FUSE: Measure-Theoretic Compact Fuzzy Set Representation for Taxonomy Expansion

Taxonomy Expansion, which models complex 001 concepts and their relations, can be formulated 002 as a set representation learning task. The gen-003 eralization of set, fuzzy set, incorporates uncer-004 tainty and measures the information within a 005 semantic concept, making it suitable for con-006 cept modeling. Existing works usually model 007 sets as vectors or geometric objects such as 008 boxes, which are not closed under set opera-009 tions. In this work, we propose a sound and 010 efficient formulation of set representation learn-011 ing based on its volume approximation as a 012 fuzzy set. The resulting embedding framework, 013 Fuzzy Set Embedding (FUSE), satisfies all set 014 operations and compactly approximates the un-015 derlying fuzzy set, hence preserving informa-016 tion while being efficient to learn, relying on 017 minimum neural architecture. We empirically 018 demonstrate the power of FUSE on the task of 019 taxonomy expansion, where FUSE achieves re-020 markable improvements up to 23% compared