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Neural Networks and Analog Computation: Beyond the Turing Limit (Progress in Theoretical Computer Science)
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Neural Networks and Analog Computation: Beyond the Turing Limit (Progress in Theoretical Computer Science) Customer Reviews
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♥♥♥♥♥ |
Elegant theoretical apparatus
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This book provides a systematic overview of a beautiful theoretical apparatus that the author and collaborators have developed for describing the computational power of neural networks. It addresses neural networks from the standpoint of computational complexity theory, not machine learning.
A central issue that arises is what values the neural couplings can take on. The book outlines the consequences of various choices. Rational-valued neural networks turn out to be Turing machines, a contribution of general significance. The book shows (and perhaps unduly emphasizes) that irrational-valued couplings can yield Superturing computation, a result which has been controversial.
If irrational numbers can arise in a computational setting, then the work outlined here is clearly a major landmark that deserves the careful, systematic exposition the book provides. On the other hand, maybe irrational numbers are just not relevant to actual computational devices. (They certainly aren't yet.) If so, the book is still a worthwhile theoretical exercise leading to an elegant set of results. Even if one leans toward the latter option - and I would say that this is probably the vast majority - I don't think any of us really _know_ where the irrational numbers stand vis-a-vis our computational universe.
Even if you intuitively see that an infinitely rich source of information, which is what an irrational number provides, should yield Super-Turing computation, the book is still valuable. (If you don't have this intuition, think about it more!) There is a lot to be gleaned from the non-obvious (at least to me) details of how that intuition works itself out.
The book has more technical flaws. The author periodically states results without really explaining fully, or even at all. This leaves a good deal of work to the reader. I would expect to spend a few hours per page, here and there, though usually it will move quicker. A major issue is also the challenging notation, which is often more difficult than it needs to be. The book's introduction to advice turing machines is also insufficient; you'll need to do a bit of background reading if you don't know much about them. |
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