Read e-book online Synergetic Computers and Cognition: A Top-Down Approach to PDF

By Hermann Haken

ISBN-10: 3642075738

ISBN-13: 9783642075735

ISBN-10: 3662101823

ISBN-13: 9783662101827

This e-book offers a unique method of neural nets and hence deals a real replacement to the hitherto recognized neuro-computers. This technique relies at the author's discovery of the profound analogy among development attractiveness and development formation in open platforms faraway from equilibrium. therefore the mathematical and conceptual instruments of synergetics could be exploited, and the concept that of the synergetic laptop formulated. an entire and rigorous concept of development acceptance and studying is gifted. The ensuing set of rules may be applied on serial desktops or learned via totally parallel nets wherein no spurious states take place. particular examples (recognition of faces and town maps) are supplied. the popularity technique is made invariant with appreciate to simultaneous translation, rotation, and scaling, and permits the popularity of complicated scenes. Oscillations and hysteresis within the conception of ambiguous styles are taken care of, in addition to the popularity of circulate styles. A comparability among the popularity talents of people and the synergetic computing device sheds new mild on attainable versions of psychological techniques. The synergetic laptop may also practice logical steps reminiscent of the XOR operation. the recent version features a part on transformation homes of the equations of the synergetic computing device and at the invariance houses of the order parameter equations. extra additions are a brand new part on stereopsis and up to date advancements within the use of pulse-coupled neural nets for trend recognition.

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Extra info for Synergetic Computers and Cognition: A Top-Down Approach to Neural Nets

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50) Clearly a 0 lies between 0 and 1 provided B>O and C>O. e. when only one ~u 0. 47): * ~6 = 1 . 3 Important Properties of v V(~k) 45 Fig. 5. 48). Note the singularity at a 0 We thus find that only one pattern can be recognized at a time. However, it is conceivably possible that there are spurious states of the potential where it has a local minimum at several non vanishing ~u. In order to show that this case is excluded, we study the stationary and stable points more closely by investigating the potential V.

36) * Note that the sum over k' k is now a double sum where k' and k each run from 1 ... M, but with the terms k' = k omitted. 36) can be easily visualized by considering a plot of the potential V in a two-dimensional feature space, where the two axes are spanned by the two prototype vectors v1 and v2 (Fig. 4). k are positive. 24) takes over and, eventually, increases much more quickly than the first term decreases. This interplay between the first and last terms generates the valleys indicated in Fig.

Interpretation of pattern recognition by means of an order parameter moving in a potential landscape with two attractors, vase and face, respectively (left). The right-hand side shows the ambiguous pattern vase/face. This interpretation of pattern recognition was given by Haken (1977) pattern formation I order parameter pattern recognition I I order parameter I 111\\\ 111\\\ DO DODD ODD DOD subsystems features Fig. 2. Analogy between pattern formation (left) and pattern recognition (right). In pattern formation the subsystems are enslaved by the order parameters; in the case of pattern recognition it is the features that are enslaved by order parameters.

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