1. Associative Learning

2. Simple Associative Network

3. Unconditioned Stimulus
Banana Associator
Unconditioned Stimulus
Conditioned Stimulus

4. Unsupervised Hebb Rule
Vector Form:
Training Sequence:

5. Banana Recognition Example
Initial Weights:
Training Sequence:
a = 1
First Iteration (sight fails): a 1 ( ) h r d l i m w p
0.5 – + ×
(no response) =

6. Example Second Iteration (sight works): Third Iteration (sight fails):2 ( ) h r d l i m w p 1
0.5 – + ×
(banana) =
Third Iteration (sight fails):
Banana will now be detected if either sensor works.

7. Problems with Hebb Rule
Weights can become arbitrarily large
There is no mechanism for weights to decrease

8. Hebb Rule with Decay
This keeps the weight matrix from growing without bound, which can be demonstrated by setting both ai and pj to 1:

9. Example: Banana Associator
g = 0.1
First Iteration (sight fails): a 1 ( ) h r d l i m w p
0.5 – + ×
(no response) =
Second Iteration (sight works): a 2 ( ) h r d l i m w p 1
0.5 – + ×
(banana) =

10. Third Iteration (sight fails):
Example
Third Iteration (sight fails):
Hebb Rule
Hebb with Decay

11. Problem of Hebb with Decay
Associations will decay away if stimuli are not occasionally presented.
If ai = 0, then
If g = 0, this becomes
Therefore the weight decays by 10% at each iteration
where there is no stimulus.

12. Instar (Recognition Network)

13. Instar Operation The instar will be active when or1 p q
cos b – =
For normalized vectors, the largest inner product occurs when the angle between the weight vector and the input vector is zero -- the input vector is equal to the weight vector.
The rows of a weight matrix represent patterns
to be recognized.

14. Vector Recognition If we setb w 1 p – =
the instar will only be active when q = 0.
If we set b w 1 p –
>
the instar will be active for a range of angles. w 1
As b is increased, the more patterns there will be (over a wider range of q) which will activate the instar.

15. Instar Rule Hebb with Decay
Modify so that learning and forgetting will only occur
when the neuron is active - Instar Rule: w i j q ( ) 1 – a p g + = or
Vector Form:

16. Graphical Representation
For the case where the instar is active (ai = 1): or
For the case where the instar is inactive (ai = 0):

17. Example

18. Training
First Iteration (a=1):

19. Orange will now be detected if either set of sensors works.
Further Training
(orange) h a 2 ( ) r d l i m w p W – + = 3 1 × è ø ç ÷ æ ö a 3 ( ) h r d l i m w p W 2 – + =
(orange) × 1 è ø ç ÷ æ ö
Orange will now be detected if either set of sensors works.

20. Kohonen Rule Learning occurs when the neuron’s index i is a member of
the set X(q). We will see in Chapter 14 that this can be used
to train all neurons in a given neighborhood.

21. Outstar (Recall Network)

22. Outstar Operation
Suppose we want the outstar to recall a certain pattern a*
whenever the input p = 1 is presented to the network. Let
Then, when p = 1
and the pattern is correctly recalled.
The columns of a weight matrix represent patterns
to be recalled.

23. Outstar Rule
For the instar rule we made the weight decay term of the Hebb
rule proportional to the output of the network. For the outstar
rule we make the weight decay term proportional to the input of the network.
If we make the decay rate g equal to the learning rate a,
Vector Form:

24. Example - Pineapple Recall

25. Definitions

26. Iteration 1
a = 1

27. Convergence