# Tensor-Train Recurrent Neural Networks for Interpretable Multi-Way Financial Forecasting

arXiv: https://arxiv.org/abs/2105.04983 · HTML: https://mlsanity.com/paper/2105.04983/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 31 references that are in the map.
- First posted on arXiv 11 May 2021.

## Builds on (most cited first, 17 of 17)

- [Tensorizing Neural Networks](https://mlsanity.com/paper/1509.06569/) (2015)
- [Tensor Decomposition for Signal Processing and Machine Learning](https://mlsanity.com/paper/1607.01668/) (2016)
- [Speeding-up Convolutional Neural Networks Using Fine-tuned CP-Decomposition](https://mlsanity.com/paper/1412.6553/) (2014)
- [Compression of Deep Convolutional Neural Networks for Fast and Low Power Mobile Applications](https://mlsanity.com/paper/1511.06530/) (2015)
- [A Theoretically Grounded Application of Dropout in Recurrent Neural Networks](https://mlsanity.com/paper/1512.05287/) (2015)
- [Tensor-Train Recurrent Neural Networks for Video Classification](https://mlsanity.com/paper/1707.01786/) (2017)
- [Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives](https://mlsanity.com/paper/1708.09165/) (2017)
- [Temporal Attention augmented Bilinear Network for Financial Time-Series Data Analysis](https://mlsanity.com/paper/1712.00975/) (2017)
- [Long-term Forecasting using Higher Order Tensor RNNs](https://mlsanity.com/paper/1711.00073/) (2017)
- [Expressive power of recurrent neural networks](https://mlsanity.com/paper/1711.00811/) (2017)
- [Compressing Recurrent Neural Network with Tensor Train](https://mlsanity.com/paper/1705.08052/) (2017)
- [Using Deep Learning for price prediction by exploiting stationary limit order book features](https://mlsanity.com/paper/1810.09965/) (2018)
- [Tensor Representation in High-Frequency Financial Data for Price Change Prediction](https://mlsanity.com/paper/1709.01268/) (2017)
- [ADA-Tucker: Compressing Deep Neural Networks via Adaptive Dimension Adjustment Tucker Decomposition](https://mlsanity.com/paper/1906.07671/) (2019)
- [Noisin: Unbiased Regularization for Recurrent Neural Networks](https://mlsanity.com/paper/1805.01500/) (2018)
- [Wider and Deeper, Cheaper and Faster: Tensorized LSTMs for Sequence Learning](https://mlsanity.com/paper/1711.01577/) (2017)
- [Analysing Global Fixed Income Markets with Tensors](https://mlsanity.com/paper/1908.02101/) (2019)

## Built on by (most cited first, 6 of 6)

- [Graph Tensor Networks: An Intuitive Framework for Designing Large-Scale Neural Learning Systems on Multiple Domains](https://mlsanity.com/paper/2303.13565/) (2023)
- [Quantum-inspired event reconstruction with Tensor Networks: Matrix Product States](https://mlsanity.com/paper/2106.08334/) (2021)
- [Quantum-inspired Techniques in Tensor Networks for Industrial Contexts](https://mlsanity.com/paper/2404.11277/) (2024)
- [Graph-Regularized Tensor Regression: A Domain-Aware Framework for Interpretable Multi-Way Financial Modelling](https://mlsanity.com/paper/2211.05581/) (2022)
- [T'ecnicas Quantum-Inspired en Tensor Networks para Contextos Industriales](https://mlsanity.com/paper/2404.17645/) (2024)
- [Quantum-inspired tensor networks in machine learning models](https://mlsanity.com/paper/2604.14287/) (2026)

## Abstract (arXiv)

Recurrent Neural Networks (RNNs) represent the de facto standard machine learning tool for sequence modelling, owing to their expressive power and memory. However, when dealing with large dimensional data, the corresponding exponential increase in the number of parameters imposes a computational bottleneck. The necessity to equip RNNs with the ability to deal with the curse of dimensionality, such as through the parameter compression ability inherent to tensors, has led to the development of the Tensor-Train RNN (TT-RNN). Despite achieving promising results in many applications, the full potential of the TT-RNN is yet to be explored in the context of interpretable financial modelling, a notoriously challenging task characterized by multi-modal data with low signal-to-noise ratio. To address this issue, we investigate the potential of TT-RNN in the task of financial forecasting of currencies. We show, through the analysis of TT-factors, that the physical meaning underlying tensor decomposition, enables the TT-RNN model to aid the interpretability of results, thus mitigating the notorious "black-box" issue associated with neural networks. Furthermore, simulation results highlight the regularization power of TT decomposition, demonstrating the superior performance of TT-RNN over its uncompressed RNN counterpart and other tensor forecasting methods.