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.

翻译：本文采用低秩张量模型（LTM）作为函数逼近器，结合梯度下降方法求解包含拉普拉斯算子和谐振子在内的特征值问题。实验结果表明，基于多项式的低秩张量模型（PLTM）相较于张量神经网络（TNN）具有显著优越性。我们还在MNIST数据集上测试了此类低秩架构的分类性能。