Neural models of mental transformations and invariants (Q1329119)

Experimental evidence [see \textit{R. N. Shepard} and \textit{J. Metzler}, Science 171, 701-703 (1971)] suggests that humans can perform mental rotations of geometric figures. In particular it is observed that people take longer to make matches of figures where the degree of rotation is larger. This paper discusses a connectionist network that is able to perform rotations in a way that fits this experimental evidence. Sufficient conditions for the delta rule algorithm suggested by \textit{R. P. Goebel} [J. Math. Psychol. 34, No. 4, 435-444 (1990; Zbl 0707.92025)] to converge are given. It is shown that the matrix that realizes the connections is related to the irreducible representations of the group of rotations.