Various hardware accelerators have been developed for energy-efficient and real-time inference of neural networks on edge devices. However, most training is done on high-performance GPUs or servers, and the huge memory and computing costs prevent training neural networks on edge devices. This paper proposes a novel tensor-based training framework, which offers orders-of-magnitude memory reduction in the training process. We propose a novel rank-adaptive tensorized neural network model, and design a hardware-friendly low-precision algorithm to train this model. We present an FPGA accelerator to demonstrate the benefits of this training method on edge devices. Our preliminary FPGA implementation achieves $59times$ speedup and $123times$ energy reduction compared to embedded CPU, and $292times$ memory reduction over a standard full-size training.
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