In this paper, we seek solutions for reducing the computation complexity of transformer-based models for speech representation learning. We evaluate 10 attention algorithms; then, we pre-train the transformer-based model with those attention algorithms in a self-supervised fashion and treat them as feature extractors on downstream tasks, including phoneme classification and speaker classification. With the assistance of t-SNE, PCA and some observation, the attention weights in self-supervised audio transformers can be categorized into four general cases. Based on these cases and some analyses, we are able to use a specific set of attention weights to initialize the model. Our approach shows comparable performance to the typical self-attention yet requires 20% less time in both training and inference.