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 "hierarchical-memory" 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 "folded-feedback" 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.
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 "folded-feedback" 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.
Interesting. I am seeing practical applications such as you have proposed. In the future, I imagine an audio system where a system of cameras spatially resolves the listeners head, specifically his ears, and dynamically adjusts the response of an array of transducers to provide true 3 dimensional surround sound or modal and reverberance correction. It sounds like science fiction, but something like that could very well be possible with a hierarchical-memory feedback system. I can't even begin to comprehend how complex such a system would be.
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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If you're interested in understanding why 'invariant representations of the world' are a red herring and not actually used by brains (Freeman has evidence from rabbits that they're not), here's an essay to cut your teeth on:
Hubert Dreyfus's "Intelligence Without Representation"
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