Polynomial Nets

[A Buggy AI Program]

Here is a list  of papers that address the use of "higher order" neurons
or links that maybe interpreted as computing terms of a polynomial:

Giles, C. L., & Maxwell, T., Learning, invariance, and generalization in
higher order neural networks, Applied Optics, vol 26, pp 4972-4978, 1987.

Klassen, M. S., & Pao, Y. H., Characteristics of the functional link net:
A higher order delta rule net, Proc. of the 2nd annual IEEE conference on
Neural Networks, San Diego, CA, 1988.

Honavar, V., and Uhr, L. A network of neuron-like units that learns to 
perceive by generation as well as reweighting of links, Proc. of the 1988
Connectionist models summer school, ed: Touretzky, Hinton, and Sejnowski,
Morgan Kaufmann, CA. 1988.

Honavar, V., and Uhr, L. Generation, Local receptive fields, and global 
convergence improve perceptual learning in connectionsit networks, Proc.
of IJCAI-89, Morgan Kaufmann, CA. 1989.

L. Uhr, Generation+Extraction gives optimal space-time learning of Boolean
functions, to appear, Connection Science, 1989.

Honavar, V., & Uhr, L. Brain-Structured Connectionist networks that perceive
and learn, to appear, Connection Science, 1989.

Durbin, R., & Rumelhart, D. E., Product unit: A computationally powerful and
biologically plausible extension to backpropagation networks, 
Neural Computation, vol. 1, pp 133-142.

There is also some work in more traditional (inductive) machine learning
that falls in this category. Hope this helps.

Vasant 
honavar at cs.wisc.edu