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One aspect that I'd like to add to the previous answers is the so-called Curse of dimensionality. This concept refers to the problem that many algorithms have a time complexity that grows exponentially with the dimension of the data. As a simple example, let us consider a set $\{0,1\}^{D}$ that has only two values per dimension. For example, \$\{0,1\}^{2} = \{...

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Actually, the hierarchical learning explanation given by mindcrime is not that acceptable anymore (This was also indicated by Ian Goodfellow). Since there are neural networks with 150 layers or more, and this explanation does not make sense for such neural networks. However, we can think of it as solving the knots of high dimensional manifolds, i.e. we ...

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I don't know of any neural network that can do cryptography well, so you would have to do a little experimenting yourself. The main thing that sticks out to me is that doing operations in the elliptical curve requires the modulus operator since it works in finite field, and I think neural networks have a hard time learning the modulus operator in general. So ...

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