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Old 05-29-2013, 04:26 PM
Elroch Elroch is offline
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Posts: 143
Default Re: Gradient Descent on complex parameters (weights)

The purpose of a quality function for comparing options, such as an error function, requires at the very least a total order on the range. It would be reasonable for this to be topological, rather than explicitly metric: this would do no harm to the ideas of minima, or comparisons between errors. [One indication of this was in the lectures, where an error function was replaced by its logarithm, in the knowledge that this would preserve the total order].

But as Yaser indicates, complex numbers lack such an order (at least a natural one), so can't be the range of an error function.
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