# FLEX: Feature-Logic Embedding Framework for CompleX Knowledge Graph Reasoning

arXiv: https://arxiv.org/abs/2205.11039 · HTML: https://mlsanity.com/paper/2205.11039/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 38 references that are in the map.
- First posted on arXiv 23 May 2022.

## Builds on (most cited first, 16 of 16)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Complex Embeddings for Simple Link Prediction](https://mlsanity.com/paper/1606.06357/) (2016)
- [RotatE: Knowledge Graph Embedding by Relational Rotation in Complex Space](https://mlsanity.com/paper/1902.10197/) (2019)
- [TuckER: Tensor Factorization for Knowledge Graph Completion](https://mlsanity.com/paper/1901.09590/) (2019)
- [DeepPath: A Reinforcement Learning Method for Knowledge Graph Reasoning](https://mlsanity.com/paper/1707.06690/) (2017)
- [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)
- [Multi-Hop Knowledge Graph Reasoning with Reward Shaping](https://mlsanity.com/paper/1808.10568/) (2018)
- [Complex Query Answering with Neural Link Predictors](https://mlsanity.com/paper/2011.03459/) (2020)
- [ConE: Cone Embeddings for Multi-Hop Reasoning over Knowledge Graphs](https://mlsanity.com/paper/2110.13715/) (2021)
- [Neural Subgraph Matching](https://mlsanity.com/paper/2007.03092/) (2020)
- [Self-Supervised Hyperboloid Representations from Logical Queries over Knowledge Graphs](https://mlsanity.com/paper/2012.13023/) (2020)
- [M-Walk: Learning to Walk over Graphs using Monte Carlo Tree Search](https://mlsanity.com/paper/1802.04394/) (2018)
- [Probabilistic Entity Representation Model for Reasoning over Knowledge Graphs](https://mlsanity.com/paper/2110.13522/) (2021)
- [Logic Embeddings for Complex Query Answering](https://mlsanity.com/paper/2103.00418/) (2021)

## Built on by (most cited first, 3 of 3)

- [Neural Graph Reasoning: Complex Logical Query Answering Meets Graph Databases](https://mlsanity.com/paper/2303.14617/) (2023)
- [TFLEX: Temporal Feature-Logic Embedding Framework for Complex Reasoning over Temporal Knowledge Graph](https://mlsanity.com/paper/2205.14307/) (2022)
- [NQE: N-ary Query Embedding for Complex Query Answering over Hyper-Relational Knowledge Graphs](https://mlsanity.com/paper/2211.13469/) (2022)

## Abstract (arXiv)

Current best performing models for knowledge graph reasoning (KGR) introduce geometry objects or probabilistic distributions to embed entities and first-order logical (FOL) queries into low-dimensional vector spaces. They can be summarized as a center-size framework (point/box/cone, Beta/Gaussian distribution, etc.). However, they have limited logical reasoning ability. And it is difficult to generalize to various features, because the center and size are one-to-one constrained, unable to have multiple centers or sizes. To address these challenges, we instead propose a novel KGR framework named Feature-Logic Embedding framework, FLEX, which is the first KGR framework that can not only TRULY handle all FOL operations including conjunction, disjunction, negation and so on, but also support various feature spaces. Specifically, the logic part of feature-logic framework is based on vector logic, which naturally models all FOL operations. Experiments demonstrate that FLEX significantly outperforms existing state-of-the-art methods on benchmark datasets.