Title: COMBINED FLEXIBLE ACTIVATION FUNCTIONS FOR DEEP NEURAL NETWORKS. Abstract: Activation in deep neural networks is fundamental to achieving non-linear mappings. Traditional studies mainly focus on finding fixed activations for a particular set of learning tasks or model architectures. The research on flexible activation is quite limited in both designing philosophy and application scenarios. In this study, we propose a general combined form of flexible activation functions as well as three principles of choosing flexible activation component. Based on this, we develop two novel flexible activation functions that can be implemented in LSTM cells and auto-encoder layers. Also two new regularisation terms based on assumptions as prior knowledge are proposed. We find that LSTM and auto-encoder models with proposed flexible activations provides significant improvements on time series forecasting and image compressing tasks, while layer-wise regularization can improve the performance of CNN (LeNet-5) models with RPeLu activation in image classification tasks.