# Deep Learning Topological Invariants of Band Insulators

arXiv: https://arxiv.org/abs/1805.10503 · HTML: https://mlsanity.com/paper/1805.10503/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 May 2018.

## Built on by (most cited first, 10 of 10)

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- [Learning Chern Numbers of Topological Insulators with Gauge Equivariant Neural Networks](https://mlsanity.com/paper/2502.15376/) (2025)
- [Can a CNN trained on the Ising model detect the phase transition of the q-state Potts model?](https://mlsanity.com/paper/2104.03632/) (2021)
- [Topological, or Non-topological? A Deep Learning Based Prediction](https://mlsanity.com/paper/2310.18907/) (2023)
- [Quantum circuit complexity and unsupervised machine learning of topological order](https://mlsanity.com/paper/2508.04486/) (2025)
- [Topological Learning in Multi-Class Data Sets](https://mlsanity.com/paper/2301.09734/) (2023)
- [Why is topology hard to learn?](https://mlsanity.com/paper/2509.26261/) (2025)
- [Adjusted Cup-Product Neural Layer](https://mlsanity.com/paper/2606.13568/) (2026)

## Abstract (arXiv)

In this work we design and train deep neural networks to predict topological invariants for one-dimensional four-band insulators in AIII class whose topological invariant is the winding number, and two-dimensional two-band insulators in A class whose topological invariant is the Chern number. Given Hamiltonians in the momentum space as the input, neural networks can predict topological invariants for both classes with accuracy close to or higher than 90%, even for Hamiltonians whose invariants are beyond the training data set. Despite the complexity of the neural network, we find that the output of certain intermediate hidden layers resembles either the winding angle for models in AIII class or the solid angle (Berry curvature) for models in A class, indicating that neural networks essentially capture the mathematical formula of topological invariants. Our work demonstrates the ability of neural networks to predict topological invariants for complicated models with local Hamiltonians as the only input, and offers an example that even a deep neural network is understandable.