  Action Units (AU) are muscular activations used to describe facial
expressions. Therefore accurate AU recognition unlocks unbiaised face
representation which can improve face-based affective computing applications.
From a learning standpoint AU detection is a multi-task problem with strong
inter-task dependencies. To solve such problem, most approaches either rely on
weight sharing, or add explicit dependency modelling by decomposing the joint
task distribution using Bayes chain rule. If the latter strategy yields
comprehensive inter-task relationships modelling, it requires imposing an
arbitrary order into an unordered task set. Crucially, this ordering choice has
been identified as a source of performance variations. In this paper, we
present Multi-Order Network (MONET), a multi-task method with joint task order
optimization. MONET uses a differentiable order selection to jointly learn
task-wise modules with their optimal chaining order. Furthermore, we introduce
warmup and order dropout to enhance order selection by encouraging order
exploration. Experimentally, we first demonstrate MONET capacity to retrieve
the optimal order in a toy environment. Second, we validate MONET architecture
by showing that MONET outperforms existing multi-task baselines on multiple
attribute detection problems chosen for their wide range of dependency
settings. More importantly, we demonstrate that MONET significantly extends
state-of-the-art performance in AU detection.
