# Towards High-Order Complementary Recommendation via Logical Reasoning Network

arXiv: https://arxiv.org/abs/2212.04966 · HTML: https://mlsanity.com/paper/2212.04966/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 22 references that are in the map.
- First posted on arXiv 9 Dec 2022.

## Builds on (most cited first, 8 of 8)

- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [LightGCN: Simplifying and Powering Graph Convolution Network for Recommendation](https://mlsanity.com/paper/2002.02126/) (2020)
- [RotatE: Knowledge Graph Embedding by Relational Rotation in Complex Space](https://mlsanity.com/paper/1902.10197/) (2019)
- [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)
- [Inferring Networks of Substitutable and Complementary Products](https://mlsanity.com/paper/1506.08839/) (2015)
- [Complete the Look: Scene-based Complementary Product Recommendation](https://mlsanity.com/paper/1812.01748/) (2018)
- [Knowledge-aware Complementary Product Representation Learning](https://mlsanity.com/paper/1904.12574/) (2019)

## Built on by (most cited first, 5 of 5)

- [Are Large Language Models Really Good Logical Reasoners? A Comprehensive Evaluation and Beyond](https://mlsanity.com/paper/2306.09841/) (2023)
- [Neural Graph Reasoning: Complex Logical Query Answering Meets Graph Databases](https://mlsanity.com/paper/2303.14617/) (2023)
- [Complementary Recommendation in E-commerce: Definition, Approaches, and Future Directions](https://mlsanity.com/paper/2403.16135/) (2024)
- [A Survey of Reasoning for Substitution Relationships: Definitions, Methods, and Directions](https://mlsanity.com/paper/2404.08687/) (2024)
- [Bi-NAS: Towards Effective and Personalized Explanation for Recommender Systems via Bi-Level Neural Architecture Search](https://mlsanity.com/paper/2607.01387/) (2026)

## Abstract (arXiv)

Complementary recommendation gains increasing attention in e-commerce since it expedites the process of finding frequently-bought-with products for users in their shopping journey. Therefore, learning the product representation that can reflect this complementary relationship plays a central role in modern recommender systems. In this work, we propose a logical reasoning network, LOGIREC, to effectively learn embeddings of products as well as various transformations (projection, intersection, negation) between them. LOGIREC is capable of capturing the asymmetric complementary relationship between products and seamlessly extending to high-order recommendations where more comprehensive and meaningful complementary relationship is learned for a query set of products. Finally, we further propose a hybrid network that is jointly optimized for learning a more generic product representation. We demonstrate the effectiveness of our LOGIREC on multiple public real-world datasets in terms of various ranking-based metrics under both low-order and high-order recommendation scenarios.