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I have come across a few main ways of understanding neural networks.

  • Neural networks as neurons with synapses.
  • Neural networks as probabilistic inference machines. (Bayes, information etc)
  • Neural networks as transformations on data. (similar to the matrix transforms you see in graphics)
  • Neural networks as aggregations of experts (also called features). (each node is some sort of expert, wisdom of crowds etc..)
  • Neural networks as a player in a game with nature. Where nature is an adversary trying to get the NN to make as many mistakes as possible

Are there other ways to think about what neural networks?? What are they?

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  • $\begingroup$ cool. yea, of course. like parameter fitting, except for functions. and the turing thing makes sense as well, were we are considering a (R)NN as a finite state machine/automata. $\endgroup$ Commented Mar 28, 2016 at 8:09
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Neural networks as finite approximations of continuous functions:

https://en.wikipedia.org/wiki/Universal_approximation_theorem

In short, neural networks can approximate continuous functions with arbitrary accuracy (that depends on the number of neurons) and consequently form a dense set in the space of continuous functions on any closed and bounded sets. This is tangentially related to stuff like fourier series, and polynomial approximation.

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