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Gaussian processes (GPs) are powerful but computationally expensive machine learning models, requiring an estimate of the kernel covariance matrix for every prediction. In large and complex domains, such as graphs, sets, or images, the choice of suitable kernel can also be non-trivial to determine, providing an additional obstacle to the learning task. Over the last decade, these challenges have resulted in significant advances being made in terms of scalability and expressivity, exemplified by, e.g., the use of inducing points and neural network kernel approximations. In this paper, we propose inducing Gaussian process networks (IGN), a simple framework for simultaneously learning the feature space as well as the inducing points. The inducing points, in particular, are learned directly in the feature space, enabling a seamless representation of complex structured domains while also facilitating scalable gradient-based learning methods. We consider both regression and (binary) classification tasks and report on experimental results for real-world data sets showing that IGNs provide significant advances over state-of-the-art methods. We also demonstrate how IGNs can be used to effectively model complex domains using neural network architectures.