In recommender systems (RSs), predicting the next item that a user interacts with is critical for user retention. While the last decade has seen an explosion of RSs aimed at identifying relevant items that match user preferences, there is still a range of aspects that could be considered to further improve their performance. For example, often RSs are centered around the user, who is modeled using her recent sequence of activities. Recent studies, however, have shown the effectiveness of modeling the mutual interactions between users and items using separate user and item embeddings. Building on the success of these studies, we propose a novel method called DeePRed that addresses some of their limitations. In particular, we avoid recursive and costly interactions between consecutive short-term embeddings by using long-term (stationary) embeddings as a proxy. This enable us to train DeePRed using simple mini-batches without the overhead of specialized mini-batches proposed in previous studies. Moreover, DeePRed's effectiveness comes from the aforementioned design and a multi-way attention mechanism that inspects user-item compatibility. Experiments show that DeePRed outperforms the best state-of-the-art approach by at least 14% of Mean Reciprocal Rank (MRR) on next item prediction task, while gaining more than an order of magnitude speedup over the best performing baselines. Although this study is mainly concerned with temporal interaction networks, we also show the power and flexibility of DeePRed by adapting it to the case of static interaction networks, substituting the short- and long-term aspects with local and global ones.