1. Simple learning in connectionist networks

2. Learning associations in connectionist networks
Associationism (James, 1890)
Association by contiguity
Generalization by similarity
Connectionist implementation
Represent items as patterns of activity, where similarity is measured in terms of overlap/correlation of patterns
Represent contiguity of items as simultaneous presence of their patterns over two groups of units (A and B)
Adjust weights on connections between units in A and units in B so that the
pattern on A tends to cause the corresponding pattern on B
As a result, when we next present the same or similar pattern on A, it tends to produce the corresponding pattern on B (perhaps somewhat weakened or distorted)

3. Correlational learning: Hebb rule
What Hebb actually said:
When an axon of cell A is near enough to excite a cell B and repeatedly and consistently takes part in firing it, some growth process or metabolic change takes place in one or both cells such that A’s efficacy, as one of the cells firing B, is increased.
The minimal version of the Hebb rule:
When there is a synapse between cell A and cell B, increment the strength of the synapse whenever A and B fire together (or in close succession).
The minimal Hebb rule as implemented in a network:

4. Why?

6. So weight from sending to receiving unit
ends up being proportional to their correlation
over patterns…

8. Final weights: +4, 0

10. Jennifer
Lawrence
Face perception units
Aniston
Postle
Brad
Pitt

11. Face perception neurons (“Sending units”)
“Synapses”
Name neurons
(“receiving units”)

12. Simple learning model
Imagine neurons have a threshold set at 0. If input is above threshold (positive number), the neuron fires strongly. If it is below threshold (negative number), the neuron fires weakly.
When a face is directly observed, the features it possesses get positive input, all others get negative input.
When a name is presented, it gets positive input, all others get negative input.

13. Face perception neurons
Brad Pitt
Name neurons

14. Face perception neurons
Brad Postle
Name neurons

15. Learning to name faces
Goal: Encode “memory” of which name goes with which name…
…so, when given face, correct name units activate.
Face units are “sending units”, name units are “receiving units”
Synapse has a “weight” that describes effect of sending unit on receiving unit
Negative weight= inhibitory influence, positive weight = excitatory influence
Activation rule for name units:
Take state of sending unit * value of synapse (weight), summed over all sending units to get net input.
Activate strongly if net input >0, otherwise activate weakly.

16. What happens if the synapses (weights) are all zero?

17. Face perception neurons
Brad Pitt
Name neurons

18. Face perception neurons
Name neurons

19. Face perception neurons
Brad Postle
Name neurons

20. Face perception neurons
Name neurons
Brad Postle

21. Face perception neurons
Name neurons
Brad Pitt

22. What about new inputs?

23. Face perception neurons
Name neurons
Not Brad Pitt or Postle

24. What about more memories?

25. Face perception neurons
Jennifer
Aniston
Name neurons

26. Face perception neurons
Jennifer
Lawrence
Name neurons

27. Face perception neurons
Name neurons

28. With Hebbian learning, many different patterns can be stored in a single configuration of weights.
What would happen if we kept training this model with the same four faces?
Same weight configuration, just with larger weights.

29. Hebbian learning
Captures “contiguity” of learning (things that occur together should become associated in memory)
Learning rule (∆wij = ε aj ai) is proportional to correlation coefficient between units.
Captures effects of “similarity” in learning (a learned response should generalize to things with similar representations)
With linear units (ai = neti), output is a weighted sum of the unit’s previous activation to stored patterns…
…where the “weight” in the sum is proportional to the similarity (dot product) between the current input pattern and the previously stored pattern
So, a test pattern that is completely dissimilar to a stored pattern (dot product of zero) will not be affected by the stored pattern at all.

30. Limitations of Hebbian learning
Many association problems it cannot solve
Especially where similar input patterns must produce quite different outputs.
Without further constraints, weights grow without bound
Each weight is learned independently of all others
Weight changes are exactly the same from pass to pass.

31. Error-correcting learning
(delta rule)

32. Face perception neurons
Brad Pitt
Squared error!
Name neurons
Error!
Target states

35. Input 1
Input 2
Output 1 1 2 3 w1 w2

36. Delta-rule learning with linear units
Captures intuition that learning should reduce discrepancy between what you predict and what actually happens (error).
Basic approach: Measure error for current input/output pair; compute derivative of this error with respect to each weight; change weight by small amount to reduce error.
For squared error, change in weight is proportional to (tj – aj) ai
…that is, the correlation between the input activation and the current error.
Weight changes can be viewed as performing “gradient descent” in error (each change will reduce total error).
Algorithm is inherently multi-pass: changes to a given weight will vary from pass to pass, b/c error depends on state of weights.

37. Delta rule will learn any association for which a solution exists!