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.
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