PMID: 8581887Feb 15, 1996Paper

Circular nodes in neural networks

Neural Computation
M J Kirby, R Miranda

Abstract

In the usual construction of a neural network, the individual nodes store and transmit real numbers that lie in an interval on the real line; the values are often envisioned as amplitudes. In this article we present a design for a circular node, which is capable of storing and transmitting angular information. We develop the forward and backward propagation formulas for a network containing circular nodes. We show how the use of circular nodes may facilitate the characterization and parameterization of periodic phenomena in general. We describe applications to constructing circular self-maps, periodic compression, and one-dimensional manifold decomposition. We show that a circular node may be used to construct a homeomorphism between a trefoil knot in R3 and a unit circle. We give an application with a network that encodes the dynamic system on the limit cycle of the Kuramoto-Sivashinsky equation. This is achieved by incorporating a circular node in the bottleneck layer of a three-hidden-layer bottleneck network architecture. Exploiting circular nodes systematically offers a neural network alternative to Fourier series decomposition in approximating periodic or almost periodic functions.

Citations

Jan 13, 2001·Neural Networks : the Official Journal of the International Neural Network Society·W W Hsieh
Aug 20, 2005·Bioinformatics·Matthias ScholzJoachim Selbig
Oct 23, 2010·Neural Computation·Arta A Jamshidi, Michael J Kirby
May 22, 2007·Neural Networks : the Official Journal of the International Neural Network Society·William W Hsieh
Apr 26, 2017·Proceedings of the National Academy of Sciences of the United States of America·Ron C AnafiJunhyong Kim

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