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The semantic pointer architecture is a vector symbolic architecture where high-dimensional sparse vectors represent concepts. These concepts can be mathematical, linguistic or sensory. In all of the experiments I've seen these vectors are assigned randomly

In the case of mathematical and linguistic, are there any theories or experiments investigating how these vectors may be formed? Is this a relevant topic for investigation? If not, why?

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I do not know for sure, but I believe that the vectors would be created in a domain-specific manner. Vectors in the visual system would be created in a way that is particular to the needs of visual processing, etc. The reason why the vectors are represented as random in the semantic pointer architecture, is because from the point of view of the architecture itself, the information encoded in the vector is irrelevant. What is relevant is how to manipulate those concepts once they are already formed.

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