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8th September 2010, 04:20 PM  #1 
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Join Date: Dec 2005
Location: west lafayette

Mathematical background for theory of hierarchicalmemory feedback systems
I just finished Jeff Hawkin's work, On Intelligence. In it, he discusses a theoretical model of the human brain which uses a "folded feedback" system to create invariant representations of the world. He refers to it as a "hierarchicalmemory" system which analyzes sequences of sequences, rather than data at the highest level.
I am interested in learning more about the behavior of such systems. I understand the complexity of such a system would be enormous, but the implications for such a system are even greater. I am also interested in mathematical evolution (ex. Genetic algorithms). Genetic algorithms border on chaos and little is known about their behavior. A "foldedfeedback" system similar to what Hawkins has proposed could search for patterns in the chaos of evolution and dynamically adjust the mutation operators, crossover functions, inheritance functions, and fitness functions to optimize the evolutionary process. An invariant representation of the global optimal solution could greatly enhance the usefulness of genetic algorithms. A shroud of mysticism with regards to these systems pervades my mind. I am only capable of a primitive qualitative understanding of such systems at this moment. What topics of mathematics would I have to be fluent in to truly understand the theory quantitatively? I understand how ridiculous this may sound, but I am genuinely interested in the topic.
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8th September 2010, 04:34 PM  #2 
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If you want a topic that relates to audio check out genetic algorithms for designing IIR digital filters. It surprised me that some very simple problems have no closed form solution.
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8th September 2010, 05:00 PM  #3  
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Quote:
Also, please note that this is not an attempt to model the human brain, but rather a desire to create a mathematical model (which could be implemented in software) which is qualitatively similar to the type of system proposed by Hawkins. What field of mathematics would be appropriate to analyze nested sequences of sequences of sequences? Chaos theory? Something else?
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"It is a profound and necessary truth that the deep things in science are not found because they are useful; they are found because it was possible to find them." Last edited by thadman; 8th September 2010 at 05:09 PM. 

9th September 2010, 12:12 AM  #4  
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Hubert Dreyfus's "Intelligence Without Representation"
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