# Multi-Class and Multi-Task Strategies for Neural Directed Link Prediction

arXiv: https://arxiv.org/abs/2412.10895 · HTML: https://mlsanity.com/paper/2412.10895/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 28 of its 48 references that are in the map.
- First posted on arXiv 14 Dec 2024.

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

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [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)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [Knowledge Graphs](https://mlsanity.com/paper/2003.02320/) (2020)
- [GraphVAE: Towards Generation of Small Graphs Using Variational Autoencoders](https://mlsanity.com/paper/1802.03480/) (2018)
- [MAGNN: Metapath Aggregated Graph Neural Network for Heterogeneous Graph Embedding](https://mlsanity.com/paper/2002.01680/) (2020)
- [Graph neural networks for materials science and chemistry](https://mlsanity.com/paper/2208.09481/) (2022)
- [Query2box: Reasoning over Knowledge Graphs in Vector Space using Box Embeddings](https://mlsanity.com/paper/2002.05969/) (2020)
- [Anti-Money Laundering in Bitcoin: Experimenting with Graph Convolutional Networks for Financial Forensics](https://mlsanity.com/paper/1908.02591/) (2019)
- [A Survey on Graph Neural Networks for Time Series: Forecasting, Classification, Imputation, and Anomaly Detection](https://mlsanity.com/paper/2307.03759/) (2023)
- [MagNet: A Neural Network for Directed Graphs](https://mlsanity.com/paper/2102.11391/) (2021)
- [Edge Directionality Improves Learning on Heterophilic Graphs](https://mlsanity.com/paper/2305.10498/) (2023)
- [What's Behind the Mask: Understanding Masked Graph Modeling for Graph Autoencoders](https://mlsanity.com/paper/2205.10053/) (2022)
- [Revisiting Scalarization in Multi-Task Learning: A Theoretical Perspective](https://mlsanity.com/paper/2308.13985/) (2023)
- [Realistic Synthetic Financial Transactions for Anti-Money Laundering Models](https://mlsanity.com/paper/2306.16424/) (2023)
- [Gravity-Inspired Graph Autoencoders for Directed Link Prediction](https://mlsanity.com/paper/1905.09570/) (2019)
- [Provably Powerful Graph Neural Networks for Directed Multigraphs](https://mlsanity.com/paper/2306.11586/) (2023)
- [Directed Graph Auto-Encoders](https://mlsanity.com/paper/2202.12449/) (2022)
- [Temporal Link Prediction: A Unified Framework, Taxonomy, and Review](https://mlsanity.com/paper/2210.08765/) (2022)
- [PyTorch Geometric Signed Directed: A Software Package on Graph Neural Networks for Signed and Directed Graphs](https://mlsanity.com/paper/2202.10793/) (2022)
- [Adversarial Directed Graph Embedding](https://mlsanity.com/paper/2008.03667/) (2020)
- [Finding Money Launderers Using Heterogeneous Graph Neural Networks](https://mlsanity.com/paper/2307.13499/) (2023)

## Abstract (arXiv)

Link Prediction is a foundational task in Graph Representation Learning, supporting applications like link recommendation, knowledge graph completion and graph generation. Graph Neural Networks have shown the most promising results in this domain and are currently the de facto standard approach to learning from graph data. However, a key distinction exists between Undirected and Directed Link Prediction: the former just predicts the existence of an edge, while the latter must also account for edge directionality and bidirectionality. This translates to Directed Link Prediction (DLP) having three sub-tasks, each defined by how training, validation and test sets are structured. Most research on DLP overlooks this trichotomy, focusing solely on the "existence" sub-task, where training and test sets are random, uncorrelated samples of positive and negative directed edges. Even in the works that recognize the aforementioned trichotomy, models fail to perform well across all three sub-tasks. In this study, we experimentally demonstrate that training Neural DLP (NDLP) models only on the existence sub-task, using methods adapted from Neural Undirected Link Prediction, results in parameter configurations that fail to capture directionality and bidirectionality, even after rebalancing edge classes. To address this, we propose three strategies that handle the three tasks simultaneously. Our first strategy, the Multi-Class Framework for Neural Directed Link Prediction (MC-NDLP) maps NDLP to a Multi-Class training objective. The second and third approaches adopt a Multi-Task perspective, either with a Multi-Objective (MO-DLP) or a Scalarized (S-DLP) strategy. Our results show that these methods outperform traditional approaches across multiple datasets and models, achieving equivalent or superior performance in addressing the three DLP sub-tasks.