Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

One of my professors mentioned that a standard problem in dynamical systems is to show that if two points in your system have the same coding (ie end up in specific regions of the space you're working on) then this coding is periodic. I'm interested in seeing examples of this type of problem, preferably with solutions.

share|improve this question
1  
I think what you're talking about is symbolic dynamics. –  Chris Taylor Jul 20 '11 at 23:04
    
@ChrisTaylor the question is specific and interesting. symbolic dynamics is a whole field of dynamical systems... –  Glougloubarbaki Dec 4 '11 at 18:29
1  
@Glougloubarbaki I imagine that's why I left it as a comment instead of an answer. –  Chris Taylor Dec 4 '11 at 23:02
add comment

1 Answer 1

In neural networks, a number of invariances exist that can be used to show that NNs in general do not have unique solutions. NNs can be thought of as dynamical systems without feedback -- the inputs act as parameters to the system, and the weights themselves are the system variables.

The book Pattern Recognition and Machine Learning by Chris Bishop has a nice treatment in one of the first few chapters on weight invariances. I won't go so far as to say the invariances occur in a periodic manner across weight space -- that's a bit too many dimensions for me to even fathom periodic behavior -- but it might help you find a better answer to your question.

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.