Taxonomy Expansion, which models complex concepts and their relations, can be formulated as a set representation learning task. The generalization of set, fuzzy set, incorporates uncertainty and measures the information within a semantic concept, making it suitable for concept modeling. Existing works usually model sets as vectors or geometric objects such as boxes, which are not closed under set operations. In this work, we propose a sound and efficient formulation of set representation learning based on its volume approximation as a fuzzy set. The resulting embedding framework, Fuzzy Set Embedding (FUSE), satisfies all set operations and compactly approximates the underlying fuzzy set, hence preserving information while being efficient to learn, relying on minimum neural architecture. We empirically demonstrate the power of FUSE on the task of taxonomy expansion, where FUSE achieves remarkable improvements up to 23% compared with existing baselines. Our work marks the first attempt to understand and efficiently compute the embeddings of fuzzy sets.
View on arXiv@article{xu2025_2506.08409,
title={ FUSE: Measure-Theoretic Compact Fuzzy Set Representation for Taxonomy Expansion },
author={ Fred Xu and Song Jiang and Zijie Huang and Xiao Luo and Shichang Zhang and Adrian Chen and Yizhou Sun },
journal={arXiv preprint arXiv:2506.08409},
year={ 2025 }
}