Experimental observation on a low-rank tensor model for eigenvalue problems

TL;DR

This paper demonstrates that a polynomial-based low-rank tensor model combined with gradient descent effectively solves eigenvalue problems and outperforms tensor neural networks, with additional testing on image classification tasks.

Contribution

It introduces a polynomial-based low-rank tensor model for eigenvalue problems and compares its performance to tensor neural networks, showing superior results.

Findings

PLTM outperforms TNN in eigenvalue problems

Effective application of LTM to Laplacian and harmonic oscillator

Successful testing on MNIST classification

Abstract

Here we utilize a low-rank tensor model (LTM) as a function approximator, combined with the gradient descent method, to solve eigenvalue problems including the Laplacian operator and the harmonic oscillator. Experimental results show the superiority of the polynomial-based low-rank tensor model (PLTM) compared to the tensor neural network (TNN). We also test such low-rank architectures for the classification problem on the MNIST dataset.