Takane, Y., Oshima-Takane, Y., & Shultz, T. R. (December, 1994). Approximations of nonlinear functions by feed-forward networks. Proceedings of the 11th Annual Meeting of the Japan Classification Society (pp. 26-33). Tokyo: Japan Classification Society.
Neural network (NN) models are very popular in artificial intelligence, pattern recognition, cognitive psychology, etc. Feed-forward networks may be viewed as approximating nonlinear functions that connect inputs to outputs (e.g., Ripley, 1993). They are known to be robust and efficient approximators of nonlinear functions (e.g., Hornik, Stinchcombe, & White, 1989). We analyze how the approximations are done using a variety of multivariate and graphical techniques (Takane, Oshima-Takane, & Shultz, 1994; Oshima-Takane, Shultz, & Takane, forthcoming). The particular network architecture we are interested in is the cascade correlation (CC) learning network (Fahlman & Lebiere, 1990) which is capable of dynamically growing nets to adapt to more complicated problems We look at how the learning and representation of knowledge occur in the CC networks as it performs a variety of tasks. We also examine the generalization capability and the effect of environmental bias in the training.
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