Modeling N-ary relational data as gyro-polygons with learnable gyro-centroid

摘要

Binary Knowledge base (KB) embedding has been broadly studied, while n-ary relational KB embedding which aims to simultaneously map binary and beyond-binary facts into low-dimensional vector space is less explored. Existing n-ary KB embedding approaches typically treat entities in n-ary fact as equally important or decompose n-ary relational fact into subtuples. And they generally model n-ary relational KBs in the Euclidean space. However, n-ary facts are semantically and structurally intact, decomposition leads to intrinsic semantic information loss and undermines the structural integrity. Moreover, compared to the binary relational KBs, n-ary ones are characterized by more abundant and complicated hierarchy structures, which could not be well expressed in Euclidean space and have been greatly overlooked. To address these issues, we propose a gyro-polygon embedding framework to realize n-ary fact structure keeping, semantic integrity retaining, and hierarchy capturing, termed as PolygonE. Specifically, n-ary relational facts are modeled as gyro-polygons in the hyperbolic space, where we denote entities in facts as vertexes of gyro-polygons and relations as entity translocation operations. Importantly, we design a fact plausibility measuring strategy based on the vertex–gyrocentroid geodesic to optimize the relation-adjusted gyro-polygon. We further extend PolygonE by unsupervisedly learning the weight of each entity, and strengthening the connection between the primary triple and the whole fact with the gyrocentroid–gyromidpoint distance. Extensive experiments demonstrate the superiority of PolygonE.