new paper on the effect of analog noise in neural computation

[Mike Casey]

Dear Connectionists,


It seems that the paper "On the Effect of Analog Noise in Discrete-Time
Analog Computations" by Wolfgang Maass and Pekka Orponen has
misrepresented the work in my recent Neural Computation article
"The Dynamics of Discrete-Time Computation, with Application to 
Recurrent Neural Networks and Finite State Machine Extraction" (Volume 8,
number 6, pp. 1135-1178, 1996).

Maass and Orponen repeatedly take credit for the following result:

> We show that under very general conditions the presence of analog 
> noise reduces the power of analog computational models to that of a
> finite automaton....

This was shown in Corollary 3.1 of my paper.  
Maass and Orponen fail to mention this in their paper.

My goal, in the NC paper, was to investigate the representational powers
of RNNs, and to do so I included analog noise to avoid unrealistic
assumptions and conclusions about computation in physical systems
(including physically instantiated RNNs). The model of analog noise that I
used was originated by the mathematician Rufus Bowen and includes the
model in Maass and Orponen's paper as a special case.  So the discussion
in their paper about the generality of their model of analog noise as
opposed to those previously used is based on a misinterpretation of
Bowen's pseudo-orbit formalism, which makes no assumptions about the
distribution of the noise process beyond its boundedness (which Maass and
Orponen also assume in their paper).

If you would like to verify these claims, my paper is available in Neural
Computation or on the web at 

http://eliza.ccs.brandeis.edu/people/mcasey/papers.html


Thanks for your time and attention.

Best regards,
Mike


********************************************************************
Mike Casey
Volen Center for Complex Systems Studies
Brandeis University
Waltham, MA  02254
email:  mcasey at volen.brandeis.edu
http://eliza.cc.brandeis.edu/people/mcasey
(617) 736-3144 (voice)  (617) 736-3142 (fax)