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Real-Valued Recurrent Neural Networks more Powerful than Turing Machines May 30, 2008

Posted by olvidadorio in Machine Learning.
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Found some work by Hava Siegelmann stating exactly that.

How significant this result is — well, it’s debatable. On the one hand it should seem relatively obvious that a machine using exact real-valued parameters can be more precise when it comes to computing e.g. non-rational values. So no big deal? I wouldn’t be too sure of that. Generally speaking it’s the case that an exact, ideal machine (of what type whatsoever) cannot be found in reality. Neither an infinite-tape Turing Machine nor a Real-Valued Recurrent Neural Network.

However, the neural networks Mis Siegelmann speaks of do not require anything infinetely large, instead all they require something infinetely precise. I would argue that this requirement is much nearer to the basic assumptions made in the physics that inform our world-view. [To avoid confusion, infinite precision is only required in terms what is actually there, not in terms of what can be measured! There may be some quantum-mechanical pitfalls, however to my knowledge it still should be possible to reduce a real-valued neural net to the basic laws of contemporary physics.]

It is not a great leap to suggest that our brain might much better be modeled by a real-valued, recurrent NN. But if this is a much better model for what our brain is — and as this model has been shown to be more powerful in principle than a Turing Machine — we might actually be dealing with quite an interesting result;

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Cheating May 26, 2008

Posted by olvidadorio in Advertising, Economics, Humans, Money.
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A subject close to my heart.

I recently watched two boys fooling around in the water while relaxing at our near-by swimming-pool’s jacuzzi area. The two of them were playing this age-old game of who can stay under water for a longer period of time. Now, one of the boys had good (naive) lungs, the other was a smart cheaty little bastard. Guess who won…

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I Love Amsterdam May 6, 2008

Posted by olvidadorio in Humans.
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Am here in Amsterdam, with Nic. We are coding away at our super-sexy funtcha-project. It’s highly enjoyable.

If only I were a rich man – and could afford those exorbitant housing prices around here. I’d move in!

Some pics follow (partially by Nic)..

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