Spectral Tensor Train Parameterization of Deep Learning Layers

Anton Obukhov · Maxim Rakhuba · Alexander Liniger

Zhiwu Huang · Stamatios Georgoulis · Dengxin Dai · Luc Van Gool


We study low-rank parameterizations of weight matrices with embedded spectral properties in the Deep Learning context. The low-rank property leads to parameter efficiency and permits taking computational shortcuts when computing mappings. Spectral properties are often subject to constraints in optimization problems, leading to better models and stability of optimization. We start by looking at the compact SVD parameterization of weight matrices and identifying redundancy sources in the parameterization. We further apply the Tensor Train (TT) decomposition to the compact SVD components, and propose a non-redundant differentiable parameterization of fixed TT-rank tensor manifolds, termed the Spectral Tensor Train Parameterization (STTP). We demonstrate the effects of neural network compression in the image classification setting and both compression and improved training stability in the generative adversarial training setting.


Check out the full paper on arXiv


View the conference poster


Two patents pending, both titled "Efficient and stable training of a neural network in compressed form": 1 , 2

Source code

STTP : The official repository of this project

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AISTATS'2021 Teaser Video


  title={Spectral Tensor Train Parameterization of Deep Learning Layers},
  author={Obukhov, Anton and Rakhuba, Maxim and Liniger, Alexander and Huang, Zhiwu and Georgoulis, Stamatios and Dai, Dengxin and Van Gool, Luc},
  booktitle={Proceedings of The 24th International Conference on Artificial Intelligence and Statistics},
  editor={Banerjee, Arindam and Fukumizu, Kenji},
  series={Proceedings of Machine Learning Research},
  month={13--15 Apr},