Spectral Tensor Train Parameterization of Deep Learning Layers

TL;DR

This paper introduces Spectral Tensor Train Parameterization (STTP), a novel low-rank tensor method for neural network weights that enhances compression, stability, and efficiency in deep learning models.

Contribution

The paper proposes STTP, a non-redundant, differentiable spectral tensor train parameterization for low-rank weight matrices, improving model compression and training stability.

Findings

Effective neural network compression demonstrated on image classification.

Enhanced training stability observed in generative adversarial networks.

Spectral properties improve optimization and model robustness.

Abstract

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.