Interactive Activation and Competition: Answers
Updated by Simon Dennis, 1999.
Exercise 2: Both the Bookie and Pusher units drop in activation because they are mutually inhibitory. However, the Pusher unit also has positive weights to the active Art instance unit. Consequently, it wins the competition driving the Bookie unit down and allowing its own activation to increase when the Bookie unit is no longer inhibiting it.
Exercise 3: The value of the unit decreases quickly at first and then more slowly as it gets closer to the rest value of -0.1.
Exercise 4: The activation is below one after the first cycle.
Exercise 5: max = 1, neti = 1, decay = 0.1, rest = -0.1.
ai = (max neti + decay rest) / (decay + neti)
= (1 x 1 + 0.1 x -0.1)/ (0.1+1)
= 0.99/1.1
= 0.9
The equilibrium point is 0.9. The simulation should settle quickly to that value.
Exercise 6: let 
ai = 0 and solve for ai
0 = (a i - min) neti - decay (ai - rest)
a i decay - a i neti = decay rest - min neti
a i = (decay rest - min neti) / (decay - neti)
min = -0.2, neti = -1, decay = 0.1, rest = -0.1.
a i = (decay rest - min neti) / (decay - neti)
= (0.1 x -0.1 - -0.2 x -1) / (0.1 - -1)
= -0.21/1.1
= -0.19
Exercise 7:
| Activation of Unit 1 | Activation of Unit 2 |
|---|---|
| 0.510 | 0.500 |
| 0.514 | 0.493 |
| 0.523 | 0.482 |
| 0.536 | 0.466 |
| 0.556 | 0.442 |
| 0.586 | 0.406 |
| 0.628 | 0.354 |
| 0.686 | 0.283 |
| 0.757 | 0.192 |
| 0.834 | 0.091 |
Exercise 8: The units will settle on activations of 0.577 and 0.683. They increase in activation and keep each other alive, but not at the same level of activation.
Exercise 9: When the external input to unit 1 is cut it decays to zero removing the block on unit 2. Unit 2 then increases to a value of 0.547.
Exercise 10: Both units oscillate. When unit 1 is on unit 2 is off and vice versa.
Exercise 11:
a1 = (a1 - 0) net1
= (1 - 0) (-1)
= -1
a2 = (1 - a2) net2
= (1-0) 1
= 1
So when a units activation is zero it becomes one and when it is one it becomes zero.
Exercise 12: Art and Ralph share several properties. They are both Jets, they both went to Junior High, they are both single and they are both pushers. Because Art was active all of these properties started to become active. In turn, they activated Ralph's instance unit.
Exercise 13: While Ralph's instance unit receives activation from all of the properties, the Ralph name unit receives activation only from Ralph's instance unit. Consequently, the change in activation of the Ralph name unit is much smaller than that of the instance unit.
Exercise 14: The Ralph name unit never becomes active because it is blocked by the Art name unit and does not receive sufficient support from its instance unit to overcome the blocking.
Exercise 15: As noted above Art shares properties with other gang members. These gang members instance nodes become active and then support the properties to different degrees. For instance, the Ralph instance unit supports the 20s unit which is in competition with the 40s unit. Consequently, the 40s unit is a little less active than the other feature units. The instance units for Sam and Lance take on negative activations. When these are multiplied by the positive weights they inhibit the Jets unit. Consequently, the Jets unit is lower than the other features.
Exercise 16: Burglar = -0.13, Bookie = 0.53, Pusher = 0.65
Exercise 17: The Pusher unit receives support from the Art instance unit.
Exercise 18: The Burglar unit has been pushed low by competition from the Bookie and Pusher units.
Exercise 19: Ralph.
Exercise 20: The Rick name unit becomes active despite the erroneous information.
Exercise 21: The 40s unit deactivates and the 30s unit becomes active as it represents Rick's age.
Exercise 22: The JH, 40s, Jet and Pusher characteristics become active.
Exercise 23: Art and Ralph are very similar to each other and hence reinforce the same set of properties. Sam, however, is quite different and consequently looses the competition.
Exercise 24: At first glance it isn't obvious why the 40s unit should become active. The Single unit is connected with the Art, Sam and Ralph instance units which are connected to 40s, 20s and 30s units respectively. So there is no initial advantage. As discussed in the previous question the Sam unit dies off because it does not share features with Art and Ralph. This reduces support for the 20s unit so it will no longer compete. However, the 30s and 40s units are both receiving activation so why does the 40s unit win? The answer hinges on the the instance units that are not active. The Rick and Lance units become negative. Rick is connected to the 30s unit and Lance to the 20s unit, so the net input of both of these units is reduced and the 40s unit wins.
Exercise 25: Before removal of the weights the Ralph instance unit activates the Jet, 30s, J.H., Single and Pusher properties. After removal of the weights the Single unit becomes active as before, but now the 40s unit becomes active rather than the 30s unit. Since Ralph is similar to Art the Art instance unit becomes active. Art is single so that unit becomes active, but Art is also in his 40s so that unit becomes erroneously active. If there were more gang members who were similar to Ralph the result would depend on the average of their characteristics.
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