# Group-invariant tensor train networks for supervised learning

arXiv: https://arxiv.org/abs/2206.15051 · HTML: https://mlsanity.com/paper/2206.15051/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 45 references that are in the map.
- First posted on arXiv 30 Jun 2022.

## Builds on (most cited first, 13 of 13)

- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groups](https://mlsanity.com/paper/2104.09459/) (2021)
- [Dive into Deep Learning](https://mlsanity.com/paper/2106.11342/) (2021)
- [Tree Tensor Networks for Generative Modeling](https://mlsanity.com/paper/1901.02217/) (2019)
- [N-body Networks: a Covariant Hierarchical Neural Network Architecture for Learning Atomic Potentials](https://mlsanity.com/paper/1803.01588/) (2018)
- [Supervised Learning with Quantum-Inspired Tensor Networks](https://mlsanity.com/paper/1605.05775/) (2016)
- [Expressive power of recurrent neural networks](https://mlsanity.com/paper/1711.00811/) (2017)
- [Language as a matrix product state](https://mlsanity.com/paper/1711.01416/) (2017)
- [Explainable Natural Language Processing with Matrix Product States](https://mlsanity.com/paper/2112.08628/) (2021)
- [Segmenting two-dimensional structures with strided tensor networks](https://mlsanity.com/paper/2102.06900/) (2021)

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

- [Tensor-Tensor Products, Group Representations, and Semidefinite Programming](https://mlsanity.com/paper/2507.12729/) (2025)

## Abstract (arXiv)

Invariance has recently proven to be a powerful inductive bias in machine learning models. One such class of predictive or generative models are tensor networks. We introduce a new numerical algorithm to construct a basis of tensors that are invariant under the action of normal matrix representations of an arbitrary discrete group. This method can be up to several orders of magnitude faster than previous approaches. The group-invariant tensors are then combined into a group-invariant tensor train network, which can be used as a supervised machine learning model. We applied this model to a protein binding classification problem, taking into account problem-specific invariances, and obtained prediction accuracy in line with state-of-the-art deep learning approaches.