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Alan Turing and the Neural Networks
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INPUT-1 |
INPUT-2 |
OUTPUT |
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1 |
1 |
0 |
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1 |
0 |
1 |
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0 |
1 |
1 |
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0 |
0 |
1 |
The output of a
connection-modifier in interrupt mode is always 1. So if one of the
neuron's input connections passes via a modifier in interrupt mode,
the neuron's output is simply the opposite (or 'boolean negation') of
whatever comes in along the second input fibre. For example, the
first two lines of the table show what happens if INPUT-1 is
connected to a modifier in interrupt mode. In this case the output
from the neuron is the opposite of INPUT-2.
Turing chose nand as the basic operation of his model neurons because every other logical (or boolean) operation can be carried out by groups of nand-neurons. Turing showed that even the connection-modifier itself can be built out of nand-neurons. So each B-type network consists of nothing more than nand-neurons and their connecting fibres. This is about the simplest possible model of the cortex.
Turing wished to
investigate more complex models of the cortex as well. He longed to
do what modern connectionists are able to do: simulate a neural
network and its training regimen using an ordinary digital computer.
He would, he said, 'allow the whole system to run for an appreciable
period, and then break in as a kind of "inspector of schools"
and see what progress had been made'. But his own research on neural
networks was carried out shortly before the first general-purpose
electronic computers were up and running and he used only paper and
pencil. Thereafter he turned his attention to related research in
what is now called Artificial
Life.
It was not until 1954, the year of Turing's death, that B.G.
Farley and W.A. Clark
succeeded in running the first computer simulation of a small neural
network, at MIT.
Two Examples of B-Type Networks

When both the connection-modifiers in this tiny B-type network are in pass mode, the network behaves as shown in the table on the left. That is to say, the network computes what logicians call the inclusive disjunction of the inputs. However, if the lower connection-modifier is switched to interrupt mode, the network behaves as shown in the table on the right. In this case, the output takes the same value as A, no matter what the value of B. If both modifiers are switched to interrupt mode, the network's output is always 0.
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A |
B |
OUTPUT |
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1 |
1 |
1 |
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1 |
0 |
1 |
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0 |
1 |
0 |
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0 |
0 |
0 |
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A |
B |
OUTPUT |
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1 |
1 |
1 |
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1 |
0 |
1 |
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0 |
1 |
1 |
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0 |
0 |
0 |
The second example of a small B-type network is Turing's own and is from page 11 of his 1948 paper 'Intelligent Machinery'. Turing describes the example as 'chosen at random'. Can you work out how this network behaves? (You may like to refer to the discussion on pages 9-11 of 'On Alan Turing's Anticipation of Connectionism' by Jack Copeland and Diane Proudfoot (from Synthese, vol. 108 (1996) pp. 361-377).)

An example of a larger B-type network is given later in this article.
Making
and Breaking Connections
In 1958, Rosenblatt defined connectionism as the theory that 'stored information takes the form of new connections, or transmission channels in the nervous system, or the creation of conditions which are functionally equivalent to new connections'. The destruction of existing connections can be functionally equivalent to the creation of new connections. A network for performing a specific task may be produced by taking a network with more connections than are needed and selectively destroying some of them. Both processes, destruction and creation, are employed in the training of a B-type. In its initial state, the network that is to be trained has a large number of random inter-neural connections, and the modifiers on these connections are also set randomly, some in pass mode and some in interrupt mode. Unwanted connections are destroyed by switching their attached modifiers to interrupt mode. The output of the neuron immediately upstream of the modifier then no longer finds its way along the connection to the neuron on the downstream end. Conversely, changing the setting of the modifier on an initially interrupted connection to pass mode is in effect to create a new connection. This selective culling and enlivening of connections hones the initially random network into one organised for a given task.
Turing
discovered that a large enough B-type neural network can be
configured (via its connection-modifiers) in such a way that it
itself becomes a general-purpose computer.
B-Types
and the Brain
A large number of the output fibres of a neuron in the brain may be connected to the neuron's own input fibres, either directly or via some intervening chain of neurons. Neuroscientists have long stressed the importance and ubiquity of feedback within the brain. For example, the brain uses feedback to help us focus our attention on certain perceptions to the exclusion of others. Stefan Treue and John Maunsell have recently shown that when a monkey has its attention directed to one of several independently moving dots on a computer screen, feedback returns from neurons in the higher cortex to neurons in the lower cortical areas where motion is identified. This feedback serves to inhibit the activity of neurons that are firing in response to the motions of non-attended dots. However, despite its importance in the brain, feedback is seldom employed in modern connectionist networks. In contrast, the neurons in a B-type network interconnect very freely and, like a brain, a large network will typically be awash with feedback.
Below is a network of the sort typically studied by modern connectionists. Notice the regular, layered structure and the absence of any feedback. Information moves unidirectionally through the net from layer to layer.

A conventional neural network
In contrast, the neurons in a B-type neural network interconnect freely and a large B-type may be awash with feedback:

Part
of a large initially random B-type network
Two Examples of B-Type Networks

When both the
connection-modifiers in this tiny B-type network are in pass mode,
the network behaves as shown in the table on the left. That is to
say, the network computes what logicians call the inclusive
disjunction
of the inputs. However, if the lower connection-modifier is switched
to interrupt mode, the network behaves as shown in the table on the
right. In this case, the output takes the same value as A,
no matter what the value of B.
If both modifiers are switched to interrupt mode, the network's
output is always 0.
|
A |
B |
OUTPUT |
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1 |
1 |
1 |
|
1 |
0 |
1 |
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0 |
1 |
0 |
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0 |
0 |
0 |
|
A |
B |
OUTPUT |
|
1 |
1 |
1 |
|
1 |
0 |
1 |
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0 |
1 |
1 |
|
0 |
0 |
0 |
The second example of a small B-type network is Turing's own and is from page 11 of his 1948 paper 'Intelligent Machinery'. Turing describes the example as 'chosen at random'. Can you work out how this network behaves? (You may like to refer to the discussion on pages 9-11 of 'On Alan Turing's Anticipation of Connectionism' by Jack Copeland and Diane Proudfoot (from Synthese, vol. 108 (1996) pp. 361-377).)
An example of a
larger B-type network is given later in this article. 