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CSE 3521: Neural Networks
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Perceptron
Multi-layer Perceptron (MLP)
Introduction to Neural Networks
Researchers in this are also called “connectionists”
Introduction to Neural Networks
Feed-forward neural network
Introduction to Neural Networks
Introduction to Neural Networks
Introduction to Neural Networks
Introduction to Neural Networks
Introduction to Neural Networks
Perceptron
The brain classifies exceptionally well … let’s model it!!
Collects impulses
When a threshold is reached, generates an impulse
Perceptron (single neural for classification)
Step (sign)
Learnable weights
Perceptron (single neural for classification)
Step (sign)
Learnable weights
Perceptron (single neural for classification)
Step (sign)
Learnable weights
Perceptron
A linear classifier
Perceptron: The NOT operator
“Active” when the correct input is given
“Inactive” when the wrong input is given
The Not Operator!
Threshold: The Bias Weight
W0x0+ W1x1 > T
W0x0+ W1x1 – T > 0
Perceptron: The AND operator
y(x0, x1) = 1 x0 + x1 – 1.5 > 0
= 0 otherwise
= Output 0
= Output 1
Perceptron: The OR operator
y(x0, x1) = 1 x0 + x1 – 0.5 > 0
= 0 otherwise
= Output 0
= Output 1
Perceptron: The XOR operator
y(x0, x1) = 1 ?? > 0
= 0 otherwise
= Output 0
= Output 1
Perceptron: The XOR operator
= Output 0
= Output 1
-1 x0 x1
There is no assignment of values to W, W0 and W1 that
satisfies above inequalities. XOR cannot be represented!
Single Perceptron
Representation theorem ( & – 1969)
A single-layer perceptron could not learn a simple XOR function (amongst others that are non-linearly separable)
Widely misinterpreted as showing that artificial neural networks were inherently limited
The reputation of neural network research declined through the 70s and 80s
Perceptron Algorithm
Let and and ignore ,
Initialize weight vector
Loop for T iterations
Loop for all training examples (random order!)
Perceptron Algorithm
Perceptron Algorithm
Perceptron Algorithm
Perceptron Algorithm
Why does it work?
Perceptron Algorithm
Let and and ignore ,
Initialize weight vector
Online version: Get on training data
Perceptron Algorithm
Convergence:
If the data is linear separable
Not convergence:
If the data is not linear separable
Perceptron
Multi-layer Perceptron (MLP)
“Artificial” Neuron
A basic “computational unit” of neural networks
Multi-layer Perceptron
XOR Solved!
Multi-layer Perceptron
Complex Boolean Functions: y = (x0 x1) x2
But remember, x0 XOR x1 = (x0 x1) (x0 x1)
y(x0, x1, x2)
Multi-layer perceptron
Multi-layer perceptron
Capable to learn nonlinear functions
How to learn?
Perceptron algorithm?
Back-propagation
Mini-batch gradient descent
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