This paper proposes a novel short-path approach to solve the memory and computation constraints of on-device learning. Based on the existing low-rank decomposition method, we propose a method to reduce the memory usage and total training FLOPs by alleviating the activation memory bottleneck in the backpropagation process. The experimental results show that the activation memory usage is reduced by up to 120.09 times and the FLOPs are reduced by up to 1.86 times compared to the existing methods. This suggests that the efficiency of on-device learning can be greatly improved.