# Tensor Networks for Multi-Modal Non-Euclidean Data

arXiv: https://arxiv.org/abs/2103.14998 · HTML: https://mlsanity.com/paper/2103.14998/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 26 references that are in the map.
- First posted on arXiv 27 Mar 2021.

## Builds on (most cited first, 11 of 11)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Playing Atari with Deep Reinforcement Learning](https://mlsanity.com/paper/1312.5602/) (2013)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Gated Graph Sequence Neural Networks](https://mlsanity.com/paper/1511.05493/) (2015)
- [Tensorizing Neural Networks](https://mlsanity.com/paper/1509.06569/) (2015)
- [On the Expressive Power of Deep Learning: A Tensor Analysis](https://mlsanity.com/paper/1509.05009/) (2015)
- [Geometric Matrix Completion with Recurrent Multi-Graph Neural Networks](https://mlsanity.com/paper/1704.06803/) (2017)
- [Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives](https://mlsanity.com/paper/1708.09165/) (2017)
- [Multi-Graph Tensor Networks](https://mlsanity.com/paper/2010.13209/) (2020)

## Abstract (arXiv)

Modern data sources are typically of large scale and multi-modal natures, and acquired on irregular domains, which poses serious challenges to traditional deep learning models. These issues are partially mitigated by either extending existing deep learning algorithms to irregular domains through graphs, or by employing tensor methods to alleviate the computational bottlenecks imposed by the Curse of Dimensionality. To simultaneously resolve both these issues, we introduce a novel Multi-Graph Tensor Network (MGTN) framework, which leverages on the desirable properties of graphs, tensors and neural networks in a physically meaningful and compact manner. This equips MGTNs with the ability to exploit local information in irregular data sources at a drastically reduced parameter complexity, and over a range of learning paradigms such as regression, classification and reinforcement learning. The benefits of the MGTN framework, especially its ability to avoid overfitting through the inherent low-rank regularization properties of tensor networks, are demonstrated through its superior performance against competing models in the individual tensor, graph, and neural network domains.