Parity function Neural Networks

Many layers are needed
MPSO for sphere function

I have read an interesting paper on limitations of machine learning models: Scaling Learning Algorithms towards AI. It mentions limitation of two-layer neural networks and other two-layer models (SVMs). These shallow models are unable to learn some functions without an exponential number of components. For example, to learn the parity function over N input bits, they would need 2N hidden neurons.

On the other hand, a deep model with N layers could compute the parity with just N components.

Source: Lessoned Code

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Foreign Exchange trading up 21%-- Adios $

2005-01-12 07:32:11 by puro

Did the Romans curse Caligula, or only in historical retrospect?
"Forex trade volumes hit record levels
By Jennifer Hughes in New York
Published: January 11 2005 17:26 | Last updated: January 11 2005 17:26
Foreign exchange trading volumes leapt to record levels in the first week of 2005, according to EBS, the largest interbank trading platform, and the Chicago Mercantile Exchange.
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Average daily volume for the week on EBS reached $162bn, up 21 per cent on the same week last year and considerably higher than the average of about $100bn. Total volumes for the week were $811bn.
Trading in FX products over the CME’s Globex electronic platform last week was up 182 per cent over the same period in 2004, and pit-traded options volumes were...

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