# Versatile Ordering Network: An Attention-based Neural Network for Ordering Across Scales and Quality Metrics

arXiv: https://arxiv.org/abs/2412.12759 · HTML: https://mlsanity.com/paper/2412.12759/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 78 references that are in the map.
- First posted on arXiv 17 Dec 2024.

## Builds on (most cited first, 20 of 20)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [Pointer Networks](https://mlsanity.com/paper/1506.03134/) (2015)
- [Attention, Learn to Solve Routing Problems!](https://mlsanity.com/paper/1803.08475/) (2018)
- [Reinforcement Learning for Solving the Vehicle Routing Problem](https://mlsanity.com/paper/1802.04240/) (2018)
- [FairSight: Visual Analytics for Fairness in Decision Making](https://mlsanity.com/paper/1908.00176/) (2019)
- [Learning to Solve NP-Complete Problems - A Graph Neural Network for Decision TSP](https://mlsanity.com/paper/1809.02721/) (2018)
- [Hierarchical Neural Constructive Solver for Real-world TSP Scenarios](https://mlsanity.com/paper/2408.03585/) (2024)
- [Set-to-Sequence Ranking-based Concept-aware Learning Path Recommendation](https://mlsanity.com/paper/2306.04234/) (2023)
- [PlotThread: Creating Expressive Storyline Visualizations using Reinforcement Learning](https://mlsanity.com/paper/2009.00249/) (2020)
- [Set-to-Sequence Methods in Machine Learning: a Review](https://mlsanity.com/paper/2103.09656/) (2021)
- [Improved Evaluation and Generation of Grid Layouts using Distance Preservation Quality and Linear Assignment Sorting](https://mlsanity.com/paper/2205.04255/) (2022)
- [Data-Driven Space-Filling Curves](https://mlsanity.com/paper/2009.06309/) (2020)
- [RankAxis: Towards a Systematic Combination of Projection and Ranking in Multi-Attribute Data Exploration](https://mlsanity.com/paper/2208.01493/) (2022)
- [Shape-driven Coordinate Ordering for Star Glyph Sets via Reinforcement Learning](https://mlsanity.com/paper/2103.02380/) (2021)
- [Simultaneous Matrix Orderings for Graph Collections](https://mlsanity.com/paper/2109.12050/) (2021)
- [PC-Expo: A Metrics-Based Interactive Axes Reordering Method for Parallel Coordinate Displays](https://mlsanity.com/paper/2208.03430/) (2022)
- [A Deep Generative Model for Reordering Adjacency Matrices](https://mlsanity.com/paper/2110.04971/) (2021)
- [On Computing Optimal Linear Diagrams](https://mlsanity.com/paper/2206.08631/) (2022)

## Built on by (most cited first, 1 of 1)

- [Natural Language-Driven Viewpoint Navigation for Volume Exploration via Semantic Block Representation](https://mlsanity.com/paper/2508.06823/) (2025)

## Abstract (arXiv)

Ordering has been extensively studied in many visualization applications, such as axis and matrix reordering, for the simple reason that the order will greatly impact the perceived pattern of data. Many quality metrics concerning data pattern, perception, and aesthetics are proposed, and respective optimization algorithms are developed. However, the optimization problems related to ordering are often difficult to solve (e.g., TSP is NP-complete), and developing specialized optimization algorithms is costly. In this paper, we propose Versatile Ordering Network (VON), which automatically learns the strategy to order given a quality metric. VON uses the quality metric to evaluate its solutions, and leverages reinforcement learning with a greedy rollout baseline to improve itself. This keeps the metric transparent and allows VON to optimize over different metrics. Additionally, VON uses the attention mechanism to collect information across scales and reposition the data points with respect to the current context. This allows VONs to deal with data points following different distributions. We examine the effectiveness of VON under different usage scenarios and metrics. The results demonstrate that VON can produce comparable results to specialized solvers. The code is available at https://github.com/sysuvis/VON.