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I don't understand why the type of bint was chosen, and what impact, exactly, does it have on the usability of the network.

Or, asked differently: Given some task that you want to train your network for, how do you decide which type you should choose?

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The type bint is an encoding of binary sequences, so it's simple enough as a working example but it's nontrivial enough that you could construe any sort of learning algorithm as operating on it.

The type you choose is part of the model you're training so your question is as difficult as "what kind of network topology should I use?".

Right. In practice one would want to use more complicated types (such as the type of Turing machines, explained in Clift’s thesis) but in the talk I did not have time to explain more interesting examples.

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