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By Gary F. Marcus

An try to combine theories approximately how the brain works, person who says that the brain is a computer-like manipulator of symbols, and one other that says that the brain is a huge community of neurons operating jointly in parallel.

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There may be other kinds of operations over variables as well, such as one that determines whether a given number is odd or even. 1 Can People Generalize UQOTOM? There is ample evidence, I think, that people can generalize universally quantified one-to-one mappings. 1 Input and output data. Training Item Input Output 1010 0100 1110 0000 1010 0100 1110 0000 Test Item 1111 ? artificial example. 1. If you are like other people whom I have asked, you would guess that in the test item the output that corresponds to input item [1111] is [1111].

For example, given the training data, the conditional probability that the rightmost digit would be a 1 is exactly 0. The model thus extends a conditional probability in a way that is mathematically sound. 6 A model that performs either the “copy” function or the “invert” function, depending on the activity of the rightmost input node. If there were no cases in which organisms could freely generalize on the basis of limited input, training independence might not be a problem. In tasks in which subjects cannot freely generalize, a model that does its training independently may actually be preferred over a model that can learn only relationships that apply to all instances of a class.

In hindsight, though, my claim should seem obvious, perhaps even banal. After all, a network that implements the identity (that is, “copy”) function using a set of connections such as in the left panel has essentially the same wiring diagram as a digital logic chip that implements a copy function. My remarks so far have been purely about representation, not about generalization. To sum them up, models that allocate a single node to each variable have (putting aside the worries about nonlinear activation functions and arbitrary representational schemes) no choice but to represent abstract relationships between variables, whereas models that allocate multiple nodes to each variable sometimes represent abstract relationships between variables and sometimes do not: what they represent is a function of what their connection weights are.

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