By Gary F. Marcus
An try and combine theories approximately how the brain works, one who says that the brain is a computer-like manipulator of symbols, and one other that claims that the brain is a big community of neurons operating jointly in parallel.
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Extra info for Algebraic Mind: Integrating Connectionism and Cognitive Science
Example text
For example, people have talked about Elman’s sentence-prediction model as if it had context-dependent representations of its input words. But in fact, the input nodes are context-independent (the word cat always turns on the same node regardless of where in a sentence it appears), and the hidden nodes do not truly represent individual words; instead, the hidden units represent sentence fragments. So it’s not that cat is represented differently by the hidden units in the sentence cats chase mice as opposed to the sentence I love cats.
But it is possible to have an input variable that is represented by a single node that takes on discrete values or by a set of nodes that take on continuous activation values. What is important for present purposes is not whether a node is analog or binary but rather whether a given variable is represented by a single node or many. 1 Models That Allocate One Node to Each Variable With this distinction—between representational schemes that allocate one node per variable and representational schemes that allocate more than one node per variable—firmly in mind (and clearly distinguished from the separate question of localist versus distributed encoding), we are now ready to consider the relation between multilayer perceptrons and systems that represent and generalize operations over variables.
Put informally, the network has no way to tell that all four columns should be treated uniformly. People may not always treat the columns uniformly, but certainly under some conditions they can, and these conditions pose difficulties for the many-nodes-per-variable models that are trained by the back-propagation learning algorithm. Relations between Variables 47 Training independence A bit more formally, we can say that manynodes-per-variable multilayer perceptrons that are trained by backpropagation cannot generalize one-to-one mappings between nodes.