Can Liquid State Machines approximate continuous nonlinear functions of several variables i.e. "f(x,y)" which are not seperable?

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Honi Sanders

Yes. Liquid state machines can do arbitrary functions, e.g. the classic XOR task with simple linear readout neurons. See methods section of http://www.igi.tugraz.at/maass/psfiles/218_webversion.pdf

Nicolangelo Iannella

Thanks Honi, Is this paper published since I haven't seen it. I was sure that it should have been attempted in some fashion but just couldn't find it when I last looked. On this note, apart from XOR, have you seen any papers illustrating 2D nonlinear function approximation of say y^2sin(x)?

Yes that paper was published (http://www.jneurosci.org/content/33/28/11515.abstract). Try looking at the paper they cited in that methods section (http://cercor.oxfordjournals.org/content/17/1/149.long). I didn't read it thoroughly, but it seems like what you are looking for.