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Neural Networks

Machine Learning Techniques

Network Architecture

x 1

x 2

Input Layer

Network Architecture

x 1

x 2

h 11

h 12

h 13

Input Layer

Hidden Layer-

Network Architecture

x 1

x 2

h 11

h 12

h 13

Input Layer

Hidden Layer-

Network Architecture

x 1

x 2

h 11

h 12

h 13

Input Layer

Hidden Layer-

Network Architecture

x 1

x 2

h 11

h 12

h 13

h 21

h 22

Input Layer

Hidden Layer-

Hidden Layer-

Network Architecture

x 1

x 2

h 11

h 12

h 13

h 21

h 22

y

w^113

w^121 w^122 w^123

w^111 w^112

Input Layer

Hidden Layer-

Hidden Layer-

Output Layer

Network Architecture

x 1

x 2

h 11

h 12

h 13

h 21

h 22

y

w^113

w^121 w^122 w^123

b^11

b^12

b^13

w^111 w^112

Input Layer

Hidden Layer-

Hidden Layer-

Output Layer

-2 -1 0 1 2

1

Network Architecture

x 1

x 2

h 11

h 12

h 13

h 21

h 22

y

w^211

w^212

w^113

w^121 w^122 w^123

w^221

w^222

w^231

w^232

w 113

w^321

b^11

b^12

b^13

b^21

b^22

w^111 w^112 b 3 1

ReLU( ) z = max(0, z) 𝜎^ ( )z^ =

1 + e-z

g z( )

z

Activation Functions

Input Layer

Hidden Layer-

Hidden Layer-

Output Layer

Forward Pass

x 1

x 2

h 11

h 12

h 13

h 21

h 22

3 y

2

5

Forward Pass

x 1

x 2

h 11

h 12

h 13

h 21

h 22

3 y

2

5

h 11 = g ( 5 x 1 + 3x 2 + 2)

h 11 = max( 5 x 1 + 3x 2 + 2, 0)

ReLU

Forward Pass

x 1

x 2

h 11

h 12

h 13

h 21

h 22

3 y

2

5

h 11 = g ( 5 x 1 + 3x 2 + 2)

h 11 = max( 5 x 1 + 3x 2 + 2, 0)

h 11 = 𝜎 5( x 1 + 3x 2 + 2)

ReLU

Sigmoid

Forward Pass

x 1

x 2

h 11

h 12

h 13

h 21

h 22

y

• 1

3

2

y = g ( 2 h 21 - h 22 + 3)

Forward Pass

x 1

x 2

h 11

h 12

h 13

h 21

h 22

y

• 1

3

2

y = 2h 21 - h 22 + 3 y^ =^ g^ (^2 h^21 - h^22 + 3)

Linear