# RConE: Rough Cone Embedding for Multi-Hop Logical Query Answering on Multi-Modal Knowledge Graphs

arXiv: https://arxiv.org/abs/2408.11526 · HTML: https://mlsanity.com/paper/2408.11526/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 42 references that are in the map.
- First posted on arXiv 21 Aug 2024.

## Builds on (most cited first, 28 of 28)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Visual Genome: Connecting Language and Vision Using Crowdsourced Dense Image Annotations](https://mlsanity.com/paper/1602.07332/) (2016)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Deep High-Resolution Representation Learning for Visual Recognition](https://mlsanity.com/paper/1908.07919/) (2019)
- [Complex Embeddings for Simple Link Prediction](https://mlsanity.com/paper/1606.06357/) (2016)
- [A Survey on Knowledge Graphs: Representation, Acquisition and Applications](https://mlsanity.com/paper/2002.00388/) (2020)
- [Knowledge Graphs](https://mlsanity.com/paper/2003.02320/) (2020)
- [Neural Bellman-Ford Networks: A General Graph Neural Network Framework for Link Prediction](https://mlsanity.com/paper/2106.06935/) (2021)
- [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)
- [A Survey of Knowledge Graph Reasoning on Graph Types: Static, Dynamic, and Multimodal](https://mlsanity.com/paper/2212.05767/) (2022)
- [MMKG: Multi-Modal Knowledge Graphs](https://mlsanity.com/paper/1903.05485/) (2019)
- [Multi-Hop Knowledge Graph Reasoning with Reward Shaping](https://mlsanity.com/paper/1808.10568/) (2018)
- [ConE: Cone Embeddings for Multi-Hop Reasoning over Knowledge Graphs](https://mlsanity.com/paper/2110.13715/) (2021)
- [Multi-Modal Knowledge Graph Construction and Application: A Survey](https://mlsanity.com/paper/2202.05786/) (2022)
- [Image-embodied Knowledge Representation Learning](https://mlsanity.com/paper/1609.07028/) (2016)
- [Neural-Symbolic Models for Logical Queries on Knowledge Graphs](https://mlsanity.com/paper/2205.10128/) (2022)
- [Fully Convolutional Scene Graph Generation](https://mlsanity.com/paper/2103.16083/) (2021)
- [Knowledge Graph Embedding with Iterative Guidance from Soft Rules](https://mlsanity.com/paper/1711.11231/) (2017)
- [Neural Graph Reasoning: Complex Logical Query Answering Meets Graph Databases](https://mlsanity.com/paper/2303.14617/) (2023)
- [Embedding Uncertain Knowledge Graphs](https://mlsanity.com/paper/1811.10667/) (2018)
- [Query Embedding on Hyper-relational Knowledge Graphs](https://mlsanity.com/paper/2106.08166/) (2021)
- [TFLEX: Temporal Feature-Logic Embedding Framework for Complex Reasoning over Temporal Knowledge Graph](https://mlsanity.com/paper/2205.14307/) (2022)
- [MMKGR: Multi-hop Multi-modal Knowledge Graph Reasoning](https://mlsanity.com/paper/2209.01416/) (2022)
- [NQE: N-ary Query Embedding for Complex Query Answering over Hyper-Relational Knowledge Graphs](https://mlsanity.com/paper/2211.13469/) (2022)

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

- [The Periodic Table of LLM Reasoning: A Structured Survey of Reasoning Paradigms, Methods, and Failure Modes](https://mlsanity.com/paper/2606.11470/) (2026)
- [InductWave: Inductive Multi-Hop Logical Query Answering on Knowledge Graphs](https://mlsanity.com/paper/2607.07422/) (2026)

## Abstract (arXiv)

Multi-hop query answering over a Knowledge Graph (KG) involves traversing one or more hops from the start node to answer a query. Path-based and logic-based methods are state-of-the-art for multi-hop question answering. The former is used in link prediction tasks. The latter is for answering complex logical queries. The logical multi-hop querying technique embeds the KG and queries in the same embedding space. The existing work incorporates First Order Logic (FOL) operators, such as conjunction (wedge), disjunction (vee), and negation (neg), in queries. Though current models have most of the building blocks to execute the FOL queries, they cannot use the dense information of multi-modal entities in the case of Multi-Modal Knowledge Graphs (MMKGs). We propose RConE, an embedding method to capture the multi-modal information needed to answer a query. The model first shortlists candidate (multi-modal) entities containing the answer. It then finds the solution (sub-entities) within those entities. Several existing works tackle path-based question-answering in MMKGs. However, to our knowledge, we are the first to introduce logical constructs in querying MMKGs and to answer queries that involve sub-entities of multi-modal entities as the answer. Extensive evaluation of four publicly available MMKGs indicates that RConE outperforms the current state-of-the-art.