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1991 | Buch

Synergetic Computers and Cognition

A Top-Down Approach to Neural Nets

verfasst von: Professor Dr. Dr. h.c. Hermann Haken

Verlag: Springer Berlin Heidelberg

Buchreihe : Springer Series in Synergetics

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SUCHEN

Über dieses Buch

This book will be of interest to graduate students, researchers and teachers in the computer sciences, in the cognitive sciences andin physics. It provides the reader with a novel approach to the design and study of neural nets. The applicability of this approach is shown explicitly by means of realistic examples. In addition, detailed models of the cognitive abilities of humans are included and compared with the performance of the synergetic computer presented in this book. The work presented here would not have been possible without the important help of my coworkers. Dr. Arne Wunderlin has helped me in many respects over many years and has made essential contributions, in particular to the slaving principle of synergetics. Drs. Michael Bestehorn, Rudolf Friedrich and Wolfgang W eimer have applied the methods of synergetics to spontaneous pattern forma­ tion in fluids and have further developed these methods. Armirr Fuchs has not only implemented my algorithm on a VAX computer, but has also made his own important contributions, in particular to pattern recognition that is invariant with respect to translation, rotation, and scaling. Thomas Ditzinger, Richard Haas, and Robert Hönlinger have contributed within the work on their diploma theses to the application of our approach to a number of problems that are shared by humans and computers in the field of pattern recognition. I wish to thank all of them.

Inhaltsverzeichnis

Frontmatter

Goal

1. Goal
Abstract
The purpose of this book is at least three-fold.
1)
It presents a new computer concept with explicit examples of its applications.
 
2)
It shows how synergetics leads us to the idea that pattern recognition and, more generally, cognitive processes can be conceived as spontaneous pattern formation.
 
3)
It provides the reader with new models of cognitive processes.
 
Hermann Haken

Synergetic Computers

Frontmatter
2. What are Patterns?
Abstract
These sentences by the famous mathematician Norbert Wiener may serve us as a first guideline in defining a pattern. The idea that the nature of the elements is irrelevant for a pattern raises an important issue; namely, a pattern is defined on a specific length scale, on which the nature of the elements is irrelevant. Clearly we may focus our attention on the structure of these elements, but then the elements become the pattern and in turn are composed of still smaller elements. Rather than attempting a final definition of a pattern, let us consider instead a series of examples.
Hermann Haken
3. Associative Memory
Abstract
A simple example of an associative memory is a telephone dictionary. When we look up a name, we can read off the telephone number belonging to that person. When we use the telephone dictionary, we do this in sequential order. We first look for the first letter of the family name, then for the second letter, etc., and finally we must also, in general, look for the first name Another example is provided by the identification of a smell, e.g. the smell belonging to a rose. In such a case, on perceiving the smell we immediately associate it with a picture of a rose. A further example might be the face of a person known to us. In such a case we associate a name with this face. In a more formal manner, we may characterize the property of an associative memory as follows: Let a set of data, which we symbolize by x and y, be given.
Hermann Haken
4. Synergetics — An Outline
Abstract
Synergetics is an interdisciplinary field of research concerned with the spontaneous formation of spatial, temporal or functional structures by self-organization. Synergetics focusses its attention on situations where the macroscopic properties of a complex system change qualitatively. Instead of trying to confront the reader with still more definitions, let us rather consider some typical examples. We shall start with physics.
Hermann Haken
5. The Standard Model of Synergetics for Pattern Recognition
Abstract
order to construct our model, we use three ingredients:
a)
The concept of associative memory discussed in Chap. 3. When an incomplete set of data is given, the associative memory must be able to complement it.
 
b)
We construct a dynamical process by which pattern recognition is performed. To this end we invent a potential landscape in which a fictitious particle, which describes the patterns, moves. An example is provided by the ambivalent patterns of Fig. 5.1. Later on we shall see that ambiguous patterns require a specific treatment, but for the time being we shall stick to the idea that the system is pulled into one of its attracting states provided an initial condition is set such that the symmetry is broken. In other words, the pattern that is recognized first is the one for which a certain bias was given, or, expressed in yet another way, the pattern is recognized once it is within its basin of attraction.
 
c)
We treat the system as a synergetic system according to the following idea: In Chap. 4 we saw that a partially ordered system, e.g. a fluid in which some of the rolls have been formed, may generate its order parameter, which then competes with the other order parameters of the system. Because of the special preparation of the initial state involving partially ordered subsystems, the order parameter belonging to that specific order wins the competition and, eventually, enslaves the whole system such that it enters a particular ordered state. In pattern recognition we shall take advantage of the same mechanism. Once a set of features is given, they can form their order parameter which will compete with other order-parameters. Eventually the order parameter that had the strongest initial support will win, and will force the system to exhibit the features that were lacking with respect to the special pattern (Fig. 5.2). Thus we see that there is a complete correspondence between the complementation process during pattern formation and the associative memory during pattern recognition.
 
Hermann Haken
6. Examples: Recognition of Faces and of City Maps
Abstract
It is not our intention here to treat toy problems, but rather problems of real life in order to demonstrate the applicability of the concepts developed in Chap. 5. To this end we shall consider pattern recognition of faces. A number of persons, say ten, were photographed and the photographs were digitized, usually with 60 by 60 pixels. The background was processed so as to yield a uniform background. The resulting pictures are then supplied with labels A, B, C,..., to identify the names. As described in Chap. 5 we attribute a vector v k (5.2) to each face with its name, where the components are the grey values of each pixel. In our calculations we used four bits to characterize the grey values.
Hermann Haken
7. Possible Realizations by Networks
Abstract
In Chaps. 5 and 6 we presented our general algorithm for the recognition of patterns. This algorithm exploited strong analogies between pattern formation and pattern recognition as unearthed by synergetics. In this chapter we wish to show how this algorithm can be also implemented on a network which acts in a highly parallel manner.
Hermann Haken
8. Simultaneous Invariance with Respect to Translation, Rotation and Scaling
Abstract
In this chapter we wish to show how pattern recognition can be made invariant with respect to the above-mentioned transformations.
Hermann Haken
9. Recognition of Complex Scenes. Scene-Selective Attention
Abstract
In this brief chapter we deal with the recognition of prototype patterns within complex scenes. To be most explicit, we consider test patterns such as that shown in Fig. 9.1. The prototype patterns to be identified are those of Fig. 6.1a. Since the patterns corresponding to the prototype patterns are spatially shifted with respect to each other, we first make the process invariant with respect to translation by means of the procedure described in Sect. 8.1. In addition, we let the attention parameter λ in (5.13) and (5.33) depend on the index k which labels the specific prototype pattern. For instance k = 1 corresponds to a particular face in Fig. 6.1 a, k = 2 to a second one, and so on.
Hermann Haken
10. Learning Algorithms
Abstract
Learning is a central problem for neural and synergetic computers and in this chapter we shall present a number of learning algorithms. As we have seen in previous chapters, patterns are stored in the form of vectors v k . In order to perform pattern recognition, the formalism requires that the adjoint vectors v k + are known. These v k + occur in different ways depending on whether the formalism is realized on a serial computer or on a network. In a serial computer we have to form the scalar products (v k + q) as is evident from the basic equation (5.11). The same projection is needed when the computer consists of a parallel network with three layers, as shown in Figs. 7.2 and 7.3.
Hermann Haken
11. Learning of Processes and Associative Action
Abstract
While in the preceding chapter we did not prescribe the path (trajectory) along which the system reaches the final attractor states corresponding to the originally offered patterns (prototype patterns), we now wish to show that the system can even learn to reproduce specific paths (trajectories). Or, in other words, the system may learn to perform specific motions in its space of dynamic variables. While in Sects. 11.1 and 11.2 it will be assumed that all motions are taught, in Sect. 11.3 we shall study the case in which only examples are provided such that the system has to interpolate. It will turn out that we may proceed in analogy to Sect. 10.4, i.e., we first derive a Fokker-Planck equation by means of some generalization of the maximum information principle. We then establish an analogy to the Langevin equation which may be interpreted as a network (Sect. 11.2). The whole chapter is rather mathematical and its results will not be needed later in this book, but this approach has important potential for applications.
Hermann Haken

Cognition and Synergetic Computers

Frontmatter
12. Comparisons Between Human Perception and Machine “Perception”
Abstract
In this second part of the book we shall investigate how one can establish rela­tions between the concept and the performance of a synergetic computer and our understanding of cognitive processes in the human brain. Or, to be more modest, we shall ask the question: To what extent can the synergetic computer mimic mental abilities?
Hermann Haken
13. Oscillations in the Perception of Ambiguous Patterns
Abstract
The study of ambiguous (or ambivalent) patterns such as Fig. 13.1 has intrigued psychologists for a long time. Such patterns can be traced back as far as Roman times (Lorscheid and Hofmeister 1980) (Fig. 13.2). In 1759 Porterfield and in 1832 Necker reported on such patterns (Fig. 13.3). For more recent studies and reviews see Fisher (1967), Gombrich (1973), Gräser (1977), Pöppel (1982), Kawamoto and Anderson (1985).
Hermann Haken
14. Dynamic Pattern Recognition of Coordinated Biological Motion
Abstract
So far in this book we have been concerned with static patterns. As humans, we may also recognize patterns of movement such as walking and trotting of horses. This leads us to ask whether movement patterns can also be recognized by the synergetic computer.
Hermann Haken

Logical Operations and Outlook

Frontmatter
15. Realization of the Logical Operation XOR by a Synergetic Computer
Abstract
In this section I wish to show how the XOR operation (the exclusive “or”) can be performed by a dynamical system which has a close formal resemblance to a liquid forming hexagons in a nonequilibrium state. This will allow us to construct a synergetic computer for this operation. Historically, the XOR operation has played an important role in the discussion of parallel computers, or in other words, connectionist machines or neurocomputers. Following up the basic concepts of McCulloch and Pitts, Rosenblatt (1958) had developed his perceptron. The continuation of this work was “killed” (to use Sejmour Papert’s words) by the influential book by Minsky and Papert (1961), “Perceptrons”. In that book they showed that Rosenblatt’s perceptron cannot perform the XOR operation. Nowadays, the XOR operation can be performed by neurocomputers with several layers and a sigmoid activation curve (instead of the original steep threshold curve of McCulloch and Pitts).
Hermann Haken
16. Towards the Neural Level
Abstract
In previous chapters we have developed mathematical models that can reproduce cognitive abilities and can be implemented on serial or certain kinds of parallel computers. In this chapter we will go one step further: we shall investigate the extent to which such models can be linked to the properties of neurones that have been studied experimentally in a number of animals. It is not our task here to present all the physiological details; we merely discuss a few salient features which are decisive for the functioning of neurones within the neural network of a brain.
Hermann Haken
17. Concluding Remarks and Outlook
Abstract
Probably the most salient feature of this book is its exploitation of the profound analogy between pattern recognition and pattern formation. In this concluding chapter I wish to go one step further by claiming that pattern recognition is pattern formation. In making this statement I am referring mainly to pattern recognition by humans. To understand the implications, we must immediately address the question of what sort of patterns are being formed.
Hermann Haken
Backmatter
Metadaten
Titel
Synergetic Computers and Cognition
verfasst von
Professor Dr. Dr. h.c. Hermann Haken
Copyright-Jahr
1991
Verlag
Springer Berlin Heidelberg
Electronic ISBN
978-3-662-22450-2
Print ISBN
978-3-662-22452-6
DOI
https://doi.org/10.1007/978-3-662-22450-2