# Parallelized Tensor Train Learning of Polynomial Classifiers

arXiv: https://arxiv.org/abs/1612.06505 · HTML: https://mlsanity.com/paper/1612.06505/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Dec 2016.

## Built on by (most cited first, 16 of 16)

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- [Lower and Upper Bounds on the VC-Dimension of Tensor Network Models](https://mlsanity.com/paper/2106.11827/) (2021)
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- [Tensor Network Kalman Filtering for Large-Scale LS-SVMs](https://mlsanity.com/paper/2110.13501/) (2021)
- [Exploiting Hankel-Toeplitz Structures for Fast Computation of Kernel Precision Matrices](https://mlsanity.com/paper/2408.02346/) (2024)
- [Efficient Generative Modeling with Unitary Matrix Product States Using Riemannian Optimization](https://mlsanity.com/paper/2603.12026/) (2026)
- [Quantum-inspired tensor networks in machine learning models](https://mlsanity.com/paper/2604.14287/) (2026)
- [Tensor Network Kernel Machines: A JAX Framework for Machine Learning and Nonlinear System Identification](https://mlsanity.com/paper/2608.07043/) (2026)

## Abstract (arXiv)

In pattern classification, polynomial classifiers are well-studied methods as they are capable of generating complex decision surfaces. Unfortunately, the use of multivariate polynomials is limited to kernels as in support vector machines, because polynomials quickly become impractical for high-dimensional problems. In this paper, we effectively overcome the curse of dimensionality by employing the tensor train format to represent a polynomial classifier. Based on the structure of tensor trains, two learning algorithms are proposed which involve solving different optimization problems of low computational complexity. Furthermore, we show how both regularization to prevent overfitting and parallelization, which enables the use of large training sets, are incorporated into these methods. Both the efficiency and efficacy of our tensor-based polynomial classifier are then demonstrated on the two popular datasets USPS and MNIST.