scholarly journals Optimization of Graph Neural Networks with Natural Gradient Descent

Author(s):  
Mohammad Rasool Izadi ◽  
Yihao Fang ◽  
Robert Stevenson ◽  
Lizhen Lin
2019 ◽  
Vol 9 (21) ◽  
pp. 4568
Author(s):  
Hyeyoung Park ◽  
Kwanyong Lee

Gradient descent method is an essential algorithm for learning of neural networks. Among diverse variations of gradient descent method that have been developed for accelerating learning speed, the natural gradient learning is based on the theory of information geometry on stochastic neuromanifold, and is known to have ideal convergence properties. Despite its theoretical advantages, the pure natural gradient has some limitations that prevent its practical usage. In order to get the explicit value of the natural gradient, it is required to know true probability distribution of input variables, and to calculate inverse of a matrix with the square size of the number of parameters. Though an adaptive estimation of the natural gradient has been proposed as a solution, it was originally developed for online learning mode, which is computationally inefficient for the learning of large data set. In this paper, we propose a novel adaptive natural gradient estimation for mini-batch learning mode, which is commonly adopted for big data analysis. For two representative stochastic neural network models, we present explicit rules of parameter updates and learning algorithm. Through experiments on three benchmark problems, we confirm that the proposed method has superior convergence properties to the conventional methods.


2021 ◽  
Vol 2021 (12) ◽  
pp. 124010
Author(s):  
Ryo Karakida ◽  
Kazuki Osawa

Abstract Natural gradient descent (NGD) helps to accelerate the convergence of gradient descent dynamics, but it requires approximations in large-scale deep neural networks because of its high computational cost. Empirical studies have confirmed that some NGD methods with approximate Fisher information converge sufficiently fast in practice. Nevertheless, it remains unclear from the theoretical perspective why and under what conditions such heuristic approximations work well. In this work, we reveal that, under specific conditions, NGD with approximate Fisher information achieves the same fast convergence to global minima as exact NGD. We consider deep neural networks in the infinite-width limit, and analyze the asymptotic training dynamics of NGD in function space via the neural tangent kernel. In the function space, the training dynamics with the approximate Fisher information are identical to those with the exact Fisher information, and they converge quickly. The fast convergence holds in layer-wise approximations; for instance, in block diagonal approximation where each block corresponds to a layer as well as in block tri-diagonal and K-FAC approximations. We also find that a unit-wise approximation achieves the same fast convergence under some assumptions. All of these different approximations have an isotropic gradient in the function space, and this plays a fundamental role in achieving the same convergence properties in training. Thus, the current study gives a novel and unified theoretical foundation with which to understand NGD methods in deep learning.


2020 ◽  
Author(s):  
Artur Schweidtmann ◽  
Jan Rittig ◽  
Andrea König ◽  
Martin Grohe ◽  
Alexander Mitsos ◽  
...  

<div>Prediction of combustion-related properties of (oxygenated) hydrocarbons is an important and challenging task for which quantitative structure-property relationship (QSPR) models are frequently employed. Recently, a machine learning method, graph neural networks (GNNs), has shown promising results for the prediction of structure-property relationships. GNNs utilize a graph representation of molecules, where atoms correspond to nodes and bonds to edges containing information about the molecular structure. More specifically, GNNs learn physico-chemical properties as a function of the molecular graph in a supervised learning setup using a backpropagation algorithm. This end-to-end learning approach eliminates the need for selection of molecular descriptors or structural groups, as it learns optimal fingerprints through graph convolutions and maps the fingerprints to the physico-chemical properties by deep learning. We develop GNN models for predicting three fuel ignition quality indicators, i.e., the derived cetane number (DCN), the research octane number (RON), and the motor octane number (MON), of oxygenated and non-oxygenated hydrocarbons. In light of limited experimental data in the order of hundreds, we propose a combination of multi-task learning, transfer learning, and ensemble learning. The results show competitive performance of the proposed GNN approach compared to state-of-the-art QSPR models making it a promising field for future research. The prediction tool is available via a web front-end at www.avt.rwth-aachen.de/gnn.</div>


2020 ◽  
Author(s):  
Zheng Lian ◽  
Jianhua Tao ◽  
Bin Liu ◽  
Jian Huang ◽  
Zhanlei Yang ◽  
...  

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