  In this work, we address the problem of multi-domain image-to-image
translation with particular attention paid to computational cost. In
particular, current state of the art models require a large and deep model in
order to handle the visual diversity of multiple domains. In a context of
limited computational resources, increasing the network size may not be
possible. Therefore, we propose to increase the network capacity by using an
adaptive graph structure. At inference time, the network estimates its own
graph by selecting specific sub-networks. Sub-network selection is implemented
using Gumbel-Softmax in order to allow end-to-end training. This approach leads
to an adjustable increase in number of parameters while preserving an almost
constant computational cost. Our evaluation on two publicly available datasets
of facial and painting images shows that our adaptive strategy generates better
images with fewer artifacts than literature methods
