# Topogivity: A Machine-Learned Chemical Rule for Discovering Topological Materials

arXiv: https://arxiv.org/abs/2202.05255 · HTML: https://mlsanity.com/paper/2202.05255/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 73 references that are in the map.
- First posted on arXiv 10 Feb 2022.

## Builds on (most cited first, 2 of 2)

- [Predicting materials properties without crystal structure: Deep representation learning from stoichiometry](https://mlsanity.com/paper/1910.00617/) (2019)
- [Machine Learning Topological Invariants with Neural Networks](https://mlsanity.com/paper/1708.09401/) (2017)

## Built on by (most cited first, 7 of 7)

- [Multimodal Foundation Models for Material Property Prediction and Discovery](https://mlsanity.com/paper/2312.00111/) (2023)
- [Predicting band gap from chemical composition: A simple learned model for a material property with atypical statistics](https://mlsanity.com/paper/2501.02932/) (2025)
- [Learning simple heuristic rules for classifying materials based on chemical composition](https://mlsanity.com/paper/2505.02361/) (2025)
- [Enhancing Materials Discovery with Valence Constrained Design in Generative Modeling](https://mlsanity.com/paper/2507.19799/) (2025)
- [Can AI Follow In Einstein's Footsteps?](https://mlsanity.com/paper/2607.27794/) (2026)
- [Design Topological Materials by Reinforcement Fine-Tuned Generative Model](https://mlsanity.com/paper/2504.13048/) (2025)
- [Interpretation of Crystal Energy Landscapes with Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2604.04636/) (2026)

## Abstract (arXiv)

Topological materials present unconventional electronic properties that make them attractive for both basic science and next-generation technological applications. The majority of currently known topological materials have been discovered using methods that involve symmetry-based analysis of the quantum wavefunction. Here we use machine learning to develop a simple-to-use heuristic chemical rule that diagnoses with a high accuracy whether a material is topological using only its chemical formula. This heuristic rule is based on a notion that we term topogivity, a machine-learned numerical value for each element that loosely captures its tendency to form topological materials. We next implement a high-throughput procedure for discovering topological materials based on the heuristic topogivity-rule prediction followed by ab initio validation. This way, we discover new topological materials that are not diagnosable using symmetry indicators, including several that may be promising for experimental observation.