This paper studies how to improve the generalization performance and learning speed of the navigation agents trained with deep reinforcement learning (DRL). Although DRL exhibits huge potential in robot mapless navigation, DRL agents performing well in training scenarios are often found to perform poorly in unfamiliar scenarios. In this work, we propose that the representation of LiDAR readings is a key factor behind the degradation of agents' performance and present a powerful input pre-processing (IP) approach to address this issue. As this approach uses adaptively parametric reciprocal functions to pre-process LiDAR readings, we refer to this approach as IPAPRec and its normalized version as IPAPRecN. IPAPRec/IPAPRecN can highlight important short-distance values and compress the range of less-important long-distance values in laser scans, which well address the issues induced by conventional representations of laser scans. Their high performance was validated by extensive simulation and real-world experiments. The results show that our methods can substantially improve navigation agents' generalization performance and greatly reduce the training time compared to conventional methods.