  Deep neural networks (DNNs) and, in particular, convolutional neural networks
(CNNs) have brought significant advances in a wide range of modern computer
application problems. However, the increasing availability of large amounts of
datasets as well as the increasing available computational power of modern
computers lead to a steady growth in the complexity and size of DNN and CNN
models, respectively, and thus, to longer training times. Hence, various
methods and attempts have been developed to accelerate and parallelize the
training of complex network architectures. In this work, a novel CNN-DNN
architecture is proposed that naturally supports a model parallel training
strategy and that is loosely inspired by two-level domain decomposition methods
(DDM). First, local CNN models, that is, subnetworks, are defined that operate
on overlapping or nonoverlapping parts of the input data, for example,
sub-images. The subnetworks can be trained completely in parallel and
independently of each other. Each subnetwork then outputs a local decision for
the given machine learning problem which is exclusively based on the respective
local input data. Subsequently, in a second step, an additional DNN model is
trained which evaluates the local decisions of the local subnetworks and
generates a final, global decision. In this paper, we apply the proposed
architecture to image classification problems using CNNs. Experimental results
for different 2D image classification problems are provided as well as a face
recognition problem, and a classification problem for 3D computer tomography
(CT) scans. Therefore, classical ResNet and VGG architectures are considered.
The results show that the proposed approach can significantly accelerate the
required training time compared to the global model and, additionally, can also
help to improve the accuracy of the underlying classification problem.
