Ensemble Neural Networks (ENN): A gradient-free stochastic method

TL;DR

The paper introduces Ensemble Neural Networks (ENN), a gradient-free stochastic method based on covariance matrices and Bayesian principles, enhancing robustness, uncertainty quantification, and applicability to complex models.

Contribution

It develops ENN, a novel gradient-free neural network method using covariance matrices and EnRML, enabling uncertainty quantification and broad compatibility with existing neural network architectures.

Findings

ENN outperforms traditional Bayesian neural networks.

ENN is robust with small training datasets.

ENN can be integrated with various neural network models.

Abstract

In this study, an efficient stochastic gradient-free method, the ensemble neural networks (ENN), is developed. In the ENN, the optimization process relies on covariance matrices rather than derivatives. The covariance matrices are calculated by the ensemble randomized maximum likelihood algorithm (EnRML), which is an inverse modeling method. The ENN is able to simultaneously provide estimations and perform uncertainty quantification since it is built under the Bayesian framework. The ENN is also robust to small training data size because the ensemble of stochastic realizations essentially enlarges the training dataset. This constitutes a desirable characteristic, especially for real-world engineering applications. In addition, the ENN does not require the calculation of gradients, which enables the use of complicated neuron models and loss functions in neural networks. We experimentally demonstrate benefits of the proposed model, in particular showing that the ENN performs much better than the traditional Bayesian neural networks (BNN). The EnRML in ENN is a substitution of gradient-based optimization algorithms, which means that it can be directly combined with the feed-forward process in other existing (deep) neural networks, such as convolutional neural networks (CNN) and recurrent neural networks (RNN), broadening future applications of the ENN.