# Bilinear Scoring Function Search for Knowledge Graph Learning

arXiv: https://arxiv.org/abs/2107.00184 · HTML: https://mlsanity.com/paper/2107.00184/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 78 references that are in the map.
- First posted on arXiv 1 Jul 2021.

## Builds on (most cited first, 30 of 37)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [DARTS: Differentiable Architecture Search](https://mlsanity.com/paper/1806.09055/) (2018)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [Neural Architecture Search with Reinforcement Learning](https://mlsanity.com/paper/1611.01578/) (2016)
- [Embedding Entities and Relations for Learning and Inference in Knowledge Bases](https://mlsanity.com/paper/1412.6575/) (2014)
- [Regularized Evolution for Image Classifier Architecture Search](https://mlsanity.com/paper/1802.01548/) (2018)
- [RotatE: Knowledge Graph Embedding by Relational Rotation in Complex Space](https://mlsanity.com/paper/1902.10197/) (2019)
- [Efficient Neural Architecture Search via Parameter Sharing](https://mlsanity.com/paper/1802.03268/) (2018)
- [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)
- [Progressive Neural Architecture Search](https://mlsanity.com/paper/1712.00559/) (2017)
- [Composition-based Multi-Relational Graph Convolutional Networks](https://mlsanity.com/paper/1911.03082/) (2019)
- [TuckER: Tensor Factorization for Knowledge Graph Completion](https://mlsanity.com/paper/1901.09590/) (2019)
- [A Review of Relational Machine Learning for Knowledge Graphs](https://mlsanity.com/paper/1503.00759/) (2015)
- [SimplE Embedding for Link Prediction in Knowledge Graphs](https://mlsanity.com/paper/1802.04868/) (2018)
- [Holographic Embeddings of Knowledge Graphs](https://mlsanity.com/paper/1510.04935/) (2015)
- [Query2box: Reasoning over Knowledge Graphs in Vector Space using Box Embeddings](https://mlsanity.com/paper/2002.05969/) (2020)
- [Canonical Tensor Decomposition for Knowledge Base Completion](https://mlsanity.com/paper/1806.07297/) (2018)
- [Embedding Logical Queries on Knowledge Graphs](https://mlsanity.com/paper/1806.01445/) (2018)
- [Knowledge Graph Embedding for Link Prediction: A Comparative Analysis](https://mlsanity.com/paper/2002.00819/) (2020)
- [Learning to Exploit Long-term Relational Dependencies in Knowledge Graphs](https://mlsanity.com/paper/1905.04914/) (2019)
- [Knowledge Graph Completion via Complex Tensor Factorization](https://mlsanity.com/paper/1702.06879/) (2017)
- [Analogical Inference for Multi-Relational Embeddings](https://mlsanity.com/paper/1705.02426/) (2017)
- [PairRE: Knowledge Graph Embeddings via Paired Relation Vectors](https://mlsanity.com/paper/2011.03798/) (2020)
- [Automated Machine Learning: From Principles to Practices](https://mlsanity.com/paper/1810.13306/) (2018)
- [Traversing Knowledge Graphs in Vector Space](https://mlsanity.com/paper/1506.01094/) (2015)
- [AutoSF: Searching Scoring Functions for Knowledge Graph Embedding](https://mlsanity.com/paper/1904.11682/) (2019)

## Built on by (most cited first, 11 of 11)

- [Reason-Align-Respond: Aligning LLM Reasoning with Knowledge Graphs for KGQA](https://mlsanity.com/paper/2505.20971/) (2025)
- [Learning to Describe for Predicting Zero-shot Drug-Drug Interactions](https://mlsanity.com/paper/2403.08377/) (2024)
- [Mixture of Length and Pruning Experts for Knowledge Graphs Reasoning](https://mlsanity.com/paper/2507.20498/) (2025)
- [ColdNAS: Search to Modulate for User Cold-Start Recommendation](https://mlsanity.com/paper/2306.03387/) (2023)
- [Customized Subgraph Selection and Encoding for Drug-drug Interaction Prediction](https://mlsanity.com/paper/2411.01535/) (2024)
- [S-Path-RAG: Semantic-Aware Shortest-Path Retrieval Augmented Generation for Multi-Hop Knowledge Graph Question Answering](https://mlsanity.com/paper/2603.23512/) (2026)
- [Search to Pass Messages for Temporal Knowledge Graph Completion](https://mlsanity.com/paper/2210.16740/) (2022)
- [Relation-aware Ensemble Learning for Knowledge Graph Embedding](https://mlsanity.com/paper/2310.08917/) (2023)
- [Revisiting Edge Perturbation for Graph Neural Network in Graph Data Augmentation and Attack](https://mlsanity.com/paper/2403.07943/) (2024)
- [Flow-Modulated Scoring for Semantic-Aware Knowledge Graph Completion](https://mlsanity.com/paper/2506.23137/) (2025)
- [AutoWeird: Weird Translational Scoring Function Identified by Random Search](https://mlsanity.com/paper/2207.11673/) (2022)

## Abstract (arXiv)

Learning embeddings for entities and relations in knowledge graph (KG) have benefited many downstream tasks. In recent years, scoring functions, the crux of KG learning, have been human-designed to measure the plausibility of triples and capture different kinds of relations in KGs. However, as relations exhibit intricate patterns that are hard to infer before training, none of them consistently perform the best on benchmark tasks. In this paper, inspired by the recent success of automated machine learning (AutoML), we search bilinear scoring functions for different KG tasks through the AutoML techniques. However, it is non-trivial to explore domain-specific information here. We first set up a search space for AutoBLM by analyzing existing scoring functions. Then, we propose a progressive algorithm (AutoBLM) and an evolutionary algorithm (AutoBLM+), which are further accelerated by filter and predictor to deal with the domain-specific properties for KG learning. Finally, we perform extensive experiments on benchmarks in KG completion, multi-hop query, and entity classification tasks. Empirical results show that the searched scoring functions are KG dependent, new to the literature, and outperform the existing scoring functions. AutoBLM+ is better than AutoBLM as the evolutionary algorithm can flexibly explore better structures in the same budget.