# Tensor-to-Vector Regression for Multi-channel Speech Enhancement based on Tensor-Train Network

arXiv: https://arxiv.org/abs/2002.00544 · HTML: https://mlsanity.com/paper/2002.00544/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Feb 2020.

## Built on by (most cited first, 3 of 3)

- [QTN-VQC: An End-to-End Learning framework for Quantum Neural Networks](https://mlsanity.com/paper/2110.03861/) (2021)
- [Theoretical Error Performance Analysis for Variational Quantum Circuit Based Functional Regression](https://mlsanity.com/paper/2206.04804/) (2022)
- [SEOFP-NET: Compression and Acceleration of Deep Neural Networks for Speech Enhancement Using Sign-Exponent-Only Floating-Points](https://mlsanity.com/paper/2111.04436/) (2021)

## Abstract (arXiv)

We propose a tensor-to-vector regression approach to multi-channel speech enhancement in order to address the issue of input size explosion and hidden-layer size expansion. The key idea is to cast the conventional deep neural network (DNN) based vector-to-vector regression formulation under a tensor-train network (TTN) framework. TTN is a recently emerged solution for compact representation of deep models with fully connected hidden layers. Thus TTN maintains DNN's expressive power yet involves a much smaller amount of trainable parameters. Furthermore, TTN can handle a multi-dimensional tensor input by design, which exactly matches the desired setting in multi-channel speech enhancement. We first provide a theoretical extension from DNN to TTN based regression. Next, we show that TTN can attain speech enhancement quality comparable with that for DNN but with much fewer parameters, e.g., a reduction from 27 million to only 5 million parameters is observed in a single-channel scenario. TTN also improves PESQ over DNN from 2.86 to 2.96 by slightly increasing the number of trainable parameters. Finally, in 8-channel conditions, a PESQ of 3.12 is achieved using 20 million parameters for TTN, whereas a DNN with 68 million parameters can only attain a PESQ of 3.06. Our implementation is available online https://github.com/uwjunqi/Tensor-Train-Neural-Network.