# Quantum-Inspired Tensor Neural Networks for Option Pricing

arXiv: https://arxiv.org/abs/2212.14076 · HTML: https://mlsanity.com/paper/2212.14076/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 33 references that are in the map.
- First posted on arXiv 28 Dec 2022.

## Builds on (most cited first, 20 of 20)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Solving high-dimensional partial differential equations using deep learning](https://mlsanity.com/paper/1707.02568/) (2017)
- [Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10561/) (2017)
- [Tensorizing Neural Networks](https://mlsanity.com/paper/1509.06569/) (2015)
- [Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations](https://mlsanity.com/paper/1706.04702/) (2017)
- [Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10566/) (2017)
- [Unsupervised Generative Modeling Using Matrix Product States](https://mlsanity.com/paper/1709.01662/) (2017)
- [Train Large, Then Compress: Rethinking Model Size for Efficient Training and Inference of Transformers](https://mlsanity.com/paper/2002.11794/) (2020)
- [Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations](https://mlsanity.com/paper/1709.05963/) (2017)
- [Tree Tensor Networks for Generative Modeling](https://mlsanity.com/paper/1901.02217/) (2019)
- [Forward-Backward Stochastic Neural Networks: Deep Learning of High-dimensional Partial Differential Equations](https://mlsanity.com/paper/1804.07010/) (2018)
- [Learning Relevant Features of Data with Multi-scale Tensor Networks](https://mlsanity.com/paper/1801.00315/) (2017)
- [Machine Learning by Unitary Tensor Network of Hierarchical Tree Structure](https://mlsanity.com/paper/1710.04833/) (2017)
- [From probabilistic graphical models to generalized tensor networks for supervised learning](https://mlsanity.com/paper/1806.05964/) (2018)
- [Optimal Stopping via Randomized Neural Networks](https://mlsanity.com/paper/2104.13669/) (2021)
- [Generative Tensor Network Classification Model for Supervised Machine Learning](https://mlsanity.com/paper/1903.10742/) (2019)
- [Modeling Sequences with Quantum States: A Look Under the Hood](https://mlsanity.com/paper/1910.07425/) (2019)
- [Matrix Product State Based Quantum Classifier](https://mlsanity.com/paper/1905.01426/) (2019)
- [Deep Neural Network Framework Based on Backward Stochastic Differential Equations for Pricing and Hedging American Options in High Dimensions](https://mlsanity.com/paper/1909.11532/) (2019)
- [Quantum-Inspired Tensor Neural Networks for Partial Differential Equations](https://mlsanity.com/paper/2208.02235/) (2022)

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

- [Application of Tensor Neural Networks to Pricing Bermudan Swaptions](https://mlsanity.com/paper/2304.09750/) (2023)

## Abstract (arXiv)

Recent advances in deep learning have enabled us to address the curse of dimensionality (COD) by solving problems in higher dimensions. A subset of such approaches of addressing the COD has led us to solving high-dimensional PDEs. This has resulted in opening doors to solving a variety of real-world problems ranging from mathematical finance to stochastic control for industrial applications. Although feasible, these deep learning methods are still constrained by training time and memory. Tackling these shortcomings, Tensor Neural Networks (TNN) demonstrate that they can provide significant parameter savings while attaining the same accuracy as compared to the classical Dense Neural Network (DNN). In addition, we also show how TNN can be trained faster than DNN for the same accuracy. Besides TNN, we also introduce Tensor Network Initializer (TNN Init), a weight initialization scheme that leads to faster convergence with smaller variance for an equivalent parameter count as compared to a DNN. We benchmark TNN and TNN Init by applying them to solve the parabolic PDE associated with the Heston model, which is widely used in financial pricing theory.