditioned on both image and textual
inputs. A CNN is used to encode the image and a RNN is
implemented to encode the sentence.
Visual Question Answering

Unsupervised Learning
• Autoencoders
• Deep Autoencoders
• Denoising Autoencoders
• Stacked Denoising Autoencoders

Autoencoders
An Autoencoder is a
feedforward neural network
that learns to predict the
input itself in the output.
𝑦(𝑖) = 𝑥(𝑖)
• The input-to-hidden part
corresponds to an
encoder
• The hidden-to-output part
corresponds to a decoder.

Deep Autoencoders
• A deep Autoencoder is
constructed by
extending the encoder
and decoder of
autoencoder with
multiple hidden layers.
• Gradient vanishing
problem: the gradient
becomes too small as
it passes back through
many layers
Diagram from (Hinton and Salakhutdinov, 2006)

Training Deep Autoencoders

Denoising Autoencoders
• By adding stochastic noise to the, it can force
Autoencoder to learn more robust features.

Training Denoising Autoencoder
The loss function of Denoising autoencoder:
where
Like deep Autoencoder, we can
stack multiple denoising
autoencoders layer-wisely to form
a Stacked Denoising
Autoencoder.

Training Denoising Autoencoder on
MNIST
• The following pictures show the difference between the
resulting filters of Denoising Autoencoder trained on
MNIST with different noise ratios.
No noise (noise ratio=0%) noise ratio=30%

Deep Reinforcement Learning
• Reinforcement Learning
• Deep Reinforcement Learning
• Applications
– Playing Atari Games
– AlphaGO

Reinforcement Learning
• What’s Reinforcement Learning?
Environment
Agent
{Observation, Reward} {Actions}
• Agent interacts with an environment and learns by maximizing a
scalar reward signal
• No labels or any other supervision signal.
• Previously suffering from hand-craft states or representation.

Policies and Value Functions
• Policy 𝜋 is a behavior function selecting actions
given states
𝑎 = 𝜋(s)
• Value function 𝑄 𝜋(s,a) is expected total reward 𝑟
from state s and action a under policy 𝜋
“How good is action 𝑎 in state 𝑠?”

Approaches To
Reinforcement Learning
• Policy-based RL
– Search directly for the optimal policy 𝜋∗
– Policy achieving maximum future reward
• Value-based RL
– Estimate the optimal value function 𝑄∗(s,a)
– Maximum value achievable under any policy
• Model-based RL
– Build a transition model of the environment
– Plan (e.g. by look-ahead) using model

Bellman Equation
• Value function can be unrolled recursively
• Optimal value function Q∗ (s, a) can be unrolled
recursively
• Value iteration algorithms solve the Bellman
equation

• Human
• So what’s DEEP RL?
Environment
{Actions}{Raw Observation, Reward}

• Represent value function by deep Q-network with
weights w
• Define objective function by mean-squared error in Q-
values
• Leading to the following Q-learning gradient

DQN in Atari
• End-to-end learning of values Q(s, a) from pixels
• Input state s is stack of raw pixels from last 4 frames
• Output is Q(s, a) for 18 joystick/button positions
• Reward is the change in the score for that step
Mnih, Volodymyr, et al. 2015.

DQN in Atari :
Human Level Control
Mnih, Volodymyr, et al. 2015.

AlphaGO:
Monte Carlo Tree Search
• MCTS: Model look ahead to reduce searching
space by predicting opponent’s moves
Silver, David, et al. 2016.

AlphaGO: Learning Pipeline
• Combine SL and RL to learn the search direction
in MCTS
• SL policy Network
– Prior search probability or potential
• Rollout:
– combine with MCTS for quick simulation on leaf node
• Value Network:
– Build the Global feeling on the leaf node situation
Silver, David, et al. 2016.

Learning to Prune：
SL Policy Network
• 13-layer CNN
• Input board position 𝑠
• Output: p 𝜎 (𝑎|𝑠), where 𝑎 is the next
move

RL Policy Network
• 1 Million samples are used to train.
• RL-Policy network VS SL-Policy network.
• RL-Policy alone wins 80% games against SL-Policy.
• Combined with MCTS, SL-Policy network is better
• Used to derive the Value Network as the ground truth
– Making enough data for training
Self play

Value Network
• Regression: Similar architecture
• SL Network: Sampling to generate
a unique game.
• RL Network: Simulate to get the
game’s final result.
• Train: 50 million mini-batches of
32 positions(30 million unique
games)

AlphaGO：Evaluation
The version solely using the policy network
does not perform any searchSilver, David, et al. 2016.

Introduction to deep learning

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