# Logical Message Passing Networks with One-hop Inference on Atomic Formulas

arXiv: https://arxiv.org/abs/2301.08859 · HTML: https://mlsanity.com/paper/2301.08859/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 48 references that are in the map.
- First posted on arXiv 21 Jan 2023.

## Builds on (most cited first, 30 of 32)

- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Language Models as Knowledge Bases?](https://mlsanity.com/paper/1909.01066/) (2019)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [Embedding Entities and Relations for Learning and Inference in Knowledge Bases](https://mlsanity.com/paper/1412.6575/) (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)
- [Heterogeneous Graph Attention Network](https://mlsanity.com/paper/1903.07293/) (2019)
- [Convolutional 2D Knowledge Graph Embeddings](https://mlsanity.com/paper/1707.01476/) (2017)
- [A Survey on Knowledge Graphs: Representation, Acquisition and Applications](https://mlsanity.com/paper/2002.00388/) (2020)
- [K-BERT: Enabling Language Representation with Knowledge Graph](https://mlsanity.com/paper/1909.07606/) (2019)
- [Neural Bellman-Ford Networks: A General Graph Neural Network Framework for Link Prediction](https://mlsanity.com/paper/2106.06935/) (2021)
- [Low-Dimensional Hyperbolic Knowledge Graph Embeddings](https://mlsanity.com/paper/2005.00545/) (2020)
- [Quaternion Knowledge Graph Embeddings](https://mlsanity.com/paper/1904.10281/) (2019)
- [Query2box: Reasoning over Knowledge Graphs in Vector Space using Box Embeddings](https://mlsanity.com/paper/2002.05969/) (2020)
- [Variational Reasoning for Question Answering with Knowledge Graph](https://mlsanity.com/paper/1709.04071/) (2017)
- [Canonical Tensor Decomposition for Knowledge Base Completion](https://mlsanity.com/paper/1806.07297/) (2018)
- [Beta Embeddings for Multi-Hop Logical Reasoning in Knowledge Graphs](https://mlsanity.com/paper/2010.11465/) (2020)
- [Noise Contrastive Estimation and Negative Sampling for Conditional Models: Consistency and Statistical Efficiency](https://mlsanity.com/paper/1809.01812/) (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)
- [Relational Message Passing for Knowledge Graph Completion](https://mlsanity.com/paper/2002.06757/) (2020)
- [Neural-Symbolic Models for Logical Queries on Knowledge Graphs](https://mlsanity.com/paper/2205.10128/) (2022)
- [Mask and Reason: Pre-Training Knowledge Graph Transformers for Complex Logical Queries](https://mlsanity.com/paper/2208.07638/) (2022)
- [TorusE: Knowledge Graph Embedding on a Lie Group](https://mlsanity.com/paper/1711.05435/) (2017)
- [Probabilistic Entity Representation Model for Reasoning over Knowledge Graphs](https://mlsanity.com/paper/2110.13522/) (2021)
- [Query2Particles: Knowledge Graph Reasoning with Particle Embeddings](https://mlsanity.com/paper/2204.12847/) (2022)
- [Benchmarking the Combinatorial Generalizability of Complex Query Answering on Knowledge Graphs](https://mlsanity.com/paper/2109.08925/) (2021)
- [Geometry Interaction Knowledge Graph Embeddings](https://mlsanity.com/paper/2206.12418/) (2022)
- [Neural-Symbolic Entangled Framework for Complex Query Answering](https://mlsanity.com/paper/2209.08779/) (2022)

## Built on by (most cited first, 28 of 28)

- [Neural Graph Reasoning: Complex Logical Query Answering Meets Graph Databases](https://mlsanity.com/paper/2303.14617/) (2023)
- [Complex Query Answering on Eventuality Knowledge Graph with Implicit Logical Constraints](https://mlsanity.com/paper/2305.19068/) (2023)
- [Wasserstein-Fisher-Rao Embedding: Logical Query Embeddings with Local Comparison and Global Transport](https://mlsanity.com/paper/2305.04034/) (2023)
- [A Foundation Model for Zero-shot Logical Query Reasoning](https://mlsanity.com/paper/2404.07198/) (2024)
- [Sequential Query Encoding For Complex Query Answering on Knowledge Graphs](https://mlsanity.com/paper/2302.13114/) (2023)
- [Rethinking Complex Queries on Knowledge Graphs with Neural Link Predictors](https://mlsanity.com/paper/2304.07063/) (2023)
- [Top Ten Challenges Towards Agentic Neural Graph Databases](https://mlsanity.com/paper/2501.14224/) (2025)
- [EFOk-CQA: Towards Knowledge Graph Complex Query Answering beyond Set Operation](https://mlsanity.com/paper/2307.13701/) (2023)
- [Knowledge Graph Reasoning over Entities and Numerical Values](https://mlsanity.com/paper/2306.01399/) (2023)
- [Improving Complex Reasoning over Knowledge Graph with Logic-Aware Curriculum Tuning](https://mlsanity.com/paper/2405.01649/) (2024)
- [Is Complex Query Answering Really Complex?](https://mlsanity.com/paper/2410.12537/) (2024)
- [Enhancing Transformers for Generalizable First-Order Logical Entailment](https://mlsanity.com/paper/2501.00759/) (2025)
- [Privacy-Preserved Neural Graph Databases](https://mlsanity.com/paper/2312.15591/) (2023)
- [Conditional Logical Message Passing Transformer for Complex Query Answering](https://mlsanity.com/paper/2402.12954/) (2024)
- [KnowFormer: Revisiting Transformers for Knowledge Graph Reasoning](https://mlsanity.com/paper/2409.12865/) (2024)
- [Query2Triple: Unified Query Encoding for Answering Diverse Complex Queries over Knowledge Graphs](https://mlsanity.com/paper/2310.11246/) (2023)
- [Learning Federated Neural Graph Databases for Answering Complex Queries from Distributed Knowledge Graphs](https://mlsanity.com/paper/2402.14609/) (2024)
- [Improving Multi-hop Logical Reasoning in Knowledge Graphs with Context-Aware Query Representation Learning](https://mlsanity.com/paper/2406.07034/) (2024)
- [On the Role of Entity and Event Level Conceptualization in Generalizable Reasoning: A Survey of Tasks, Methods, Applications, and Future Directions](https://mlsanity.com/paper/2406.10885/) (2024)
- [Extending Complex Logical Queries on Uncertain Knowledge Graphs](https://mlsanity.com/paper/2403.01508/) (2024)
- [Meta Operator for Complex Query Answering on Knowledge Graphs](https://mlsanity.com/paper/2403.10110/) (2024)
- [Transformers for Complex Query Answering over Knowledge Hypergraphs](https://mlsanity.com/paper/2504.16537/) (2025)
- [Pathformer: Recursive Path Query Encoding for Complex Logical Query Answering](https://mlsanity.com/paper/2406.14880/) (2024)
- [Efficient and Scalable Neural Symbolic Search for Knowledge Graph Complex Query Answering](https://mlsanity.com/paper/2505.08155/) (2025)
- [One Model, Any Conjunctive Query: Graph Neural Networks for Answering Queries over Incomplete Knowledge Graphs](https://mlsanity.com/paper/2409.13959/) (2024)
- [Interactive Query Answering on Knowledge Graphs with Soft Entity Constraints](https://mlsanity.com/paper/2508.13663/) (2025)
- [CQD-SHAP: Explainable Complex Query Answering via Shapley Values](https://mlsanity.com/paper/2510.15623/) (2025)
- [Neural Scalable Symbolic Search Framework for Complex Logical Queries with Multiple Free Variables](https://mlsanity.com/paper/2605.25985/) (2026)

## Abstract (arXiv)

Complex Query Answering (CQA) over Knowledge Graphs (KGs) has attracted a lot of attention to potentially support many applications. Given that KGs are usually incomplete, neural models are proposed to answer the logical queries by parameterizing set operators with complex neural networks. However, such methods usually train neural set operators with a large number of entity and relation embeddings from the zero, where whether and how the embeddings or the neural set operators contribute to the performance remains not clear. In this paper, we propose a simple framework for complex query answering that decomposes the KG embeddings from neural set operators. We propose to represent the complex queries into the query graph. On top of the query graph, we propose the Logical Message Passing Neural Network (LMPNN) that connects the local one-hop inferences on atomic formulas to the global logical reasoning for complex query answering. We leverage existing effective KG embeddings to conduct one-hop inferences on atomic formulas, the results of which are regarded as the messages passed in LMPNN. The reasoning process over the overall logical formulas is turned into the forward pass of LMPNN that incrementally aggregates local information to finally predict the answers' embeddings. The complex logical inference across different types of queries will then be learned from training examples based on the LMPNN architecture. Theoretically, our query-graph represenation is more general than the prevailing operator-tree formulation, so our approach applies to a broader range of complex KG queries. Empirically, our approach yields the new state-of-the-art neural CQA model. Our research bridges the gap between complex KG query answering tasks and the long-standing achievements of knowledge graph representation learning.