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

arXiv: https://arxiv.org/abs/2506.08409 · HTML: https://mlsanity.com/paper/2506.08409/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 39 references that are in the map.
- First posted on arXiv 10 Jun 2025.

## Builds on (most cited first, 14 of 14)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [Query2box: Reasoning over Knowledge Graphs in Vector Space using Box Embeddings](https://mlsanity.com/paper/2002.05969/) (2020)
- [Beta Embeddings for Multi-Hop Logical Reasoning in Knowledge Graphs](https://mlsanity.com/paper/2010.11465/) (2020)
- [Embedding Logical Queries on Knowledge Graphs](https://mlsanity.com/paper/1806.01445/) (2018)
- [Facilitating Fine-grained Detection of Chinese Toxic Language: Hierarchical Taxonomy, Resources, and Benchmarks](https://mlsanity.com/paper/2305.04446/) (2023)
- [STEAM: Self-Supervised Taxonomy Expansion with Mini-Paths](https://mlsanity.com/paper/2006.10217/) (2020)
- [A Benchmark and Comprehensive Survey on Knowledge Graph Entity Alignment via Representation Learning](https://mlsanity.com/paper/2103.15059/) (2021)
- [Improving Hypernymy Detection with an Integrated Path-based and Distributional Method](https://mlsanity.com/paper/1603.06076/) (2016)
- [Probabilistic Box Embeddings for Uncertain Knowledge Graph Reasoning](https://mlsanity.com/paper/2104.04597/) (2021)
- [Neural-Symbolic Entangled Framework for Complex Query Answering](https://mlsanity.com/paper/2209.08779/) (2022)
- [Word2Box: Capturing Set-Theoretic Semantics of Words using Box Embeddings](https://mlsanity.com/paper/2106.14361/) (2021)
- [Concept2Box: Joint Geometric Embeddings for Learning Two-View Knowledge Graphs](https://mlsanity.com/paper/2307.01933/) (2023)

## Built on by (most cited first, 2 of 2)

- [Distributionally Robust Set Representation Learning Under Inference-Time Element Corruption](https://mlsanity.com/paper/2605.30089/) (2026)
- [ReLTEx: Reliable LLM-based Taxonomy Expansion](https://mlsanity.com/paper/2608.10970/) (2026)

## Abstract (arXiv)

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.