Jamrozik, A., & Shultz, T.
R. (2007). Learning the structure of a mathematical group. In D. McNamara &
G. Trafton (Eds.), *Proceedings of the
Twenty-ninth Annual Conference of the Cognitive Science Society* (pp.
1115-1120).

A mathematical group is a set of operations that satisfies the properties of identity, inverse, associativity, and closure. Understanding of group structure can be assessed by changing elements and operations over different versions of the same underlying group. Participants learned this structure more quickly over four different, successive versions of a subset of the Klein 4-group, suggesting some understanding of the group structure (Halford, Bain, Mayberry, & Andrews, 1998). Because an artificial neural network learning the task failed to improve, it was argued that such models are incapable of learning abstract group structures (Phillips & Halford, 1997). Here we show that an improved neural model that adheres more closely to the task used with humans does speed its learning over changing versions of the task, showing that neural networks are capable of learning and generalizing abstract structure.

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