# HSG-12M: A Large-Scale Benchmark of Spatial Multigraphs from the Energy Spectra of Non-Hermitian Crystals

arXiv: https://arxiv.org/abs/2506.08618 · HTML: https://mlsanity.com/paper/2506.08618/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 30 of its 120 references that are in the map.
- First posted on arXiv 10 Jun 2025.

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

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [The Kinetics Human Action Video Dataset](https://mlsanity.com/paper/1705.06950/) (2017)
- [Spatial Temporal Graph Convolutional Networks for Skeleton-Based Action Recognition](https://mlsanity.com/paper/1801.07455/) (2018)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [MoleculeNet: A Benchmark for Molecular Machine Learning](https://mlsanity.com/paper/1703.00564/) (2017)
- [Strategies for Pre-training Graph Neural Networks](https://mlsanity.com/paper/1905.12265/) (2019)
- [How Attentive are Graph Attention Networks?](https://mlsanity.com/paper/2105.14491/) (2021)
- [Convolutional Networks on Graphs for Learning Molecular Fingerprints](https://mlsanity.com/paper/1509.09292/) (2015)
- [TUDataset: A collection of benchmark datasets for learning with graphs](https://mlsanity.com/paper/2007.08663/) (2020)
- [NTU RGB+D: A Large Scale Dataset for 3D Human Activity Analysis](https://mlsanity.com/paper/1604.02808/) (2016)
- [Benchmarking Graph Neural Networks](https://mlsanity.com/paper/2003.00982/) (2020)
- [OGB-LSC: A Large-Scale Challenge for Machine Learning on Graphs](https://mlsanity.com/paper/2103.09430/) (2021)
- [Molecular Sets (MOSES): A Benchmarking Platform for Molecular Generation Models](https://mlsanity.com/paper/1811.12823/) (2018)
- [Long Range Graph Benchmark](https://mlsanity.com/paper/2206.08164/) (2022)
- [Temporal Graph Benchmark for Machine Learning on Temporal Graphs](https://mlsanity.com/paper/2307.01026/) (2023)
- [Low Data Drug Discovery with One-shot Learning](https://mlsanity.com/paper/1611.03199/) (2016)
- [Learning Multimodal Graph-to-Graph Translation for Molecular Optimization](https://mlsanity.com/paper/1812.01070/) (2018)
- [A Large-Scale Database for Graph Representation Learning](https://mlsanity.com/paper/2011.07682/) (2020)
- [NeuroGraph: Benchmarks for Graph Machine Learning in Brain Connectomics](https://mlsanity.com/paper/2306.06202/) (2023)
- [Provably Powerful Graph Neural Networks for Directed Multigraphs](https://mlsanity.com/paper/2306.11586/) (2023)
- [Zero-Shot Cost Models for Out-of-the-box Learned Cost Prediction](https://mlsanity.com/paper/2201.00561/) (2022)
- [TpuGraphs: A Performance Prediction Dataset on Large Tensor Computational Graphs](https://mlsanity.com/paper/2308.13490/) (2023)
- [Convolutional Learning on Multigraphs](https://mlsanity.com/paper/2209.11354/) (2022)
- [Generating Tertiary Protein Structures via an Interpretative Variational Autoencoder](https://mlsanity.com/paper/2004.07119/) (2020)
- [State of the Art and Potentialities of Graph-level Learning](https://mlsanity.com/paper/2301.05860/) (2023)
- [MBDS: A Multi-Body Dynamics Simulation Dataset for Graph Networks Simulators](https://mlsanity.com/paper/2410.03107/) (2024)

## Abstract (arXiv)

AI is transforming scientific research by revealing new ways to understand complex physical systems, but its impact remains constrained by the lack of large, high-quality domain-specific datasets. A rich, largely untapped resource lies in non-Hermitian quantum physics, where the energy spectra of crystals form intricate geometries on the complex plane -- termed as Hamiltonian spectral graphs. Despite their significance as fingerprints for electronic behavior, their systematic study has been intractable due to the reliance on manual extraction. To unlock this potential, we introduce Poly2Graph: a high-performance, open-source pipeline that automates the mapping of 1-D crystal Hamiltonians to spectral graphs. Using this tool, we present HSG-12M: a dataset containing 11.6 million static and 5.1 million dynamic Hamiltonian spectral graphs across 1401 characteristic-polynomial classes, distilled from 177 TB of spectral potential data. Crucially, HSG-12M is the first large-scale dataset of spatial multigraphs -- graphs embedded in a metric space where multiple geometrically distinct trajectories between two nodes are retained as separate edges. This simultaneously addresses a critical gap, as existing graph benchmarks overwhelmingly assume simple, non-spatial edges, discarding vital geometric information. Benchmarks with popular GNNs expose new challenges in learning spatial multi-edges at scale. Beyond its practical utility, we show that spectral graphs serve as universal topological fingerprints of polynomials, vectors, and matrices, forging a new algebra-to-graph link. HSG-12M lays the groundwork for data-driven scientific discovery in condensed matter physics, new opportunities in geometry-aware graph learning and beyond.