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It is well known that artificial neural nets can be used as approximators of any continous functions to any desired degree. Nevertheless, for a given application and a given network architecture the non-trivial task rests to determine the necessary number of neurons and the necessary accuracy (number of bits) per weight for a satisfactory operation. In this paper the problem is treated by an information theoretic approach. The values for the weights and thresholds in the approximator network are determined analytically. Furthermore, the accuracy of the weights and the number of neurons are seen as general system parameters which determine the the maximal output information (i.e. the approximation error) by the absolute amount and the relative distribution of information contained in the network. A new principle of optimal information distribution is proposed and the conditions for the optimal system parameters are derived. For the simple, instructive example of a linear approximation of a non-linear, quadratic function, the principle of optimal information distribution gives the the optimal system parameters, i.e. the number of neurons and the different resolutions of the variables.
Claesson, G. ; Krebs, Gary F. ; Miller, J. ; Roche, Guy ; Schroeder, Lee S. ; Beneson, Walter ; Plicht, Johannes van der ; Winfield, John S. ; Landaud, Gilbert ; Gilot, J.F. ; Hartnack, Christoph ; Stöcker, Horst
Performance and storage requirements of topology-conserving maps for robot manipulator control
(1989)
A new programming paradigm for the control of a robot manipulator by learning the mapping between the Cartesian space and the joint space (inverse Kinematic) is discussed. It is based on a Neural Network model of optimal mapping between two high-dimensional spaces by Kohonen. This paper describes the approach and presents the optimal mapping, based on the principle of maximal information gain. It is shown that Kohonens mapping in the 2-dimensional case is optimal in this sense. Furthermore, the principal control error made by the learned mapping is evaluated for the example of the commonly used PUMA robot, the trade-off between storage resources and positional error is discussed and an optimal position encoding resolution is proposed.
Why do banks issue contingent convertible debt? To answer this question we study comprehensive data covering all issues by publicly traded banks in Europe of contingent convertible bonds (CoCos) that count as additional tier 1 capital (AT1). We find that banks with lower asset volatility are more likely to issue AT1 CoCos than their riskier counterparts, but that CDS spreads do not react following issue announcements. Our estimates therefore suggest that agency costs play a crucial role in banks' ability to successfully issue CoCos. The agency costs may be higher for CoCos than for equity explaining why we observe riskier or lowly capitalized banks to issue equity rather than CoCos.