Classical Neural Networks - Neural Networks and Micromechanics - page 11

Fig. 2.3 Example of
EXCLUSIVE OR (XOR)
classification problem
Minsky and Seymour pointed out that a single-layer network can only classify
data sets that are linearly separable and hence cannot solve problems such as the
EXCLUSIVE OR (XOR) (Fig. 2.3 ). The input vectors (0, 0) and (1, 1) belong to
class b , while the input vectors (0, 1) and (1, 0) belong to class c . It is clear that there
is no linear decision boundary that can classify all four points correctly. This
problem can be generalized to n dimensions, when it is known as the n -bit parity
problem.
This was the sunset of neural network investigation. Artificial intelligence
methods were developed and took the place of neural network investigation.
From 1969 until 1982, neural network investigations had to go underground in
the US, but in the Soviet Union, Europe, and Japan these investigations continued
[ 25 - 30 ]. For example, in 1972-1975, the first autonomous transport robot was
created in the USSR [ 26 , 27 ]. The robot demonstrated obstacle avoidance and
purposive movement in a natural environment. TAIR was a three-wheel power
barrow equipped with a system of sensors as rangefinder and tactile sensors. It
was controlled by a hardware-implemented neural network (the network nodes
were realized as special transistor electronic circuits; connections between nodes
were realized as resistors). TAIR is presented in Fig. 2.4 .
While in motion, the robot was supposed to avoid obstacles such as people, trees,
park benches, and so on. Coordinates of a point in the environment gave the target
of the robot's motion. It was evident from the behavior of TAIR that, in principle,
it is possible to create an entirely autonomous robot operated by a hardware-
implemented neural network. At the same time, it showed the overall complexity
of organization of the robot's interaction with the natural environment, as well as
the necessity of using trainable neural networks.
2.5 Neural Networks of the 1980s
In the early 1980s, a new wave of interest arose due to the publication of John
Hopfield [ 31 ], a researcher in the field of biophysics. He described the analogy
between Hebb's neural network model and the certain class of physical systems.
His efforts allowed hundreds of highly qualified scientists and engineers to join in