  Multi-domain learning aims to benefit from simultaneously learning across
several different but related domains. In this chapter, we propose a single
framework that unifies multi-domain learning (MDL) and the related but better
studied area of multi-task learning (MTL). By exploiting the concept of a
\emph{semantic descriptor} we show how our framework encompasses various
classic and recent MDL/MTL algorithms as special cases with different semantic
descriptor encodings. As a second contribution, we present a higher order
generalisation of this framework, capable of simultaneous
multi-task-multi-domain learning. This generalisation has two mathematically
equivalent views in multi-linear algebra and gated neural networks
respectively. Moreover, by exploiting the semantic descriptor, it provides
neural networks the capability of zero-shot learning (ZSL), where a classifier
is generated for an unseen class without any training data; as well as
zero-shot domain adaptation (ZSDA), where a model is generated for an unseen
domain without any training data. In practice, this framework provides a
powerful yet easy to implement method that can be flexibly applied to MTL, MDL,
ZSL and ZSDA.
