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Number of Hidden Layers
Rule of Thumb 1
Even if the function to learn is slightly non-linear, the generalization may be better with a simple linear model than with a complicated non-linear model; if there is too little data or too much noise to estimate the non-linearities accurately.
Rule of Thumb 2
If there is only one input, there seems to be no advantage to using more than one hidden layer; things get much more complicated when there are two or more inputs.