Introduction to Training and Learning in Neural Networks

1
Introduction to Training and Learning in Neural
Networks

• CS/PY 231 Lab Presentation 4
• February 7, 2005
• Mount Union College

2
Automatic Training in Networks

• Weve seen manually adjusting weights to obtain
  desired outputs is difficult
• What do biological systems do?
• if output is unacceptable (wrong), some
  adjustment is made in the system
• how do we know it is wrong? Feedback
• pain, bad taste, discordant sound, observing that
  desired results were not obtained, etc.

3
Learning via Feedback

• Weights (connection strengths) are modified so
  that next time the same input is encountered,
  better results may be obtained
• How much adjustment should be made?
• different approaches yield various results
• goal automatic (simple) rule that is applied
  during weight adjustment phase

4
Rosenblatts Training Algorithm

• Developed for Perceptrons (1958)
• illustrative of other training rules simple
• Consider a single perceptron, with 0/1 output
• We will work with a training set
• a set of inputs for which we know the correct
  output
• weights will be adjusted based on correctness of
  obtained output

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Rosenblatts Training Algorithm

• for each input pattern in the training set, do
  the following
• obtain output from perceptron
• if output is correct (strengthen)
• if output is 1, set w w x
• if output is 0, set w w - x
• but if output is incorrect (weaken)
• if output is 1, set w w - x
• if output is 0, set w w x

6
Example of Rosenblatts Training Algorithm

• Training data
• x1 x2 out
• 0 1 1
• 1 1 1
• 1 0 0
• Pick random values as starting weights and ?
• w1 0.5, w2 -0.4, ? 0.0

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Example of Rosenblatts Training Algorithm

• Step 1 run first training case through a
  perceptron
• x1 x2 out
• 0 1 1
• (0, 1) should give answer 1 (from table), but
  perceptron produces 0
• do we strengthen or weaken?
• do we add or subtract?
• based on answer produced by perceptron!

8
Example of Rosenblatts Training Algorithm

• obtained answer is wrong, and is 0 we must ADD
  input vector to weight vector
• new weight vector (0.5, 0.6)
• w1 0.5 0 0.5
• w2 -0.4 1 0.6
• Adjust weights in perceptron now, and try next
  entry in training data set

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Example of Rosenblatts Training Algorithm

• Step 2 run second training case through a
  perceptron
• x1 x2 out
• 1 1 1
• (1, 1) should give answer 1 (from table), and it
  does!
• do we strengthen or weaken?
• do we or -?

10
Example of Rosenblatts Training Algorithm

• obtained answer is correct, and is 1 we must
  ADD input vector to weight vector
• new weight vector (1.5, 1.6)
• w1 0.5 1 1.5
• w2 0.6 1 1.6
• Adjust weights, then on to training case 3

11
Example of Rosenblatts Training Algorithm

• Step 3 run last training case through the
  perceptron
• x1 x2 out
• 1 0 0
• (1, 0) should give answer 0 (from table) does
  it?
• do we strengthen or weaken?
• do we or -?

12
Example of Rosenblatts Training Algorithm

• determine what to do, and calculate a new weight
  vector
• should have SUBTRACTED
• new weight vector (0.5, 1.6)
• w1 1.5 - 1 0.5
• w2 1.6 - 0 1.6
• Adjust weights, then try all three training cases
  again

13
Ending Training

• This training process continues until
• perceptron gives correct answers for all training
  cases, or
• a maximum number of training passes has been
  carried out
• some training sets may be impossible for a
  perceptron to calculate (e.g., XOR ftn.)
• In actual practice, we train until the error is
  less than an acceptable level

14
Introduction to Training and Learning in Neural
Networks

• CS/PY 231 Lab Presentation 4
• February 7, 2005
• Mount Union College