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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 multitask learning (MTL). By exploiting the concept of a 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 generalization of this framework, capable of simultaneous multitask-multi-domain learning. This generalization has two mathematically equivalent views in multilinear 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.

Unifying Multi-domain Multitask Learning: Tensor and Neural Network Perspectives