# Tensorized Random Projections

arXiv: https://arxiv.org/abs/2003.05101 · HTML: https://mlsanity.com/paper/2003.05101/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Mar 2020.

## Built on by (most cited first, 11 of 11)

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- [Random Fourier Signature Features](https://mlsanity.com/paper/2311.12214/) (2023)
- [More Efficient Sampling for Tensor Decomposition With Worst-Case Guarantees](https://mlsanity.com/paper/2110.07631/) (2021)
- [Cost-efficient Gaussian Tensor Network Embeddings for Tensor-structured Inputs](https://mlsanity.com/paper/2205.13163/) (2022)
- [Near-Linear Time and Fixed-Parameter Tractable Algorithms for Tensor Decompositions](https://mlsanity.com/paper/2207.07417/) (2022)
- [Rademacher Random Projections with Tensor Networks](https://mlsanity.com/paper/2110.13970/) (2021)
- [Long Sequence Modeling with Attention Tensorization: From Sequence to Tensor Learning](https://mlsanity.com/paper/2410.20926/) (2024)
- [Efficient Tensor Contraction via Fast Count Sketch](https://mlsanity.com/paper/2106.13062/) (2021)
- [Improving LSH via Tensorized Random Projection](https://mlsanity.com/paper/2402.07189/) (2024)
- [Oblivious subspace embeddings for compressed Tucker decompositions](https://mlsanity.com/paper/2406.09387/) (2024)
- [Stochastic trace estimation with tensor train random vectors](https://mlsanity.com/paper/2606.15679/) (2026)

## Abstract (arXiv)

We introduce a novel random projection technique for efficiently reducing the dimension of very high-dimensional tensors. Building upon classical results on Gaussian random projections and Johnson-Lindenstrauss transforms~(JLT), we propose two tensorized random projection maps relying on the tensor train~(TT) and CP decomposition format, respectively. The two maps offer very low memory requirements and can be applied efficiently when the inputs are low rank tensors given in the CP or TT format. Our theoretical analysis shows that the dense Gaussian matrix in JLT can be replaced by a low-rank tensor implicitly represented in compressed form with random factors, while still approximately preserving the Euclidean distance of the projected inputs. In addition, our results reveal that the TT format is substantially superior to CP in terms of the size of the random projection needed to achieve the same distortion ratio. Experiments on synthetic data validate our theoretical analysis and demonstrate the superiority of the TT decomposition.