Abstract: Pre-trained language models (e.g., BERT) have achieved significant success in various natural language processing (NLP) tasks. However, high storage and computational costs obstruct pre-trained language models to be effectively deployed on resource-constrained devices. In this paper, we propose a novel BERT distillation method based on many-to-many layer mapping, which allows each intermediate student layer to learn from any intermediate teacher layers. In this way, our model can learn from different teacher layers adaptively for different NLP tasks. In addition, we leverage Earth Mover's Distance (EMD) to compute the minimum cumulative cost that must be paid to transform knowledge from teacher network to student network. EMD enables effective matching for the many-to-many layer mapping. Furthermore, we propose a cost attention mechanism to learn the layer weights used in EMD automatically, which is supposed to further improve the model's performance and accelerate convergence time. Extensive experiments on GLUE benchmark demonstrate that our model achieves competitive performance compared to strong competitors in terms of both accuracy and model compression