Self-organisation of transformation-invariant detectors for constituents of perceptual patterns

A geometrical interpretation of the elementary constituents which make up perceptual patterns is proposed: if a number of different pattern-vectors lie approximately within the same plane in the pattern-vector space, those patterns can be interpreted as sharing a common constituent. Individual constituents are associated with individual planes of patterns: a pattern tying within an intersection of several such planes corresponds to a combination of several constituents. This interpretation can model patterns as hierarchical combinations of constituents that are themselves combinations of yet more elementary constituents.A neuron can develop transformation-invariances in its recognition-response by aligning its synaptic vector with one of the plane-normals: a pattern-vector's projection along the synaptic vector is then an invariant of all the patterns on the plane. In this way, discriminating detectors for individual constituents can self-organise through Hebbian adaptation. Transformation-invariances tha...