Together, grid cells' activity within a grid cell module forms a 2D torus [9, 20].

A central problem to understanding intelligence is the concept of generalisation. This allows previously learnt structure to be exploited to solve tasks in novel situations differing in their particularities.

Here, we showhowthis map couldbeconstructed byprobabilistic message-passing through thehippocampalentorhinal system, where messages are scheduled to reduce the propagation of redundant information.

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The biggerµ is,thebetter the error correction. For the set of( x) that form a group, a matrix representationM( x) is equivalent to another representation M( x)if there exists an invertible matrixP such that M( x)=PM( x)P 1 for each x. A matrix representation is reducible if it is equivalent to a block diagonal matrix representation, i.e., we can find a matrixP, such thatPM( x)P 1 is block diagonal for every x. IfM is block-diagonal,M =diag(Mk,k=1,...,K), with nonequivalentblocks,andeachblock Mkcannotbefurtherreduced,thenthematrixelements (Mkij( x)) are orthogonal basis functions of x. Such orthogonality relations are proved by Schur [15] for finite group, and by Peter-Weyl for compact Lie group [13].