Spectral Tensor Train Parameterization of Deep Learning Layers
This work addresses parameter efficiency and optimization stability for deep learning practitioners, but it appears incremental as it builds on existing low-rank and tensor decomposition methods.
The paper tackles the problem of parameter efficiency and training stability in deep learning by proposing a Spectral Tensor Train Parameterization (STTP) that combines low-rank and spectral properties. It demonstrates neural network compression for image classification and both compression and improved training stability in generative adversarial training.
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.