Algebraic Mind: Integrating Connectionism and Cognitive by Gary F. Marcus

By Gary F. Marcus

An try and 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 big community of neurons operating jointly in parallel.

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Extra info for Algebraic Mind: Integrating Connectionism and Cognitive Science

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Simple claims like “Multilayer perceptrons cannot represent rules” or “Multilayer perceptrons always represent ‘concealed’ rules” simply are not correct. The real situation is more complex—in part because it depends on the nature of a given model’s input representations. Models that allocate a single node to each input variable behave very differently from models that allocate more than one node to each input variable. Models that allocate a single node to each input variable are (with some caveats) simpler than models that allocate multiple nodes to each variable.

0 (and linear activation function with a slope of one and intercept of zero). 0, the model can represent and freely generalize the function f(x) = 2x, or any other function of the form f(x) = mx + b— each of which is a UQOTOM. 3 A network that uses one node to represent each variable. 5x, f(x) = 2x, and so on. Such models cannot learn arbitrary mappings. ) As such they provide a candidate hypothesis for how operations over variables can be implemented in a neural substrate and not for a mental architecture that eliminates the representation of abstract relationships between variables.

Here, the input to the model is a single variable that we might think of as current word. Although any given instantiation of that variable (say, cat) will activate only a single node, every input node can potentially indicate an instantiation of the variable current word. For example, the node for dog might not be active at this moment, but it might be active during the presentation of another sentence. The sentence-prediction model is thus an example of a localist model that allocates multiple nodes to a single input variable.

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