Application

Application

[mjhealy]

I hope people on the categories list find this interesting:

At the International Joint Conference on Neural Networks (IJCNN05) in
Montreal last week, I presented our joint work with Sandia National
Laboratories in research on category theory applied to neural networks.
We demonstrated improved performance with a modification to a standard
artificial neural architecture in generating a multispectral image from
satellite data.  To create the modified architecture, we added a neural
representation of limit cones to the standard architecture and used these
to exert fine control over the network operation.  An
information-theoretic measure we used, to compare the image we generated
with the category-theoretic modification to the image generated by the
unmodified standard architecture, increased by a factor of two with the
category-theoretic modification.  An ``eyeball comparison'' of images also
shows a clear improvement.  We believe this is the first application of
category theory directly in an engineering application (while at Boeing,
another colleague and I had demonstrated its application to the synthesis
of engineering software).

The accompanying paper is in the Proceedings of IJCNN05.  It doesn't have
the information-theoretic result (obtained after the paper was submitted);
I put that in the presentation.  Also, we only show a simple modification
just to illustrate the use of limits (the limits here are just products);
the actual architecture is just a bit more complex and includes
coproducts.  A paper we will be submitting to some journal will have the
missing material.  Of course, if you want more information I will be glad
to hear from you.

Mike Healy
mjhealy@ece.unm.edu