Abstract: Self-supervised learning has emerged as a promising approach in addressing the issues of label dependency and poor generalization performance in traditional graph neural networks (GNNs). This method leverages the inherent structure and properties of the data to generate supervisory information without relying on extensive labeled datasets. However, most existing self-supervised learning methods hold the assumption that the graphs are homophilic and consequently fail to generalize well to graphs with high heterophily, where connected nodes may have different class labels and dissimilar features. In this paper, we study the problem by developing an asymmetric self-supervised learning on non-homophilic graphs (MIRROR) framework, which is easy to implement and does not rely on random graph augmentations and homophily assumptions. Inspired by the designs of existing heterophilic graph neural networks, MIRROR learns the node representations by capturing one-hop local neighborhood information and informative distant neighbors. Such two properties are obtained through carefully designed pretext tasks that are optimized based on predicted neighborhood context and estimated high-order mutual information. Extensive experiments on various types of graph benchmarks demonstrate that our proposed framework can achieve better performance compared with competitive baselines on non-homophilic graphs. The superiority in multiple downstream tasks also demonstrates the generalization capability of MIRROR.