HoD-Net: High-Order Differentiable Deep Neural Networks and Applications
Siyuan Shen, Tianjia Shao, Kun Zhou, Chenfanfu Jiang, Feng Luo, Yin Yang
Abstract
We introduce a deep architecture named HoD-Net to enable high-order differentiability for deep learning. HoD-Net is based on and generalizes the complex-step finite difference (CSFD) method. While similar to classic finite difference, CSFD approaches the derivative of a function from a higher-dimension complex domain, leading to highly accurate and robust differentiation computation without numerical stability issues. This method can be coupled with backpropagation and adjoint perturbation methods for an efficient calculation of high-order derivatives. We show how this numerical scheme can be leveraged in challenging deep learning problems, such as high-order network training, deep learning-based physics simulation, and neural differential equations.
BibTeX
@inproceedings{aaai2022_hodnethighorderd,
title = {HoD-Net: High-Order Differentiable Deep Neural Networks and Applications},
author = {Siyuan Shen and Tianjia Shao and Kun Zhou and Chenfanfu Jiang and Feng Luo and Yin Yang},
booktitle = {AAAI 2022},
year = {2022}
}