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By solving this optimization7 problem in the online setting we derive a neural network with local learning rules. Furthermore, this approach lets us interrogate which aspects of a10 detailed model are essential for performing this optimization task. As we understand it, experimental30 observations regarding plasticity of distal dendrites range from those giving more weight to Ca2+plateaus (in the31 hippocampus [Golding et al 2002]), to those giving more weight to the back-propagating action potentials (in the32 neocortex [Sjöström et al 2006]). Asmentionedabove,thelinearityof37 the model isaprice paid for achieving asimple and analytically tractable model. However,modelsofdimensionality reduction areknown39 to be computationally effective and useful for learning.