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Notes
- 1.
As mentioned in the preface we also applied a newly developed network of ours to an economical problem, namely the forecast of the probable economical success of new types of cell phones.
- 2.
Mathematicians and theoretical physicists often speak of “elegance” when they apply the principle of Occam’s Razor . The simpler a theory or model respectively is the more elegant it is.
- 3.
A “teacher” is not necessarily a human being and not even a living system. If for example a child is learning to ride a bicycle then gravity acts as teacher: the child learns from falling over and crashing on the ground that it must keep the bicycle moving in order to avoid the consequences of the force of gravity.
- 4.
Recently the German mark system has slightly changed. The worst mark now is a “4.3”, which means “not fair enough”. The basic principle, though, is the same.
- 5.
It must be noted, however, that there are different versions of the Delta rule and accordingly it is possible to construct different versions of the supervised learning enforcing rule , which we shall show below. The Delta rule is often also called Widrow-Hoff rule in honor to their inventors Widrow and Hoff (Widrow and Hoff 1960).
- 6.
Benjamin Berg, Remigius Kijak and Jörg Krampitz.
- 7.
In honor, of course, to John Steinbeck, although he certainly had no idea of neural networks and learning rules.
- 8.
Sometimes reinforcement learning is defined in another manner: the learning system constructs by itself an inner picture or model of the desired goal. The learning results, i.e. the output after each variation of the weight matrix, are then compared with the goal. A detailed description of this procedure give Jordan and Rummelhart (2002) who call this “distal learning”. In this article we only use the definition of reinforcement learning given above. It must be noted, by the way, that the Hebbian learning rule may also be used for self-organized learning in cases where the learning system gets no feed back, although with greater difficulty than the application of the enforcing for this learning type (see below).
- 9.
Experiments and simulations with reinforcement learning are not frequently done with neural networks . That is another reason why we show the simulations of instrumental conditioning in detail.
- 10.
The whole model was implemented as a JAVA program by two of our students Richard Kucharek and Volker Zischka. Interested readers may obtain it from the authors.
- 11.
The details can be looked up in the implemented model mentioned in footnote 10.
- 12.
More correctly speaking all neural connections that represent a blind alley do not change their according weight values.
- 13.
Here a similar assumption is made as in the models with semantical networks where those neurons represent the meaning of a message whose final activation values are the largest.
- 14.
Chomsky was right when he pointed out that a theory of language acquisition could not be obtained by using only Behaviorist assumptions. But he was certainly wrong when he suggested that this would make Behaviorism generally useless.
- 15.
The network, therefore, is a simple version of a recurrent network.
- 16.
We proposed the second model ourselves in Klüver and Klüver (2007), but now we think otherwise.
- 17.
By the way, the interest in classical conditioning is still very strong. At present American biologists for example try to condition certain fishes to return to a cave when hearing a specific signal . The idea is to condition the young fishes, let them free in order that they feed themselves in the free ocean and catch them again when the fish is big enough to eat it. Source: Der Spiegel (Germany’s most important News Magazine) 44, 2008.
- 18.
In the first chapter we defined adaptive systems by the duality of rules and meta rules . The concept of self-organized learning shows that adaptive behavior can occur via corrections from the environment, as in the case of biological evolution , and without such environmental corrections.
- 19.
This example can be looked up in more detail in Klüver and Klüver (2007).
- 20.
“More or less” are mathematically speaking concepts of “Fuzzy Logic”. Therefore, it is possible to model Tom’s biography with fuzzy-based models too. In our opinion it is not by chance that, e.g., the linguist Lakoff (loc. cit.) used both prototype theory and fuzzy logic.
- 21.
The development of this SEN -system was sponsored by the Deutsche Telekom. We used it for the forecast of probable market chances of new cell phones by applying the prototype approach.
- 22.
The second procedure is a so-called input vector centered modus that we used for example for marketing purposes.
- 23.
Actually the visualization technique is a bit more complicated, in particular for taking into regard the construction of circles. Yet the formula above is sufficient to understand the basic logic of this visualization algorithm.
- 24.
The details of the story can be looked up in Klüver and Klüver (2007); there only a SOM , an IN and a suited expert system were compared with respect to this murder case. In the next chapter we shall come back to this story in another context; some more details of the content will be given there.
- 25.
There are many different versions of the SOM ; accordingly different functions can be implemented, which, though, always are much more complicated than the SEN rule.
- 26.
The TSP is the problem to find the shortest route between different towns if all towns must be visited but only once. It belongs to the class of so-called NP-complete problems that are very hard to solve, i.e. they need very much and often too much computing time to generate a satisfactory solution.
- 27.
It is possible to change the learning process of a SOM that way that only a part of the weight matrix must changed when inserting new inputs; we did this already (cf. Klüver 2002). Yet even then it is a process of accommodation and additionally it is often not easy to decide which part of the matrix should be changed.
- 28.
For a historical and critical overview cf., e.g., Kamin (1974); at present once more the “nature” position seems to be the more attractive one after the dominance of the nurture position in the seventies and eighties of the last century.
- 29.
This proposal certainly seems just to shift the debate to the question where such abilities of self-enforcing come from. As we are no experts on the field of, e.g. hormonal processes we must leave this to the specialists. Yet it is probably more fruitful to look for the biological source of self-enforcing abilities and more simple than the quest for genetic differences and differences in social milieus.
- 30.
Idioms like “the sun is rising” and “the sun is setting” demonstrate that in everyday thinking and speaking the geocentric model is still a firm part of our physical world-view.
- 31.
We were by far not the first to construct a system for the automatic generation of neural networks (cf. for example Stanley and Miikkulainen (2002) or Zell (2003), to name only these), although we of course think that our system has several advantages in comparison to already existing systems. The students were Kay Timmermann and Daniel Tang who did this as their master thesis.
- 32.
Sometimes the so-called super string theory in quantum physics is quoted as an example for theories that have no immediate reference to empirical reality but are linked to experimental facts only by other theories (cf. Greene 2000). The only condition for the construction of such theories is that they must be consistent with other and accepted theories.
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Klüver, J., Klüver, C. (2011). The Understanding of Learning. In: Social Understanding. Theory and Decision Library A:, vol 47. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9911-2_4
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