Mathematical Perspectives on Neural Networks

By Paul Smolensky; Michael C. Mozer et al. | Go to book overview

of learning in general as a mechanism for constructing the transformations which will convert the original physically based configuration of the input vectors into an appropriate functional or psychological space, with the proper similarity relationships between concepts for making generalizations and transfer of learning occur automatically and correctly.


CONCLUSION

In this chapter we have tried to provide a kind of overview and rationale for the design and understanding of networks. Although it is possible to design and use interesting networks without any of the ideas presented here, it is, in our experience, very valuable to understand networks in terms of these probabilistic interpretations. The value is primarily in providing an understanding of the networks and their behavior so that one can craft an appropriate network for an appropriate problem. Although it has been commonplace to view networks as kinds of black boxes, this leads to inappropriate applications which may fail not because such networks cannot work but because the issues are not well understood.


REFERENCES

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Durbin, R., & Rumelhart, D. E. ( 1989). Product units: A computationally powerful and biologically lausible extension to backpropagation networks. Neural Computation, 1, 133-142.

Durbin, R., & Willshaw, D. ( 1987). "An analogue approach to the travelling salesman problem using an elastic net method". Nature, 326, 689-691.

Hornik, K., Stinchcombe, M., & White, H. ( 1989). Multilayer Feed-forward Networks are Universal Approximators, Neural Networks, 2, pp. 359-366.

Jacobs, R. A., Jordan, M. I., Nowlan, S. J., & Hinton, G. E. ( 1991). Adaptive mixtures of local experts. Neural Computation, 3(1).

Jordan, M. I., & Rumelhart, D. E. ( 1992). Forward models: Supervised learning with a distal teacher. Cognitive Science, 16, pp. 307-354.

Keeler, J. D., Rumelhart, D. E., & Loew, W. ( 1991). Integrated segmentation and recognition of hand-printed numerals. In R. P. Lippmann, J. E. Moody, and D. S. Touretzky (Eds.), Neural information processing systems (Vol. 3). San Mateo, CA: Morgan Kaufmann.

Kolmogorov, A. N. ( 1991). Selected Works of A. N. Kolmogorov, Dordrecht; Boston; Kluwer Academic.

Le Y. Cun, Boser, Y. B., Denke, J. S., Henderson, R. D., Howard, R. E., Hubbard, W., & Jackel, L. D. ( 1990). In D. S. Touretzky (Ed.), Handwritten digit recognition with a back-propagation network (Vol. 2). San Mateo, CA: Morgan Kaufmann.

McCullagh, P. & Nelder, J. A. ( 1989). Generalized linear models. London: Chapman and Hall.

Mitchison, G. J., & Durbin, R. M. ( 1989). "Bounds on the learning capacity of some multi-layer networks". Biological Cybernetics, 60, 345-356.

Nowlan, S. J. ( 1991). "Soft Competitive Adaptation: Neural Network Learning Algorithm based onFitting Statistical Mixtures"

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