Artificial Minds - Spring 2009

Class notes for Monday, March 9 (week 8)

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DISCLAIMER:  These are my own working lecture notes, which I'm posting here in
case they're useful.  I'll try to post my notes on a more or less regular
basis (assuming that I have some to post), but I make no guarantees as to
their completeness or comprehensibility.  They're also not too pretty, unless
you're a fan of plain text and ASCII art, so I'd recommend using them as a
supplement rather than a replacement for your own note-taking.  In other words,
you're still responsible for the material we cover in class, whether or not
that material is included here.
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Biological Neurons
- you have around 100 billion neurons in your brain
- each neuron is connected to roughly 1000-10000 others
- hundreds of trillions of connections in all
- connection strengths change with experience

Draw picture of a neuron
- cell body
- dendrites
- synapses
- axon

Brains are good at:
- pattern matching
- face recognition
- speech recognition
- language understanding
- language generation
- analogical thinking

Brain-style computation
- parallel, not serial
- minimax search is an example of serial processing
- von Neumann architecture vs. connectionist architecture
- the 100-step limit
- graceful degradation
- can handle noisy, incomplete, or inconsistent information
- adaptable (learning)

Artificial neurons
- inputs (binary or continuous)
- output (binary or continuous)
- weights
- net input: weighted sum of inputs * weights
- activation function: threshold
- activation function: sigmoid
- activation function: linear

  output:         [ ]  threshold
                 /   \
  weights:   w1 /     \ w2
               /       \
             [  ]     [  ]
  inputs:     x1       x2

  net input = x1 * w1 + x2 * w2

Example:
  weights: w1 = 0.8, w2 = 0.4
  input pattern: x1 = 0.7, x2 = 0.9
  threshold = 0.5
  net input = 0.7 * 0.8 + 0.9 * 0.4 = 0.92
  0.92 > threshold, so output of neuron = 1 in response to input pattern

McCulloch and Pitts (1943): With suitable choices for threshold and weight
values, networks of artificial neurons can be made to simulate any logical
function.

Example:
                      output
input1  input2       OR   AND
------------------------------
  0       0          0     0
  0       1          1     0
  1       0          1     0
  1       1          1     1

logical AND
threshold = 0.5
weights = 0.3, 0.3

logical OR
threshold = 0.1
weights = 0.2, 0.4

How to set the weights?
- perceptron learning rule
- error = target - output
- w(t+1) = w(t) + learning_rate * input * error

Example:
- learning_rate = 0.2
- random weights = -0.2, 0.4
- threshold = 0.1
- training data (OR):
  0   0   ->   0
  0   1   ->   1
  1   0   ->   1
  1   1   ->   1

1. present 0 0 -> output 0 (correct)
2. present 0 1 -> output 1 (correct)
3. present 1 0 -> output 0 (wrong! should have produced 1)
   error = target - output = 1 - 0 = 1
4. adjust weights:
   w1 = -0.2 + (0.2 * 1 * 1) = 0
   w2 =  0.4 + (0.2 * 0 * 1) = 0.4
5. present 1 1 -> output 1 (correct)
6. repeat until no further adjustments are necessary