demystifying deep learning - university of waterloo · playing chess - cool classifying cat videos...

Demystifying Deep Learning2017 Workshop on Deep Learning in Medicine

Mark CrowleyAssistant Professor

Electrical and Computer EngineeringUniversity of [email protected]

Aug 28, 2017

Mark Crowley Demystifying Deep Learning Aug 28, 2017 1 / 89

Introduction

Outline

Introduction

Machine Learning

Artificial Neural Networks

Making Neural Networks Work

Convolutional Neural Networks

Summary


Introduction My Research

My Background

Waterloo : Assistant Professor, ECE Department since 2015

PhD at UBC in Computer Science with Prof. David Poole

Postdoc at Oregon State University

UW ECE ML Lab: https://uwaterloo.ca/scholar/mcrowley/lab

Waterloo Institute for Complexity and Innovation (WICI)



Good Problems vs Important Problems

Playing Chess - cool

Classifying cat videos - surprising

Alpha Go amazing!

Text and speech recognition, translation - also handy!

Advertisement Ranking profit!!!

no seriously though, how about something important?

Some of these can be important, but they have low risk if yourewrong.



My Research

Topics

ComputationalSustainability

Deep Learning

ReinforcementLearning

Anomaly Detection

Natural LanguageProcessing

Deep RL

Security

PAC MDP Learning

Graphical Models

Projects

Forest Harvest Simulators

Forest Fire SatelliteImages/Simulations

Invasive Species Simulations

Embedded System Log Traces

Driver Behaviour Modelling

Formation Control and Learningin Remote Control Cars

diffusion MRI Brain Scans

Learning to Detect AnomalousNetwork Traffic

Therapeutic Chatbots for theElderly


Machine Learning Landscape of Big Data/AI/ML

Outline

Introduction

Machine LearningLandscape of Big Data/AI/MLClassificationLinear ClassifiersBeyond Linear Classifiers




SummaryMark Crowley Demystifying Deep Learning Aug 28, 2017 6 / 89


Data, Big Data, Machine Learning, AI, etc, etc,

Machine Learning

Artificial Intelligence

Big Data Tools

Human Decision Making

Automated Decision MakingData

Data Analysis

X f1 f2 … fk

x1.5 104.2 China

x2.34 92.0 USA

…

xn.2 85.2 Canada

Reports, statistics,Charts, trends

Policies, Decision Rules,Summaries

Classification,Patterns, PredictionsProbabilities



Data, Big Data, Machine Learning, AI, etc, etc,

Machine Learning

Artificial Intelligence

Big Data Tools

Human Decision Making

Automated Decision Making

DataData Analysis Classification,

Patterns, PredictionsProbabilities

X f1 f2 … fk

x1.5 104.2 China

x2.34 92.0 USA

…

xn.2 85.2 Canada

Reports, statistics,Charts, trends

Policies, Decision Rules,Summaries

Multi-agent

systems

CNN DQN

Game Theory

Deep Learning

ReinforcementLearning

RNN

LSTM

ILP

Probabilistic Programming

ConstraintProgramming

SAT

SMP

A3C

Nat Lang Processing

RoboticsVision



Machine Learning

Supervised LearningAlso called: predictive, inferentialGiven inputs and outputsModel based: model or distribution is known

Parameter Estimation: distribution known, fitting parametersLinear Regresion, least squares estimation

output is linear: regression, predictionoutput is categorical (label) : classification

Unsupervised LearningAlso called: descriptive, knowledge discoveryGiven inputs onlyoutput is categorical : clustering

Reinforcement LearningInput and output given only when action (prediction, choice, activity)provided.Given feedback about utility of choice made.No given model or labels ahead of time.Learning is interactive.


Machine Learning Classification

Classification Definition

Definition:

Classification is a learning method that uses training samples (withknown class labels) to learn how to assign the samples into theirproper classes. The task of the clasifier is to use the feature vectorprovide by the feature extractor to assign the object (datapoint) to acategory.

This learning can then be used to label test samples (with unknownlabels).

Classification can be facilitated if the features (or a subset of them)of samples in the same class share characteristics that discriminatethem from other classes.

It can be seen as the discrete form of Prediction, can you map theinput values to a discrete set of output values rather than to acontinuous number.



Clustering vs. Classification

Clustering

Unsupervised

Uses unlabeled data

Organize patterns w.r.t. anoptimization criteria

Notion of similarity

Hard to evaluate

Example: K-means, FuzzyC-means, Hierarchical

Classification

Supervised

Uses labeled data

Requires training phase

Domain sensitive

Easy to evaluate

Examples: Naive Bayes,KNN,SVM, Decision Trees



Classification Definition

Given a dataset X = {x1, x2, . . . , xn} where each datapoint xi ∈ Xcontains F features denoted xi ,f ,

and given a set of classes C = {C1, . . . ,CK},the classification problem is to define a mapping δ(xi ) : X → Cwhere each xi is assigned to one class.

A class, Cj , contains precisely those points mapped to it, no moreand no less.

Note: the classes are predefined, nonoverlapping and partition theentire set of datapoints.


Machine Learning Two Classic Linear Classifiers

Outline

Introduction

Machine LearningLandscape of Big Data/AI/MLClassificationLinear ClassifiersBeyond Linear Classifiers






Linear Regression vs. Logistic Regression

A simple type of Generalized Linear Model

Linear regression learns a function to predict a continuous variableoutput of continous or discrete input variables

Y = b0 +∑

(biXi ) + ε

Logistic regression predicts the probability of an outcome, theappropriate class for an input vector or the odds of one outcomebeing more likely than another.



Logistic Regression

Define probability of label being 1 by fitting a linear weight vector to thelogistic (a.k.a sigmoid) function.

P(Y = 1|X ) =1

1 + e−(w0+∑

i wixi )

=1

1 + exp(−(w0 +∑

i wixi ))

Advantage of this is you can turn the continuous [−∞,∞] featureinformation into [0, 1] and treat it like a probability.bias: w0 is called the bias, it basically adjusts the sigmoid curve to the leftor right, biasing what the expected outcome is. The other weights wi

adjust the steepness of the curve in each dimension.



Logistic Regression as a Graphical Model

o(x) = σ(wT xi ) = σ(w0 +∑

i

wixi ) =1

1 + exp(−(w0 +∑

i wixi ))



Logistic Regression Used as a Classifier

Logistic Regression can be used as a simple linear classifier.

Compare probabilities of each class P(Y = 0|X ) and P(Y = 1|X ).

Treat the halfway point on the sigmoid as the decision boundary.

P(Y = 1|X ) > 0.5 classify X in class 1

w0 +∑

i

wixi = 0



Training Logistic Regression Model via Gradient Descent

Can’t easily perform Maximum Likelihood Estimation

The negative log-likehood of the logistic function is given by NLL andit’s gradient by g

NLL(w) =N∑

i=1

log

(1 + exp(−(w0 +

∑

i

wixi ))

)

g =∂

∂w=∑

i

(σ(wT xi )− yi )xi

Then we can update the parameters iteratively

θk+1 = θk − ηkgk

where ηk is the learning rate or step size.Mark Crowley Demystifying Deep Learning Aug 28, 2017 18 / 89


Support Vector Machines (SVMs)

SVM learns a discriminant function and threshold to divide pointsinto two classes.

Originally this was a line wTx + b where weights w and offset b arelearned so that possitive training points are above the line.

More generally we can learn a nonlinear function using the kernaltrick.

We rewrite the linear system as a dot product:

wTx + b = b +m∑

i=1

αixTx(i)

where

x(i) is a training example

α is a vector of coefficients



Support Vector Machines

Method Description

Class 2

Class 1

�Optimal separation: 1. No errors.

2. The distance from theclosest vector to thehyper plane ismaximized.

� The vectors closest to the hyper plane are called support vectors.

m

4 of 22



Support Vector Machines (SVMs)

More generally we can learn a nonlinear function using the kernaltrick.

We rewrite the linear system as a dot product:

wTx + b = b +m∑

i=1

αixTx(i)

f (x) = b +∑

i

αik(x, x(i))

where

x(i) is a training example

α is a vector of coefficients

k(x, x(i)) = φ(x) · φ(x)T is a kernal.



Pros and Cons of Kernal Methods

Pro:

They map low dimensional linear space to higher dimensionalnonlinear space.

Cons:

Evaluation is expensive - linear in the weighted data points usdαik(xx(i))

kernal SVMs avoid this problem because most of αi = 0, only thesupport vectors x(i) are computed.

Training is expensive - for large datasets

Do not Generalize well - the kernal determines what kind of generalpatterns it can learn.

Choosing the kernal is hard - too general or too specific to theproblem, how to choose it?


Artificial Neural Networks History and Overview

Outline

Introduction

Machine Learning

Artificial Neural NetworksHistory and OverviewClassic Neural Network BasicsNeural Networks as Universal ApproximatorsTraining Neural Networks - Backpropagation





A Short History

40’s Early work in NN goes back to the 40s with a simple modelof the neuron by McCulloh and Pitt as a summing andthresholding devices.

1958 Rosenblatt in 1958 introduced the Perceptron,a two layernetwork (one input layer and one output node with a bias inaddition to the input features.

1969 Marvin Minsky: 1969. Perceptrons are ’just’ linear, AI goeslogical, beginning of ”AI Winter”

1980s Neural Network resurgence: Backpropagation (updatingweights by gradient descent)

1990s SVMs! Kernals can do anything! (no, they can’t)



A Short History

1993 LeNet 1 for digit recognition

2003 Deep Learning (Convolutional Nets Dropout/RBMs, DeepBelief Networks)

1986, 2006 Restricted Boltzman Machines2006 Neural Network outperform RBF SVM on MNIST

handwriting dataset (Hinton et al.)2012 AlexNet for ImageNet challenge - this algorithm beat

competition by error rate of 16% vs 26% for next best

ImageNet : contains 15 million annotated images inover 22,000 categories.ZFNet paper (2013) extends this and has gooddescription of network structure

2012-present Google Cat Youtube, speech recognition, self driving cars,computer defeats regional Go champion, ...

2014 GoogLeNet added many layers and introduced inceptionmodules (allows parallel computation rather than seriallyconnected CNN layers)



A Short History

1993 LeNet 1 for digit recognition2003 Deep Learning (Convolutional Nets Dropout/RBMs, Deep

Belief Networks)

1986, 2006 Restricted Boltzman Machines2006 Neural Network outperform RBF SVM on MNIST

handwriting dataset (Hinton et al.)2012 AlexNet for ImageNet challenge - this algorithm beat

competition by error rate of 16% vs 26% for next best






A Short History


Belief Networks)1986, 2006 Restricted Boltzman Machines

2006 Neural Network outperform RBF SVM on MNISThandwriting dataset (Hinton et al.)

2012 AlexNet for ImageNet challenge - this algorithm beatcompetition by error rate of 16% vs 26% for next best






A Short History





ImageNet : contains 15 million annotated images inover 22,000 categories.

ZFNet paper (2013) extends this and has gooddescription of network structure





A Short History










A Short History







2014 GoogLeNet added many layers and introduced inceptionmodules (allows parallel computation rather than seriallyconnected CNN layers)Mark Crowley Demystifying Deep Learning Aug 28, 2017 25 / 89


A “New” Age of Neural Networks

Geoffrey Hinton (UofT, now Google Research), paper references

early work on back-propogationRestricted Boltzman Machines - first deep architecture, idea forunsupervised pretraining of layers for RBMs was used for firstsuccessful use of deep networks.Several applications of Deep Learning to image recognition, speechrecognition,...

Yoshua Bengio (University of Montreal, MILA, ElememntAI, ...)

ReLU improves efficiencyunsupervised representation learning of autoencodersword2vec - learn general representation of words for classification,translation, etc.General Adversarial Networks - an exciting new approach to training

Yann LeCun (NYU, now Facebook AI Research)



Artificial Neural Networks Classic Neural Network Basics

Neural Networks

A Neural Network (NN) connects many nonlinear (classicallylogistic/sigmoid) units together into a network

Central difference from the Perceptron: a layer of hidden units

Also called: Multi-layer Perceptrons (MLP), Artificial NeuralNetworks (ANNs)



Neural Networks to learn f : X → Y

f can be a non-linear function

X (vector of) continuous and/or discrete variables

Y (vector of) continuous and/or discrete variables

Feedforward Neural networks - Represent f by network of non-linear(logistic/sigmoid/ReLU) units:

Input layer, X

Output layer, Y

Hidden layer, H

Sigmoid Unit



Basic Three Layer Neural Network

Input Layer

vector data, each input collects one feature/dimension of the dataand passes it on to the (first) hidden layer.

Hidden Layer

Each hidden unit computes a weighted sum of all the units from theinput layer (or any previous layer) and passes it through a nonlinearactivation function.

Output Layer

Each output unit computes a weighted sum of all the hidden unitsand passes it through a (possibly nonlinear) threshold function.



Three-layer Artificial Neural Network



Properties of Neural Networks

Given a large enough layer of hidden units (or multiple layers) a NNcan represent any function.

One challenge is regularization: how many hidden units or layers toinclude in the network? Number of inputs and outputs are providedbut internal structure can be arbitrary.

too few units, network will have too few parameters, may not be ableto learn complex functionstoo many units, network will be overparameterized and won’t be forcedto learn a generalizable model

Representation Learning: classic statistical machine learning is aboutlearning functions to map input data to output. But Neural Networks, andespecially Deep Learning, are more about learning a representation inorder to perform classification or some other task.



Properties of Neural Networks

The hidden layer will have a number of units ( design parameter).

The hidden layers allow extracting more complex features andfacilitates solving complex problems.

Connection between the units (neurons) of all the layers can beforward, backward or both.

Units can be fully or partially connected.

Different arrangements make different types or models of the NN.

Each unit will have a activation function (a thresholding function)and connections between the units that have weights



Net Activation

netj =d∑

i=1

xiwji + wj0 =d∑

i=0

xiwji

where:

i indexes the inputs units

j indexes the hidden units

Wji denotes the weights on input to hidden layer (“synaptic weights”)



Hidden Layer: Adding Nonlinearity

Each hidden unit emits an output that is a nonlinear activationfunction of its net activiation.

yj = f (netj)

This is essential to neural networks power, if it’s linear then it allbecomes just linear regression.

The output is thus thresholded through this nonlinear activationfunction.



Activation Functions

tanh was another common function.

sigmoid is now discourage except for final layer to obtainprobabilities. Can over-saturate easily.

ReLU is the new standard activation function to use.



Rectified Linear Activation

CHAPTER 6. DEEP FEEDFORWARD NETWORKS

0

z

0

g(z

)=

max{0

,z}

Figure 6.3: The rectified linear activation function. This activation function is the defaultactivation function recommended for use with most feedforward neural networks. Applyingthis function to the output of a linear transformation yields a nonlinear transformation.However, the function remains very close to linear, in the sense that is a piecewise linearfunction with two linear pieces. Because rectified linear units are nearly linear, theypreserve many of the properties that make linear models easy to optimize with gradient-based methods. They also preserve many of the properties that make linear modelsgeneralize well. A common principle throughout computer science is that we can buildcomplicated systems from minimal components. Much as a Turing machine’s memoryneeds only to be able to store 0 or 1 states, we can build a universal function approximatorfrom rectified linear functions.

175

(Goodfellow 2016)

Rectified Linear Units (ReLU) have become standard max(0, netj)

strong signals are alwasy easy to distinguishmost values are zero, deritive is mostly zerothey do not saturate as easily as sigmoid

new Exponential linear units - evidence that they perform better thanReLU in some situations.



Output Layer

Regardless of activation function, the output layer then combines all theprevious hidden layers.

netk =

nH∑

j=1

yjwkj + wk0

where:

k indexes the output units

nH denotes the number of hidden units in the previous layer



Output Layer

The output layer adds another level of thresholding, usually nonlinear aswell.

zk = f (netk)

f (netk) could be any thresholding function such as the previous activationfunctions.


Artificial Neural Networks Neural Networks as Universal Approximators

Outline

Introduction

Machine Learning

Artificial Neural NetworksHistory and OverviewClassic Neural Network BasicsNeural Networks as Universal ApproximatorsTraining Neural Networks - Backpropagation





Failing on the XOR Problem

How is XOR a hard problem? It is if you’re too linear. XOR is the simplestnonlinear classification problem.

Two binary features x1 and x2 and four patterns to be assigned thecorrect labels True or False

(Goodfellow 2016)


0 1

x1

0

1

x2

Original x space

0 1 2

h1

0

1

h2

Learned h space

Figure 6.1: Solving the XOR problem by learning a representation. The bold numbersprinted on the plot indicate the value that the learned function must output at each point.(Left)A linear model applied directly to the original input cannot implement the XORfunction. When x1 = 0, the model’s output must increase as x2 increases. When x1 = 1,the model’s output must decrease as x2 increases. A linear model must apply a fixedcoefficient w2 to x2. The linear model therefore cannot use the value of x1 to changethe coefficient on x2 and cannot solve this problem. (Right)In the transformed spacerepresented by the features extracted by a neural network, a linear model can now solvethe problem. In our example solution, the two points that must have output 1 have beencollapsed into a single point in feature space. In other words, the nonlinear features havemapped both x = [1, 0]> and x = [0, 1]> to a single point in feature space, h = [1, 0]>.The linear model can now describe the function as increasing in h1 and decreasing in h2.In this example, the motivation for learning the feature space is only to make the modelcapacity greater so that it can fit the training set. In more realistic applications, learnedrepresentations can also help the model to generalize.

173



Neural Nets Can Model XOR Problem

Use a simple sign activationfunction for hidden and output units:

f (net) = 1 if net ≥ 0

= −1 if net < 0

First hidden unit:

y1 computes x1 + x2 + 0.5 = 0y1 = 1 if net1/ge0, y1 = −1otherwise

Second hidden unit:

y1 computes x1 + x2 − 1.5 = 0y2 = 1 if net2/ge0, y2 = −1otherwise

single output unit z1:

emits z1 = 1 iff y1 = 1 andy2 = 1.y1 models AND gatey2 models OR gatez1 models y1 AND NOT y2



Full Neural Network Descriminant Function

The class of decision functions that can be described by a three-layerneural network are:

gk(x) = zk = f

nH∑

j=1

wkj f

(d∑

i=1

wjixi + wj0

)+ w0

The Universal Approximation Theorem [Hornik, 1989] shows thatthis covers any possible decision function mapping continuous inputsto a finite set of classes to any desired level of accuracy.

But it does not say how many hidden unites would be needed.

In general, for a single layer it could be exponential (degrees offreedom).

But, using more layers can reduce the number of hidden units neededand make it more generalizable.


Artificial Neural Networks Training Neural Networks - Backpropagation

Gradient Descent

d

E – Error function, MSE, cross-entropy loss

For Neural Networks,

E[w] no longer convex in w

Error Function: Mean Squared Error, cross-entropy loss, etc.

Gradient: 5E [w] =[

∂E∂w0

, ∂E∂w1

, . . . , ∂E∂wd

]

Training Update Rule: ∆wi = −η ∂E∂wi

where η is the training rate.Note: For regression, others, this gradient is convex. In ANNs it is not. Sowe must solve iteratively

(Slides from Tom Mitchell ML Course, CMU, 2010)



Incremental Gradient Descent

Let error function be : El [w] = 12 (y l − o l)2

Do until satisfied:

For each training example l in D1 Compute the gradient 5E [w]2 update weights : w = w − η5 E [w]

Note: can also use batch gradient descent on many points at once.



Backpropagation Algorithm

We need an iterative algorithm for getting the gradient efficiently.For each training example:

1 Forward propagation: Input the training example to the network andcompute outputs

2 Compute output units errors:

δlk = o lk(1− o lk)(y lk − o lk)

3 Compute hidden units errors:

δlh = o lh(1− o lh)∑

k

wh,kδlk

4 Update network weights:

wi ,j = wi ,j + ∆w li ,j = wi ,j + ηδljo

li



More about Backpropagation

Still underlies all of Deep Learning

Can be easily peformed on mulidimensional outputs.

No guarantee of global optimal solution, only local, but often goodenough.

Can be paralellized very well, most deep learning tools now do this onGPUs automatically.

Remember that it is minimizing errors on training examples, ability togeneralize relies on network structure, training approach, otherfactors.



Outline

Introduction

Machine Learning


Making Neural Networks WorkImproving PerformanceThe Threat of OverfittingRegularizationGoing Deep




Problems with ANNs

Overfitting

Very inneficient for images, timeseries, large numbers ofinputs-outputs

Overfitting

Slow to train

Hard to interpret the resulting model

Overfitting


Making Neural Networks Work Improving Performance

Heuristics for Improving Backpropagation

There are a number of useful heuristics for training Neural Networks thatare useful in practice (maybe we’ll learn more today):

Less hidden nodes, just enough complexity to work, not too much tooverfit.

Train multiple networks with different sizes and search for the bestdesign.

Validation set: train on training set until error on validation set startsto rise, then evaluate on evaluation set.

Try different activiation functions: tanh, ReLU, ELU, ...?

Dropout (Hinton 2014) - randomly ignore certain units duringtraining, don’t update them via gradient descent, leads to hiddenunits that specialize

Modify learning rate over time (cooling schedule)


Making Neural Networks Work The Threat of Overfitting

The Threat of OverfittingOverfitting 1n ANNs

Error versu s weight updates (example 1) 0 .01

0 .009 T raining set error • Validation set error +

0 .008

0 .007 ,_, 8 ,_,

i:.rJ 0 .006

0 .005

0 .004

0 .003

0 .002 0 5000 10000 15000 20000

Num ber of weight u pdates

Error v ersus weight updates (example 2) 0 .08

O.ITT Trai aing set e rror • Validation set enor +

0 .06

0 .05 .... e 0 .04 .... !LI • 0 .03 •

0 .02 •

0 .01

0 0 1000 2000 3000 4000 5000 6000

N umber of weight updates


Making Neural Networks Work Regularization

Regularization to Reduce Overfitting

L2 regularization - augmenting the error function, add 12λw

2 to allweights in the neural network

Need to choose lambda carefullyInterpretation - heavily penalizing ”peaky” weight vectors andpreferring diffuse weight vectors.Encourages network to use all its inputs instead of relying on strongestsignal.Also called weight decay since weights would reduce over time duringgradient descent without input.

L1 regularization - add λ|w | to each weight error function(encourages all weights to zero)



Regularization to Reduce Overfitting

Figure: From http://www.kdnuggets.com/2015/04/preventing-overfitting-neural-networks.html/2



Dropout

Dropout (Hinton 2014) - randomly ignore certain units duringtraining, don’t update them via gradient descent, leads to hiddenunits that specialize.With probability p don’t include a weight in the gradient updates.Reduces overfitting by encouraging robustness of weights in thenetwork.


Making Neural Networks Work Going Deep

Advantage of Increased Depth

(Goodfellow 2016)

Exponential Advantage of Depth


(2014) showed that functions representable with a deep rectifier net can requirean exponential number of hidden units with a shallow (one hidden layer) network.More precisely, they showed that piecewise linear networks (which can be obtainedfrom rectifier nonlinearities or maxout units) can represent functions with a numberof regions that is exponential in the depth of the network. Figure 6.5 illustrates howa network with absolute value rectification creates mirror images of the functioncomputed on top of some hidden unit, with respect to the input of that hiddenunit. Each hidden unit specifies where to fold the input space in order to createmirror responses (on both sides of the absolute value nonlinearity). By composingthese folding operations, we obtain an exponentially large number of piecewiselinear regions which can capture all kinds of regular (e.g., repeating) patterns.

Figure 6.5: An intuitive, geometric explanation of the exponential advantage of deeperrectifier networks formally by Montufar et al. (2014). (Left)An absolute value rectificationunit has the same output for every pair of mirror points in its input. The mirror axisof symmetry is given by the hyperplane defined by the weights and bias of the unit. Afunction computed on top of that unit (the green decision surface) will be a mirror imageof a simpler pattern across that axis of symmetry. (Center)The function can be obtainedby folding the space around the axis of symmetry. (Right)Another repeating pattern canbe folded on top of the first (by another downstream unit) to obtain another symmetry(which is now repeated four times, with two hidden layers). Figure reproduced withpermission from Montufar et al. (2014).

More precisely, the main theorem in Montufar et al. (2014) states that thenumber of linear regions carved out by a deep rectifier network with d inputs,depth l, and n units per hidden layer, is

O

✓n

d

◆d(l 1)

nd

!, (6.42)

i.e., exponential in the depth l. In the case of maxout networks with k filters perunit, the number of linear regions is

O⇣k(l 1)+d

⌘. (6.43)

200

Using Hidden LeRU units, each hidden layer increases power, exponentialadvantage of additional layers.



Better Generalization with Greater Depth

(Goodfellow 2016)

Better Generalization with Greater DepthCHAPTER 6. DEEP FEEDFORWARD NETWORKS

3 4 5 6 7 8 9 10 11

92.0

92.5

93.0

93.5

94.0

94.5

95.0

95.5

96.0

96.5Test

accuracy

(percent)

Figure 6.6: Empirical results showing that deeper networks generalize better when usedto transcribe multi-digit numbers from photographs of addresses. Data from Goodfellowet al. (2014d). The test set accuracy consistently increases with increasing depth. Seefigure 6.7 for a control experiment demonstrating that other increases to the model sizedo not yield the same effect.

Another key consideration of architecture design is exactly how to connect apair of layers to each other. In the default neural network layer described by a lineartransformation via a matrix W , every input unit is connected to every outputunit. Many specialized networks in the chapters ahead have fewer connections, sothat each unit in the input layer is connected to only a small subset of units inthe output layer. These strategies for reducing the number of connections reducethe number of parameters and the amount of computation required to evaluatethe network, but are often highly problem-dependent. For example, convolutionalnetworks, described in chapter 9, use specialized patterns of sparse connectionsthat are very effective for computer vision problems. In this chapter, it is difficultto give much more specific advice concerning the architecture of a generic neuralnetwork. Subsequent chapters develop the particular architectural strategies thathave been found to work well for different application domains.

202

Figure 6.6Increasing accuracy from number of layers in detection of numbers inphotos of adresses.



Large, Shallow Models Overfit More

(Goodfellow 2016)


0.0 0.2 0.4 0.6 0.8 1.0

Number of parameters

⇥10

8

91

92

93

94

95

96

97

Test

accuracy

(percent)

3, convolutional

3, fully connected

11, convolutional

Figure 6.7: Deeper models tend to perform better. This is not merely because the model islarger. This experiment from Goodfellow et al. (2014d) shows that increasing the numberof parameters in layers of convolutional networks without increasing their depth is notnearly as effective at increasing test set performance. The legend indicates the depth ofnetwork used to make each curve and whether the curve represents variation in the size ofthe convolutional or the fully connected layers. We observe that shallow models in thiscontext overfit at around 20 million parameters while deep ones can benefit from havingover 60 million. This suggests that using a deep model expresses a useful preference overthe space of functions the model can learn. Specifically, it expresses a belief that thefunction should consist of many simpler functions composed together. This could resulteither in learning a representation that is composed in turn of simpler representations (e.g.,corners defined in terms of edges) or in learning a program with sequentially dependentsteps (e.g., first locate a set of objects, then segment them from each other, then recognizethem).

203



Outline

Introduction

Machine Learning



Convolutional Neural NetworksConvolution OperationPoolingExamplesOther CNN ModificationsInterpretting CNN ModelsMajor Architectures



Example Applications of CNNs

(Karpathy Blog, Oct, 25, 2015 - http:karpathy.github.io20151025selfie)



CNN History

After deep networks, ReLU’s the third major innovation are ConvolutionalNeural Networks (CNNs).

Work by Yann LeCun in 80s)

LeNet 1 (1993) for digit recognition

AlexNet (2012) for ImageNet challenge - beat competition by errorrate of 16% vs 26% for next best

Cat videos (2012) Quoc Le - the Google cat youtube paper at ICML.

ZFNet (2013), GoogLeNet (2014), ...



Benefits of CNNs

Simple - repeated operation across each image - essentially a visualfilter applied at every location.

Related to kernals discussed earlier, but automatically learns the rightkernal mapping.

Efficient - for images compared to a naive ANN approach.

Still takes a long time to train, but uses structure of images to reduceduplicated work.

Effective - Computer vision applications are now mostly using someform of CNNs, but mostly for low risk tasks.

Natural? - possible connection to animal visual system



What Makes a Deep Neural Network a CNN?

Essential Property: a neural network that uses convolution in place ofgeneral matrix multiplaction in at least one of its layers.Additional properties:

Sparse connectivity

Parameter sharing (tied weights)

Equivariant Representations



Kinds of Network Connectivity

(Goodfellow 2016)

Kinds of ConnectivityCHAPTER 9. CONVOLUTIONAL NETWORKS

x1x1 x2x2 x3x3

s2s2s1s1 s3s3

x4x4

s4s4

x5x5

s5s5

x1x1 x2x2

s1s1 s3s3

x5x5

s5s5

x1x1 x2x2 x3x3

s2s2s1s1 s3s3

x4x4

s4s4

x5x5

s5s5

a b a b a b a b a

a b c d e f g h i

x4x4x3x3

s4s4s2s2

Figure 9.14: Comparison of local connections, convolution, and full connections.(Top)A locally connected layer with a patch size of two pixels. Each edge is labeled witha unique letter to show that each edge is associated with its own weight parameter.(Center)A convolutional layer with a kernel width of two pixels. This model has exactlythe same connectivity as the locally connected layer. The difference lies not in which unitsinteract with each other, but in how the parameters are shared. The locally connected layerhas no parameter sharing. The convolutional layer uses the same two weights repeatedlyacross the entire input, as indicated by the repetition of the letters labeling each edge.(Bottom)A fully connected layer resembles a locally connected layer in the sense that eachedge has its own parameter (there are too many to label explicitly with letters in thisdiagram). However, it does not have the restricted connectivity of the locally connectedlayer.

353

Figure 9.14

Local connection

Convolution

Fully connected



Convolutional Network Structure

input data: image (eg. 256x256 pixels x3 channels RGB)



Convolutional Network Structure

(Goodfellow 2016)

Convolutional Network Components

CHAPTER 9. CONVOLUTIONAL NETWORKS

Convolutional Layer

Input to layer

Convolution stage:Affine transform

Detector stage:Nonlinearity

e.g., rectified linear

Pooling stage

Next layer

Input to layers

Convolution layer:Affine transform

Detector layer: Nonlinearitye.g., rectified linear

Pooling layer

Next layer

Complex layer terminology Simple layer terminology

Figure 9.7: The components of a typical convolutional neural network layer. There are twocommonly used sets of terminology for describing these layers. (Left)In this terminology,the convolutional net is viewed as a small number of relatively complex layers, witheach layer having many “stages.” In this terminology, there is a one-to-one mappingbetween kernel tensors and network layers. In this book we generally use this terminology.(Right)In this terminology, the convolutional net is viewed as a larger number of simplelayers; every step of processing is regarded as a layer in its own right. This means thatnot every “layer” has parameters.

341

Figure 9.7

(Goodfellow 2016)


Convolutional Neural Networks Convolution Operation

Sparse connectivity

ANN: matrix multiplication for parameters mapping all inputs to alloutputs.CNN: sparse weights, many input pixels (millions), small number ofoutputs (hundreds, thousands).

(Goodfellow 2016)


x1x1 x2x2 x3x3

s2s2s1s1 s3s3

x4x4

s4s4

x5x5

s5s5

x1x1 x2x2 x3x3

s2s2s1s1 s3s3

x4x4

s4s4

x5x5

s5s5

Figure 9.3: Sparse connectivity, viewed from above: We highlight one output unit, s3,and also highlight the input units in x that affect this unit. These units are knownas the receptive field of s3. (Top)When s is formed by convolution with a kernel ofwidth 3, only three inputs affect s3. (Bottom)When s is formed by matrix multiplication,connectivity is no longer sparse, so all of the inputs affect s3.

x1x1 x2x2 x3x3

h2h2h1h1 h3h3

x4x4

h4h4

x5x5

h5h5

g2g2g1g1 g3g3 g4g4 g5g5

Figure 9.4: The receptive field of the units in the deeper layers of a convolutional networkis larger than the receptive field of the units in the shallow layers. This effect increases ifthe network includes architectural features like strided convolution (figure 9.12) or pooling(section 9.3). This means that even though direct connections in a convolutional net arevery sparse, units in the deeper layers can be indirectly connected to all or most of theinput image.

337

Sparse connections due to small convolution

kernel

Dense connections



Convolution

A filter (kernal/tensor) is defined and passed across all the pixels,providing a response for each pixel that provides a weighted average overnearby pixels.

s(t) =

∫x(a)w(t − a)da

s(t) = (x ∗ w)(t) =∞∑

a=−∞x(a)w(t − a)

S(i , j) = (I ∗ K )(i , j) =∑

m

∑

n

I (m, n)K (i −m, j − n)

where

a - age of measurement in a timeseries

I - 2D input image

K - 2D kernalMark Crowley Demystifying Deep Learning Aug 28, 2017 66 / 89


2D Convolution

(Goodfellow 2016)


a b c d

e f g h

i j k l

w x

y z

aw + bx +ey + fzaw + bx +ey + fz

bw + cx +fy + gzbw + cx +fy + gz

cw + dx +gy + hzcw + dx +gy + hz

ew + fx +iy + jzew + fx +iy + jz

fw + gx +jy + kzfw + gx +jy + kz

gw + hx +ky + lzgw + hx +ky + lz

InputKernel / Tensor

Output

Figure 9.1: An example of 2-D convolution without kernel-flipping. In this case we restrictthe output to only positions where the kernel lies entirely within the image, called “valid”convolution in some contexts. We draw boxes with arrows to indicate how the upper-leftelement of the output tensor is formed by applying the kernel to the correspondingupper-left region of the input tensor.

334



Parameter sharingCHAPTER 9. CONVOLUTIONAL NETWORKS

x1x1 x2x2 x3x3

s2s2s1s1 s3s3

x4x4

s4s4

x5x5

s5s5

x1x1 x2x2 x3x3 x4x4 x5x5

s2s2s1s1 s3s3 s4s4 s5s5

Figure 9.5: Parameter sharing: Black arrows indicate the connections that use a particularparameter in two different models. (Top)The black arrows indicate uses of the centralelement of a 3-element kernel in a convolutional model. Due to parameter sharing, thissingle parameter is used at all input locations. (Bottom)The single black arrow indicatesthe use of the central element of the weight matrix in a fully connected model. This modelhas no parameter sharing so the parameter is used only once.

for every location, we learn only one set. This does not affect the runtime offorward propagation—it is still O(k ⇥ n)—but it does further reduce the storagerequirements of the model to k parameters. Recall that k is usually several ordersof magnitude less than m. Since m and n are usually roughly the same size, k ispractically insignificant compared to m⇥n. Convolution is thus dramatically moreefficient than dense matrix multiplication in terms of the memory requirementsand statistical efficiency. For a graphical depiction of how parameter sharing works,see figure 9.5.

As an example of both of these first two principles in action, figure 9.6 showshow sparse connectivity and parameter sharing can dramatically improve theefficiency of a linear function for detecting edges in an image.

In the case of convolution, the particular form of parameter sharing causes thelayer to have a property called equivariance to translation. To say a function isequivariant means that if the input changes, the output changes in the same way.Specifically, a function f(x) is equivariant to a function g if f(g(x)) = g(f(x)).In the case of convolution, if we let g be any function that translates the input,i.e., shifts it, then the convolution function is equivariant to g. For example, let Ibe a function giving image brightness at integer coordinates. Let g be a function

338

Convolution shares the same

parameters across all spatial

locations

Traditional matrix

multiplication does not share any parameters

(Goodfellow 2016)



A simple example

Edge detection by convolution with a kernal that subtracts the value fromthe neighbouring pixel on the left for every pixel.

Edge Detection by Convolution


Figure 9.6: Efficiency of edge detection. The image on the right was formed by takingeach pixel in the original image and subtracting the value of its neighboring pixel on theleft. This shows the strength of all of the vertically oriented edges in the input image,which can be a useful operation for object detection. Both images are 280 pixels tall.The input image is 320 pixels wide while the output image is 319 pixels wide. Thistransformation can be described by a convolution kernel containing two elements, andrequires 319 ⇥ 280 ⇥ 3 = 267, 960 floating point operations (two multiplications andone addition per output pixel) to compute using convolution. To describe the sametransformation with a matrix multiplication would take 320⇥ 280⇥ 319⇥ 280, or overeight billion, entries in the matrix, making convolution four billion times more efficient forrepresenting this transformation. The straightforward matrix multiplication algorithmperforms over sixteen billion floating point operations, making convolution roughly 60,000times more efficient computationally. Of course, most of the entries of the matrix would bezero. If we stored only the nonzero entries of the matrix, then both matrix multiplicationand convolution would require the same number of floating point operations to compute.The matrix would still need to contain 2 ⇥ 319 ⇥ 280 = 178, 640 entries. Convolutionis an extremely efficient way of describing transformations that apply the same lineartransformation of a small, local region across the entire input. (Photo credit: PaulaGoodfellow)

340


Figure 9.6: Efficiency of edge detection. The image on the right was formed by takingeach pixel in the original image and subtracting the value of its neighboring pixel on theleft. This shows the strength of all of the vertically oriented edges in the input image,which can be a useful operation for object detection. Both images are 280 pixels tall.The input image is 320 pixels wide while the output image is 319 pixels wide. Thistransformation can be described by a convolution kernel containing two elements, andrequires 319 ⇥ 280 ⇥ 3 = 267, 960 floating point operations (two multiplications andone addition per output pixel) to compute using convolution. To describe the sametransformation with a matrix multiplication would take 320⇥ 280⇥ 319⇥ 280, or overeight billion, entries in the matrix, making convolution four billion times more efficient forrepresenting this transformation. The straightforward matrix multiplication algorithmperforms over sixteen billion floating point operations, making convolution roughly 60,000times more efficient computationally. Of course, most of the entries of the matrix would bezero. If we stored only the nonzero entries of the matrix, then both matrix multiplicationand convolution would require the same number of floating point operations to compute.The matrix would still need to contain 2 ⇥ 319 ⇥ 280 = 178, 640 entries. Convolutionis an extremely efficient way of describing transformations that apply the same lineartransformation of a small, local region across the entire input. (Photo credit: PaulaGoodfellow)

340

-1 -1

Input

KernelOutput

(Goodfellow 2016)



Efficiency of Convolution

(Goodfellow 2016)

Efficiency of ConvolutionInput size: 320 by 280 Kernel size: 2 by 1 Output size: 319 by 280

Convolution Dense matrix Sparse matrix

Stored floats 2 319*280*320*280 > 8e9

2*319*280 = 178,640

Float muls or adds

319*280*3 = 267,960 > 16e9

Same as convolution (267,960)

(Goodfellow 2016)


Convolutional Neural Networks Pooling

Max Pooling

problem: Still too much density and repetition in the network.

observation: Nearby pixels tend to represent the samething/class/object.

solution: Combine, or “pool”, responses from nearby nodes.

Could use average, median, minimum, but maximum often works well.



Max Pooling and Invariance to Translation

Pooling refers to aproximating the outputs of a layer by aggregatingnearby values.This improves invariance to small translations in the input.

(Goodfellow 2016)


0.1 1. 0.2

1.1. 1.

0.1

0.2

... ...

... ...

0.3 0.1 1.

1.0.3 1.

0.2

1.

... ...

... ...

DETECTOR STAGE

POOLING STAGE

POOLING STAGE

DETECTOR STAGE

Figure 9.8: Max pooling introduces invariance. (Top)A view of the middle of the outputof a convolutional layer. The bottom row shows outputs of the nonlinearity. The toprow shows the outputs of max pooling, with a stride of one pixel between pooling regionsand a pooling region width of three pixels. (Bottom)A view of the same network, afterthe input has been shifted to the right by one pixel. Every value in the bottom row haschanged, but only half of the values in the top row have changed, because the max poolingunits are only sensitive to the maximum value in the neighborhood, not its exact location.

343



Cross-Channel Pooling and Invariance to LearnedTransformations


Large responsein pooling unit


Largeresponse

in detectorunit 1

Largeresponse

in detectorunit 3

Figure 9.9: Example of learned invariances: A pooling unit that pools over multiple featuresthat are learned with separate parameters can learn to be invariant to transformations ofthe input. Here we show how a set of three learned filters and a max pooling unit can learnto become invariant to rotation. All three filters are intended to detect a hand-written 5.Each filter attempts to match a slightly different orientation of the 5. When a 5 appears inthe input, the corresponding filter will match it and cause a large activation in a detectorunit. The max pooling unit then has a large activation regardless of which detector unitwas activated. We show here how the network processes two different inputs, resultingin two different detector units being activated. The effect on the pooling unit is roughlythe same either way. This principle is leveraged by maxout networks (Goodfellow et al.,2013a) and other convolutional networks. Max pooling over spatial positions is naturallyinvariant to translation; this multi-channel approach is only necessary for learning othertransformations.

0.1 1. 0.2

1. 0.2

0.1

0.1

0.0 0.1

Figure 9.10: Pooling with downsampling. Here we use max-pooling with a pool width ofthree and a stride between pools of two. This reduces the representation size by a factorof two, which reduces the computational and statistical burden on the next layer. Notethat the rightmost pooling region has a smaller size, but must be included if we do notwant to ignore some of the detector units.

344

Figure 9.9(Goodfellow 2016)



Pooling with Downsampling

We can also use pooling to reduce the size of each layer to create ahierarchical model.

(Goodfellow 2016)

Pooling with Downsampling




Largeresponse

in detectorunit 1

Largeresponse

in detectorunit 3

Figure 9.9: Example of learned invariances: A pooling unit that pools over multiple featuresthat are learned with separate parameters can learn to be invariant to transformations ofthe input. Here we show how a set of three learned filters and a max pooling unit can learnto become invariant to rotation. All three filters are intended to detect a hand-written 5.Each filter attempts to match a slightly different orientation of the 5. When a 5 appears inthe input, the corresponding filter will match it and cause a large activation in a detectorunit. The max pooling unit then has a large activation regardless of which detector unitwas activated. We show here how the network processes two different inputs, resultingin two different detector units being activated. The effect on the pooling unit is roughlythe same either way. This principle is leveraged by maxout networks (Goodfellow et al.,2013a) and other convolutional networks. Max pooling over spatial positions is naturallyinvariant to translation; this multi-channel approach is only necessary for learning othertransformations.

0.1 1. 0.2

1. 0.2

0.1

0.1

0.0 0.1

Figure 9.10: Pooling with downsampling. Here we use max-pooling with a pool width ofthree and a stride between pools of two. This reduces the representation size by a factorof two, which reduces the computational and statistical burden on the next layer. Notethat the rightmost pooling region has a smaller size, but must be included if we do notwant to ignore some of the detector units.

344Figure 9.10

(Goodfellow 2016)(Goodfellow 2016)

(Goodfellow 2016)


Convolutional Neural Networks Examples

CNN Architecture Examples

(Goodfellow 2016)

Example Classification ArchitecturesCHAPTER 9. CONVOLUTIONAL NETWORKS

Input image: 256x256x3

Output of convolution +

ReLU: 256x256x64

Output of pooling with stride 4:

64x64x64


ReLU: 64x64x64


16x16x64

Output of reshape to vector:

16,384 units

Output of matrix multiply: 1,000 units

Output of softmax: 1,000 class

probabilities



ReLU: 256x256x64


64x64x64


ReLU: 64x64x64

Output of pooling to 3x3 grid: 3x3x64

Output of reshape to vector:

576 units

Output of matrix multiply: 1,000 units


probabilities



ReLU: 256x256x64


64x64x64


ReLU: 64x64x64

Output of convolution:16x16x1,000

Output of average pooling: 1x1x1,000


probabilities


16x16x64

Figure 9.11: Examples of architectures for classification with convolutional networks. Thespecific strides and depths used in this figure are not advisable for real use; they aredesigned to be very shallow in order to fit onto the page. Real convolutional networksalso often involve significant amounts of branching, unlike the chain structures usedhere for simplicity. (Left)A convolutional network that processes a fixed image size.After alternating between convolution and pooling for a few layers, the tensor for theconvolutional feature map is reshaped to flatten out the spatial dimensions. The restof the network is an ordinary feedforward network classifier, as described in chapter 6.(Center)A convolutional network that processes a variable-sized image, but still maintainsa fully connected section. This network uses a pooling operation with variably-sized poolsbut a fixed number of pools, in order to provide a fixed-size vector of 576 units to thefully connected portion of the network. (Right)A convolutional network that does nothave any fully connected weight layer. Instead, the last convolutional layer outputs onefeature map per class. The model presumably learns a map of how likely each class is tooccur at each spatial location. Averaging a feature map down to a single value providesthe argument to the softmax classifier at the top.

346

Figure 9.11


Convolutional Neural Networks Examples

AlexNet


Convolutional Neural Networks Other CNN Modifications

Other CNN Modification

Strides - number of pixels overlap between adjacent filters

Zero padding - removing edge pixels from filter scan, can reduce sizeof network and deal with edge effects

Alternate local connectivity options

Partial connectivity between channels



Convolutions with Strides

(Goodfellow 2016)


x1x1 x2x2 x3x3

s1s1 s2s2

x4x4 x5x5

s3s3

x1x1 x2x2 x3x3

z2z2z1z1 z3z3

x4x4

z4z4

x5x5

z5z5

s1s1 s2s2 s3s3

Stridedconvolution

Downsampling

Convolution

Figure 9.12: Convolution with a stride. In this example, we use a stride of two.(Top)Convolution with a stride length of two implemented in a single operation. (Bot-tom)Convolution with a stride greater than one pixel is mathematically equivalent toconvolution with unit stride followed by downsampling. Obviously, the two-step approachinvolving downsampling is computationally wasteful, because it computes many valuesthat are then discarded.

350



Effect of Zero Padding on Network Size

(Goodfellow 2016)


... ...

...

... ...

... ...

... ...

Figu workwith a kernel of width six at every layer. In this example, we do not use any pooling, soonly the convolution operation itself shrinks the network size. (Top)In this convolutionalnetwork, we do not use any implicit zero padding. This causes the representation toshrink by five pixels at each layer. Starting from an input of sixteen pixels, we are onlyable to have three convolutional layers, and the last layer does not ever move the kernel,so arguably only two of the layers are truly convolutional. The rate of shrinking canbe mitigated by using smaller kernels, but smaller kernels are less expressive and someshrinking is inevitable in this kind of architecture. (Bottom)By adding five implicit zeroesto each layer, we prevent the representation from shrinking with depth. This allows us tomake an arbitrarily deep convolutional network.

351

With zero padding

Without zero padding

re 9.13: The e?ect of zero padding on network size: Consider aconvolutional n



Tiled Convolution

(Goodfellow 2016)


x1x1 x2x2 x3x3

s2s2s1s1 s3s3

x4x4

s4s4

x5x5

s5s5

x1x1 x2x2 x3x3

s2s2s1s1 s3s3

x4x4

s4s4

x5x5

s5s5

a b a b a b a b a

a b c d e f g h i

x1x1 x2x2 x3x3

s2s2s1s1 s3s3

x4x4

s4s4

x5x5

s5s5

a b c d a b c d a

Figure 9.16: A comparison of locally connected layers, tiled convolution, and standardconvolution. All three have the same sets of connections between units, when the samesize of kernel is used. This diagram illustrates the use of a kernel that is two pixels wide.The differences between the methods lies in how they share parameters. (Top)A locallyconnected layer has no sharing at all. We indicate that each connection has its own weightby labeling each connection with a unique letter. (Center)Tiled convolution has a set oft different kernels. Here we illustrate the case of t = 2. One of these kernels has edgeslabeled “a” and “b,” while the other has edges labeled “c” and “d.” Each time we move onepixel to the right in the output, we move on to using a different kernel. This means that,like the locally connected layer, neighboring units in the output have different parameters.Unlike the locally connected layer, after we have gone through all t available kernels,we cycle back to the first kernel. If two output units are separated by a multiple of tsteps, then they share parameters. (Bottom)Traditional convolution is equivalent to tiledconvolution with t = 1. There is only one kernel and it is applied everywhere, as indicatedin the diagram by using the kernel with weights labeled “a” and “b” everywhere.

355

Local connection (no sharing)

Tiled convolution (cycle between groups of shared parameters) Convolution (one group shared everywhere)


Convolutional Neural Networks Interpretting CNN Models

CNNs Learn Meaningful Filters

When trained on photographic images the filters learned by CNNs oftencorrespond to prior image processing constructs or to identifiable realworld patterns:

low level stages learn filters like lines, curves, directional vectors.Similar to Gabor filters from animal visual systems.

Unsupervised training - top layers can correspond to clusters of images



Gabor Functions

(Goodfellow 2016)


Figure 9.18: Gabor functions with a variety of parameter settings. White indicateslarge positive weight, black indicates large negative weight, and the background graycorresponds to zero weight. (Left)Gabor functions with different values of the parametersthat control the coordinate system: x0, y0, and ⌧ . Each Gabor function in this grid isassigned a value of x0 and y0 proportional to its position in its grid, and ⌧ is chosen sothat each Gabor filter is sensitive to the direction radiating out from the center of the grid.For the other two plots, x0, y0, and ⌧ are fixed to zero. (Center)Gabor functions withdifferent Gaussian scale parameters �x and �y. Gabor functions are arranged in increasingwidth (decreasing �x) as we move left to right through the grid, and increasing height(decreasing �y) as we move top to bottom. For the other two plots, the � values are fixedto 1.5⇥ the image width. (Right)Gabor functions with different sinusoid parameters fand �. As we move top to bottom, f increases, and as we move left to right, � increases.For the other two plots, � is fixed to 0 and f is fixed to 5⇥ the image width.

(replacing black with white and vice versa).Some of the most striking correspondences between neuroscience and machine

learning come from visually comparing the features learned by machine learningmodels with those employed by V1. Olshausen and Field (1996) showed thata simple unsupervised learning algorithm, sparse coding, learns features withreceptive fields similar to those of simple cells. Since then, we have found thatan extremely wide variety of statistical learning algorithms learn features withGabor-like functions when applied to natural images. This includes most deeplearning algorithms, which learn these features in their first layer. Figure 9.19shows some examples. Because so many different learning algorithms learn edgedetectors, it is difficult to conclude that any specific learning algorithm is the“right” model of the brain just based on the features that it learns (though it cancertainly be a bad sign if an algorithm does not learn some sort of edge detectorwhen applied to natural images). These features are an important part of thestatistical structure of natural images and can be recovered by many differentapproaches to statistical modeling. See Hyvärinen et al. (2009) for a review of thefield of natural image statistics.

370



Gabor Like Learned Kernals Learned via CNNs


Figure 9.19: Many machine learning algorithms learn features that detect edges or specificcolors of edges when applied to natural images. These feature detectors are reminiscent ofthe Gabor functions known to be present in primary visual cortex. (Left)Weights learnedby an unsupervised learning algorithm (spike and slab sparse coding) applied to smallimage patches. (Right)Convolution kernels learned by the first layer of a fully supervisedconvolutional maxout network. Neighboring pairs of filters drive the same maxout unit.

9.11 Convolutional Networks and the History of DeepLearning

Convolutional networks have played an important role in the history of deeplearning. They are a key example of a successful application of insights obtainedby studying the brain to machine learning applications. They were also some ofthe first deep models to perform well, long before arbitrary deep models wereconsidered viable. Convolutional networks were also some of the first neuralnetworks to solve important commercial applications and remain at the forefrontof commercial applications of deep learning today. For example, in the 1990s, theneural network research group at AT&T developed a convolutional network forreading checks (LeCun et al., 1998b). By the end of the 1990s, this system deployedby NEC was reading over 10% of all the checks in the US. Later, several OCRand handwriting recognition systems based on convolutional nets were deployed byMicrosoft (Simard et al., 2003). See chapter 12 for more details on such applicationsand more modern applications of convolutional networks. See LeCun et al. (2010)for a more in-depth history of convolutional networks up to 2010.

Convolutional networks were also used to win many contests. The currentintensity of commercial interest in deep learning began when Krizhevsky et al.

(2012) won the ImageNet object recognition challenge, but convolutional networks

371



Unsupervised Training of CNNs

Cat videos (2012) Quoc Le - the Google cat youtube paper at ICML.


Convolutional Neural Networks Major Architectures

Major Deep CNN Architectures

Spatial Transducer Net: input size scales with output size, all layers areconvolutional

All Convolutional Net: no pooling layers, just use strided convolution toshrink representation size

Inception: complex architecture designed to achieve high accuracy withlow computational cost

ResNet: blocks of layers with same spatial size, with each layersoutput added to the same buffer that is repeatedly updated.Very many updates = very deep net (over 150 layers!) butwithout vanishing gradient.

(Goodfellow, 2016)



Other Types of Deep Neural Networks

RBM: Restricted Boltzman Machines (RBM) - older directed deepmodel.

RNN: Recurrent Neural Networks (RNN) - allow links from outputsback to inputs, over time, good for time series learning

LSTM: Long-Term Short-Term networks - more complex form ofRNN

DeepRL: Deep Reinforcement Learning

GAN: General Adversarial Networks - train two networks at once







integrate strategically remembering particularinformation from the pastformalizes a process for forgetting information overtime.










CNNs + Fully Connected Deep Network for learning arepresentation of a policyReinforcement Learning for updating the policy throughexperience to make improved decision decisionsRequires a value/reward function




General Adversarial Networks

one network produces/hallucinates new answers (generative)

second network distinguishes between the real and the generatedanswers (adversary/critic)

similar in idea to Deep RL but does not require a value/rewardfunction.

could be used in combination with any other type: CNN, LSTM,RNN, ...

Blog/Code: ”GANS in 50 lines of code PyTorch code.” easy way toget started


Summary

Summary

Machine Learning

Learning models from data for prediction, classification, clustering andanomaly detectionMany models are linear, kernal methods allow mapping from lowdimensional nonlinear to highdimensional linear, but have limitations.


Ideas have been around a long time.Limitations: overfit easily, slow to train, not great for images


Regularization : DropoutReLU activation functionsMore layers, more structure


Basic use of convolutional filtersMany network architectures


Summary Useful Materials

Useful Books

All three ages of Machine Learning:

[Goodfellow, 2016]Goodfellow, Bengio and Courville. “Deep Learning”, MIT Press, 2016.

http://www.deeplearningbook.org/Website has free copy of book as pdf’s.

[Murphy, 2012]Kevin Murphy, Machine Learning: A Probabilistic Perspective, MITPress, 2012.

[Duda, Pattern Classification, 2001]R. O. Duda, P. E. Hart and D. G. Stork, Pattern Classification (2nded.), John Wiley and Sons, 2001.


http://www.deeplearningbook.org/

Summary Useful Materials

Useful Papers and Blogs

[lecun2015]Y. LeCun, Y. Bengio, G. Hinton, L. Y., B. Y., and H. G., “Deeplearning”, Nature, vol. 521, no. 7553, pp. 436444, 2015. Greatreferences at back with comments on seminal papers.

[bengio2009]Y. Bengio, “Learning Deep Architectures for AI”, Foundations andTrends in Machine Learning, vol. 2, no. 1. 2009. An earlier generalreferenceon the fundamentals of Deep Learning.

[krizhevsky2012]A. Krizhevsky, G. E. Hinton, and I. Sutskever,“ImageNet Classificationwith Deep Convolutional Neural Networks”, Adv. Neural Inf. Process.Syst. pp. 19, 2012. The beginning of the current craze.

[Karpathy, 2015]Andrej Karpathy’s Blog - http://karpathy.github.io Easy tofollow explanations with code.

[desphande2016]A. Desphande. ”The 9 Deep Learning Papers You Need To KnowAbout”. github.io blog post, 2016.https://adeshpande3.github.io/adeshpande3.github.io/

The-9-Deep-Learning-Papers-You-Need-To-Know-About.html


http://karpathy.github.io

https://adeshpande3.github.io/adeshpande3.github.io/The-9-Deep-Learning-Papers-You-Need-To-Know-About.html

https://adeshpande3.github.io/adeshpande3.github.io/The-9-Deep-Learning-Papers-You-Need-To-Know-About.html

demystifying deep learning - university of waterloo · playing chess - cool classifying cat videos...

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