Capturing the topological and temporal information of interactions and predicting future interactions are crucial for many domains, such as social networks, financial transactions, and e-commerce. With the advent of co-evolutional models, the mutual influence between the interacted users and items are captured. However, exist- ing models only update the interaction information of nodes along the timeline. It causes the problem of information lag, where early updated nodes often have much less information than the most recently updated nodes. We propose HILI (Highly Liquid Temporal Interaction Graph Embeddings) to predict highly liquid embed- dings on temporal interaction graphs. Our embedding model makes interaction information highly liquid without information lag. A specific least recently used-based and frequency-based windows are used to determine the priority of the nodes that receive the latest interaction information. HILI updates node embeddings by attention layers. The attention layers learn the correlation between nodes and update node embedding simply and quickly. In addition, HILI elaborately designs, a self-linear layer, a linear layer initialized in a novel method. A self-linear layer reduces the expected space of predicted embedding of the next interacting node and makes pre- dicted embedding focus more on relevant nodes. We illustrate the geometric meaning of a self-linear layer in the paper. Furthermore, the results of the experiments show that our model outperforms other state-of-the-art temporal interaction prediction models.