Recent developments in deep learning (DL) are putting a lot of pressure and pushing the demand for intelligent edge devices capable of on-site learning. The realization of such systems is, however, a massive challenge due to the limited resources available in an embedded context and the massive training costs for state-of-the-art deep neural networks. In order to realize the full potential of DL, it is imperative to improve existing network training methodologies and the hardware being used. LeanAI will attack these problems at the arithmetic and algorithmic levels and explore the design of new mixed numerical precision hardware architectures that are at the same time more energy-efficient and offer increased performance in a resource-restricted environment. The expected outcome of the project includes new mixed-precision algorithms for neural network training, together with open-source tools for training acceleration at the arithmetic level on edge devices.