Minds and Computers : An Introduction to the Philosophy of Artificial Intelligence

Figure 19.1
Computing AND.

---

threshold value  of C is such that it will only fire if both A and B fire.
If A alone fires, then the activation value of C will be 3 which is below
the threshold value of 5. Similarly if B alone fires. If, however, they
both fire, then the weighted sum transfer function tells us that the acti-
vation value of C will be the sum of the values of the a
fferent con-
nection weights, which in this case will be 6. This activation value of
6 is higher than the threshold value of 5 assigned to C, so it will fire
in accordance with its threshold activation function.
This network serves as a logic gate. It computes the binary logical
truth function of conjunction. The output unit fires i
ff both A and B
fire.
Exercise 19.1
(a) How might we modify the network depicted in Figure
19.1 such that it computes the binary logical function of
disjunction – i.e. so that the output node fires i
ff either A
or B (or both) fire.
(b) Design a network with two input nodes and one output
node such that the output node will fire if either of the
input nodes fire but not if they both fire.
If you succeeded in completing Exercise 19.1(b) then you have
designed a network which computes the binary logical truth function
of exclusive disjunction. This is not a straightforward exercise since we
need to do two things that are new to us. One is to assign inhibitory
weights; the other is to add a hidden unit to the network between the
input and output units. The solution is depicted in Figure 19.2.
If we disregard node D in Figure 19.2 for a moment, then we have
the solution to Exercise 19.1(a). All we needed to do was lower the
threshold value of C to a value below either of the a
fferent connec-
tion weights. (Alternatively we could have raised both connection
weights to a value above the threshold.) In order to prevent C from
firing when both A and B fire, however, we need to add node D.
Node D will fire i
ff both A and B fire and will inhibit the activation
of C to prevent it from firing. If A alone fires, then the activation value
of D will be below the threshold value and it will not fire, but the acti-
vation value of C will be above its threshold and it will fire. Similarly
if B alone fires. If A and B both fire, however, then D will fire, as its
activation will be above its threshold value. The activation value of C
will be the sum of its a
fferent connection weights (3  3  5 
 1)
190
  

---

which is below its threshold value so, by virtue of being inhibited by
D, it will not fire. To recap, C will fire if either A fires or B fires but not
if they both fire, quod erat demonstrandum.
19.3 SYNTHESISING SPEECH
In this section we’re going to design an artificial neural network to
function as an English speech synthesiser. This is a nice example of
the kind of contextually sensitive processing tasks at which connec-
tionist networks excel.
English orthography is not phonemic – it does not admit of a regular
mapping onto English phonemes. Unlike Japanese, for instance, which
is such that the pronunciation of any given grapheme is contextually
invariant, the pronunciation of a given English grapheme is dependent
on its orthographic context. In other words, English is not ‘pronounced
as it is written’, to speak loosely. Rather, the sound that a given letter
stands for is contextually dependent – one and the same letter can stand
for di
fferent sounds and the same sound can be represented by various
letters, depending on the spelling context.
Consequently, designing a speech synthesiser for English involves,
inter alia, implementing the contextually sensitive processing task of
converting orthographic representations to phonemic representa-
tions. We’re going to begin constructing an artificial neural network
for implementing this conversion of orthographic input to phonemic
output.
  
191