We present a novel and mathematically transparent approach to function approximation and the training of large, high-dimensional neural networks, based on the approximate least-squares solution of associated Fredholm integral equations of the first kind by Ritz-Galerkin discretization, Tikhonov regularization and tensor-train methods. Practical application to supervised learning problems of regression and classification type confirm that the resulting algorithms are competitive with state-of-the-art neural network-based methods.

翻译：我们提出了一种新颖且数学上透明的函数逼近方法，用于训练大规模高维神经网络。该方法基于第一类Fredholm积分方程的近似最小二乘解，通过Ritz-Galerkin离散化、Tikhonov正则化与张量列技术实现。对回归与分类型监督学习问题的实际应用表明，所得算法与基于神经网络的最先进方法具有竞争力。