Mind, Body, World- Foundations of Cognitive Science, 2013a

Decision Point
From Table 4-4
Equivalent Production
Network
Cluster
Rule 4 Poisonous
P7: if (odor = none) (spore print colour = white) (gill
size = narrow) ((stalk surface above ring = silky)
(stalk surface above ring = scaly)) not edible
5
Rule 5 Edible
P8: if (odor = none) (spore print colour = white) (gill
size = narrow) (stalk surface above ring = smooth)
(bruises = no) edible
8 or 12
Rule 5 Poisonous
P9: if (odor = none) (spore print colour = white) (gill
size = narrow) (stalk surface above ring = smooth)
(bruises = yes) not edible
10
Table 4-5. Dawson et al.’s (2000) production system translation of Table 4-4.
Conditions are given as sets of features. The Network Cluster column pertains
to their artificial neural network trained on the mushroom problem and is
described later in the text.
The other nine output units were used to provide extra output learning, which was
the technique employed to insert a classical theory into the network. Normally, a
pattern classification system is only provided with information about what correct
pattern labels to assign. For instance, in the mushroom problem, the system
would typically only be taught to generate the label edible or the label poisonous.
However, more information about the pattern classification task is frequently available.
In particular, it is often known why an input pattern belongs to one class
or another. It is possible to incorporate this information to the pattern classification
problem by teaching the system not only to assign a pattern to a class (e.g.,
“edible”, “poisonous”) but to also generate a reason for making this classification
(e.g., “passed Rule 1”, “failed Rule 4”). Elaborating a classification task along such
lines is called the injection of hints or extra output learning (Abu-Mostafa, 1990;
Suddarth & Kergosien, 1990).
Dawson et al. (2000) hypothesized that extra output learning could be used
to insert the decision tree from Table 4-4 into a network. Table 4-4 provides nine
different terminal branches of the decision tree at which mushrooms are assigned
to categories (“Rule 1 edible”, “Rule 1 poisonous”, “Rule 2 edible”, etc.). The network
learned to “explain” why it classified an input pattern in a particular way by turning
on one of the nine extra output units to indicate which terminal branch of the decision
tree was involved. In other words, the network (which required 8,699 epochs
of training on the 8,124 different input patterns!) classified networks “for the same
Elements of Connectionist Cognitive Science 181