# TTML: tensor trains for general supervised machine learning

arXiv: https://arxiv.org/abs/2203.04352 · HTML: https://mlsanity.com/paper/2203.04352/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 48 references that are in the map.
- First posted on arXiv 8 Mar 2022.

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

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [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)
- [Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives](https://mlsanity.com/paper/1708.09165/) (2017)
- [Tensor Completion Algorithms in Big Data Analytics](https://mlsanity.com/paper/1711.10105/) (2017)
- [Implicit Regularization in Tensor Factorization](https://mlsanity.com/paper/2102.09972/) (2021)
- [Generalized Canonical Polyadic Tensor Decomposition](https://mlsanity.com/paper/1808.07452/) (2018)
- [Compressing Recurrent Neural Network with Tensor Train](https://mlsanity.com/paper/1705.08052/) (2017)
- [Learning with tree-based tensor formats](https://mlsanity.com/paper/1811.04455/) (2018)
- [Nonlinear System Identification via Tensor Completion](https://mlsanity.com/paper/1906.05746/) (2019)
- [Tensor Completion via Gaussian Process Based Initialization](https://mlsanity.com/paper/1912.05179/) (2019)

## Built on by (most cited first, 2 of 2)

- [Tensor Train for Global Optimization Problems in Robotics](https://mlsanity.com/paper/2206.05077/) (2022)
- [Lightweight Cloud Masking Models for On-Board Inference in Hyperspectral Imaging](https://mlsanity.com/paper/2507.08052/) (2025)

## Abstract (arXiv)

This work proposes a novel general-purpose estimator for supervised machine learning (ML) based on tensor trains (TT). The estimator uses TTs to parametrize discretized functions, which are then optimized using Riemannian gradient descent under the form of a tensor completion problem. Since this optimization is sensitive to initialization, it turns out that the use of other ML estimators for initialization is crucial. This results in a competitive, fast ML estimator with lower memory usage than many other ML estimators, like the ones used for the initialization.