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Reactive Behavior ModelingNeural Networks

(GATE-561)

Dr.Çağatay ÜNDEĞER

InstructorMiddle East Technical University, GameTechnologies

Bilkent University, Computer Engineering

&

General ManagerSimBT Inc.

e-mail : cagatay@undeger.com

Game Technologies Program – Middle East Technical University – Fall 2009

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Outline• Neural Networks

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Artificial Neural Networks (NNets)

• Inspired by human brain.• Fundamental functional units of brain are:

– Neurons / soma / nerve cells and– Axons / dendrites connecting nerve cells.

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Artificial Neural Networks (NNets)

• Signals can be thought as simple electrical impulses from axons to dendrites.

• Dendrites collect the signals.• Soma performs a kind of summation.• Axon fire and transmit the signal.

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Artificial Neural Networks (NNets)

• Neural networks use a similar approach.• Consist of:

– Input arcs collect the signals,– Neuron sums the signals and– Output arcs transmit the summed signal based on

a transmit function.

• Neural networks can be learned.

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Neural Network Architecture

i

i

i

h

h

h

h

h

h

o

o

h h

input layer hidden layers output layer

input 1

input 2

input 3

output 1

output 2

Arcs (storing weights) Neurons

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Usage of NNets

• Environmental Scanning and Classification:– Interpret vision and auditory information

• Memory:– Can learn through experience

• Behavior Control:– Outputs can be used as actions to be

performed.• Response Mapping:

– Any input output mapping and association.

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Usage of NNets

• The usage of NNets is a little bit fuzzy.• No exact cases and rules.• Assume it as a tool and use your creativity to

get whatever you like.

• What NNets do is– To seperate a solution space into partitions

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A Neuron Architecture

Y

X1

X2

Xi

Xn

w1

w2

wi

wn

Xi = input i of neuron

wi = weight of input i

Y = summing junction

y = output of neuron

yto input of other

neurons

y is based on a transfer or activation function

B=1

b

B = a constant bias node, which may represent past history

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Neuron Architecture

Y

X1

X2

Xi

Xn

w1

w2

wi

wn

y

B=1

b

Ya = B*b + Σ Xi*wii=1

n

Summing is referred as the input activation Ya

Input activation is fed into the activation function fa(x)

and output y is acquired

y = fa(x) Inputs and weights can be in

range (-∞, +∞)

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Some Activation Functions

1

0 x

y

θ

Step function

fs(x) = 1, if x≥θ0, if x<θ

1

0 x

y

Linear function

fs(x) = x

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Common Activation Function

1

0 x

y

Exponential / Sigmoid function

fs(x) = 1 / ( 1 + e-θx )

θ = 1

You can also scale and shift the output if required

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A Group Of Neurons

• A single neuron will not do a lot for us• We need a group of them

A single layer NNet A two layer NNet

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Simple Logic Functions

• Created by McCulloch and Pitts in 1943.• AND, OR, XOR functions could be done with

simple neural network structures.

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Simple Logic Function

AND

OR

XOR

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Learning NNets

• Weights of NNets can be learned by various algorithms.

• The most common algorşthm is the Backpropagation.

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Backpropagation

• Can learn weights of a multi-layer network – With fixed set of units and interconnections

• Employs a gradient descent search– To minimize the squared errors between

target output and network output• It is sub-optimal and may fail to reach true

optimal point.

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Backpropagation

• Can learn weights of a multi-layer network – With fixed set of units and interconnections

• Employs a gradient descent search– To minimize the squared errors between

target output and network output

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Backpropagation

• Error surface of the network may have multiple local minima.

• Therefore backprogation guarantees only to converge a local-optimum and may fail to reach the true-optimum.

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Backpropagation

01

02

03

11

12

13

21

22

14

input 1

input 2

input 3

output 1

output 2

Initialize the network weights with small random numbers (e.g. -0.5 ... 0.5) Train the network with m training examples repeatedly for multiple iterations.Stop training when a convergence criteria is met.

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Backpropagation

01

02

03

11

12

13

21

22

14

o1

o2

For one training example, assume that:Inputs are x01, x02 and x03 andExpected outputs are t1 and t2

We propogate the inputs through the network and Compute the actual outputs o1, o2 and o3

t1

t2

expectedactualx01

x02

x03

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Backpropagation11

12

13

21

22

14

o1

o2

Errors will occur between actual and expected outputs.We propagate errors backward through the network.

Compute error on each output unit k ( δk ) using:

δk = ok (1 - ok) (tk - ok)

t1

t2

expectedactual

δ21

δ22

output errors

e.g. δ21 = o21 (1 - o21) (t21 - o21)

x01

x02

x03

01

02

03

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Backpropagation11

12

13

21

22

14

o1

o2

Compute error on each hidden unit h (δh) using:

δh = oh (1 - oh) Σ wh-k δk

t1

t2

expectedactual

δ21

δ22

output errors

w11-21

w11-22

e.g. δ11 = o11 (1 - o11) (w11-21 δ21 + w11-22 δ22 )

δ11

δ12

δ13

δ14

hidden unit errors

x01

x02

x03

01

02

03

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Backpropagation11

12

13

21

22

14

o1

o2

Update each weight w (wf-t) using:

wf-t = wf-t + η δt xf-t

t1

t2

expectedactual

δ21

δ22

output errors

w11-21

w11-22

δ11

δ12

δ13

δ14

hidden unit errors

w01-11

w01-12x01

x02

x03

η = learning rate (e.g. 0.05)e.g. w01-11 = w01-11 + η δ11 x01-11

x01

01

02

03

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Backpropagation

• The main loop of the algorithm should repeatedly iterate over the training examples

• May iterate thousands of times using the same training examples.

• Until the network performs acceptably well:– Test with the entire training set or– A better way: test with a sparate test set.

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An Action Selector Neural Network

• The inputs are state variables that equal to either 0 (no) or 1 (yes).

• Outputs are action variables that are between 0 and 1.

• The action with the greatest output is selected.

Enemy

Sound

Dead

Low Health

Attack

Retreat

Wander

Search

Spawn

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A Number Recognizer Neural Network

• Problem : To recognize normalized bitmaps of handwritten digits from “0” to “9”.

• Data Set : Collected from 43 people– 30 people to training set– 13 people to test set– 32x32 bitmaps are divided into 4x4 blocks and

black pixels are counted– So we have 8x8 matrices and each member

stores a number between 0 and 16

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A Number Recognizer Neural Network

• 8x8 pixels = 64 inputs• No Missing Input Value• Target Value : class number

from 0 to 9

• Training Set : 3823 Instances• Test Set : 1797 Instances

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A Number Recognizer Neural Network

x011 = 1x111 1

x0641 = 1x1641 64

x012 = 1

x112 1

n

x212

x6412

x013 = 1

x113 1

10

x213

xn13

“0”

“9”

.

.

.

.

.

Max

Bias Control Unit

64 Pixel values (0..16) of 8x8 image

.

.

.

.

.

.

.

.

.

.

.

.

Result

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A Number Recognizer Neural Network

• For each optic character (0..9), an output unit is used

• The class of the output unit having the highest value is chosen as result.

• Sample target values for training:

‘0’ 0.9 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1

‘1’ 0.1 0.9 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1

‘2’ 0.1 0.1 0.9 0.1 0.1 0.1 0.1 0.1 0.1 0.1

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A Number Recognizer Neural Network

• Random weights are given (–0.5 ... 0.5)• A fixed number of iterations are performed on

Training Set– Meanwhile weights of iterations are saved

• A test phase is performed using saved weights on Test Set to avoid overfitting

• The iteration weights that maximizes the test set accuracy is chosen

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Test Platform

General InformationNew InstanceReal Value

Result of NNet

Output layer of NNet

Loaded Instance Set

Current instance

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First Attempt

• 4 hidden units • 0.1 as learning rate• 5000 iterations are performed (>12 hours)• Best on Test Set = 86.9% on 450th iteration

– Meanwhile 92.2% on Training Set– 82.5% accuracy on 5000th iteration

• Best on Training Set = 93.0% on 1110th iteration– Meanwhile 86.1% on Test Set

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Graph of First Attempt

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Second Attempt

• 4 hidden units to 8• 0.1 as learning rate (same)• 5000 iterations to 2500• Best on Test Set = 94.0% on 100th iteration

– Meanwhile 97.7% on Training Set– 88.9% accuracy on 2500th iteration

• Best on Training Set = 98.0% on 140th iteration– Meanwhile 93.6% on Test Set

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Graph of Second Attempt

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Third Attempt

• 8 hidden units to 16• 0.1 as learning rate (same)• 2500 iterations to 200• Best on Test Set = 95.2% on 176th iteration

– Meanwhile 98.7% on Training Set– 95.2% accuracy on 200th iteration

• Best on Training Set = 98.7% on 176th iteration– Meanwhile 95.2% on Test Set

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Graph of Third Attempt

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Fourth Attempt

• 16 hidden units (same)• 0.1 as learning rate to 0.05• 200 iterations to 400• Best on Test Set = 95.0% on 122th iteration

– Meanwhile 98.4% on Training Set– 94.4% accuracy on 400th iteration

• Best on Training Set = 98.7% on 394th iteration– Meanwhile 94.4% on Test Set

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Graph of Fourth Attempt

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Last Attempt

• 16 hidden units to 32• 0.05 as learning rate (same)• 400 iterations to 1000 (4 hours and 38 minutes)• Best on Test Set = 96.4% on 315th iteration

– Meanwhile 99.5% on Training Set– 96.0% accuracy on 1000th iteration

• Best on Training Set = 99.9% on 945th iteration– Meanwhile 96.1% on Test Set

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Graph of Last Attempt

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Advantages

• Handle errors well.

• Graceful degradation.

• Can learn novel solutions.

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Disadvantages

• Can’t understand how the learned network works, therefore they are the second best way to do something.

• Need as many examples as possible.

• Learning takes too much time / processing.

• Sometimes the network may not converge.