Abstract
The application of signal flow graphs to the learning process of neural networks is presented. By introducing the so-called adjoint graph, new insight into the mechanism of learning phenomena of the weights in neural networks has been obtained. The derived updating formulas are valid for both feedforward and recurrent neural networks and are especially useful from the hardware implementation point of view of the self-learning networks. The presented numerical experiments confirmed the usefulness of the presented approach.
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Acar C (1991) New transformations in signal flow graphs. Electronics Lett 7:27–28
Almeida L (1987) Backpropagation in perceptrons with feedback. In: Eckmiller R, Malsburg C (eds) Neural computers. (NATD ASI Ser F, vol 41) Springer, Berlin Heidelberg New York, pp 199–208
Chua LO, Lin PM (1975) Computer aided analysis of electronic circuits. Prentice Hall, Englewood Cliffs, NJ
Cichocki A (1992) Neural network for singular value decomposition. Electronics Lett 28:784–786
Cichocki A, Osowski S (1978) Analysis of active networks using flow graph technique. Electronics Lett 14:227–228
Cichocki A, Unbehauen R (1992) Neural networks for computing eigenvalues and eigenvectors, Biol Cybern 68:155–164
Golub G, Van Loan C (1990) Matrix computation. North Oxford Academic, Oxford
Hasler M (1993) The backpropagation learning algorithm realized by an analogue circuit. Int J Cir Theor Appl 21:177–181
Hertz J, Krogh A, Palmer R (1990) Introduction to the theory of neural computation. Addison-Wesley, Amsterdam
Lee AY (1974) Signal flow graphs — computer aided system analysis and sensitivity calculation. IEEE Trans CAS 21:209–216
Lippman R (1987) An introduction to computing with neural nets. IEEE ASSP April
Mason S, Zimmerman H (1960) Electronic circuits, signals and systems. Wiley, New York
Osowski S (1991) Electrical circuit optimization through neural network application. AEÜ 45:105–110
Osowski S (1992) Signal flow graph approach to the learning rule of neural networks. Workshop on Massively Parallel Computations, Leysin, 9–11 March 1992, pp 13–24
Robichaud L, Boisverd M, Robert J (1962) Signal flow graphs and applications. Prentice Hall, Englewood Cliffs, NJ
Rumelhard D, McClelland J (1986) Parallel distributed processing. IT Press, Cambridge, Mass
Tank D, Hopfield J (1986) Simple neural optimization networks. IEEE Trans CAS 33:533–541
Widrow B, Lehr M (1990) 30 years of adaptive neural networks: perceptron, madaline and backpropagation. Proc IEEE 78:1415–1441
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Osowski, S. Signal flow graphs and neural networks. Biol. Cybern. 70, 387–395 (1994). https://doi.org/10.1007/BF00200336
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DOI: https://doi.org/10.1007/BF00200336