# Rademacher Random Projections with Tensor Networks

arXiv: https://arxiv.org/abs/2110.13970 · HTML: https://mlsanity.com/paper/2110.13970/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 39 references that are in the map.
- First posted on arXiv 26 Oct 2021.

## Builds on (most cited first, 9 of 9)

- [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)
- [Unsupervised Generative Modeling Using Matrix Product States](https://mlsanity.com/paper/1709.01662/) (2017)
- [Learning Relevant Features of Data with Multi-scale Tensor Networks](https://mlsanity.com/paper/1801.00315/) (2017)
- [Supervised Learning with Quantum-Inspired Tensor Networks](https://mlsanity.com/paper/1605.05775/) (2016)
- [Sketching for Kronecker Product Regression and P-splines](https://mlsanity.com/paper/1712.09473/) (2017)
- [Tensorized Random Projections](https://mlsanity.com/paper/2003.05101/) (2020)
- [Tensor Random Projection for Low Memory Dimension Reduction](https://mlsanity.com/paper/2105.00105/) (2021)
- [Tensor Train Random Projection](https://mlsanity.com/paper/2010.10797/) (2020)

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

- [Improving LSH via Tensorized Random Projection](https://mlsanity.com/paper/2402.07189/) (2024)

## Abstract (arXiv)

Random projection (RP) have recently emerged as popular techniques in the machine learning community for their ability in reducing the dimension of very high-dimensional tensors. Following the work in [30], we consider a tensorized random projection relying on Tensor Train (TT) decomposition where each element of the core tensors is drawn from a Rademacher distribution. Our theoretical results reveal that the Gaussian low-rank tensor represented in compressed form in TT format in [30] can be replaced by a TT tensor with core elements drawn from a Rademacher distribution with the same embedding size. Experiments on synthetic data demonstrate that tensorized Rademacher RP can outperform the tensorized Gaussian RP studied in [30]. In addition, we show both theoretically and experimentally, that the tensorized RP in the Matrix Product Operator (MPO) format is not a Johnson-Lindenstrauss transform (JLT) and therefore not a well-suited random projection map