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ANNs were build with the assumption of point neurons as nodes in a network and many of their training algorithms are biophysically unrealistic. While ANNs can be good function approximators, they are a very inaccurate representation of brain neuronal neurons and networks (which have intricate dendrites and biophysics). We don't know yet how fundamental processes like memory storage work in the brain; it's one of the great mysteries of neuroscience.

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