On strong convergence of the two-tower model for recommender system

Recommender system is capable of predicting preferred items for a user by integrating information from similar users or items. A popular model in recommender system is the so-called two-tower model, which employs two deep neural networks to embed users and items into a low-dimensional space, and predicts ratings via the geometrical relationship of the embeddings of user and item in the embedded space. Even though it is popularly used for recommendations, its theoretical properties remain largely unknown. In this paper, we establish some asymptotic results of the two-tower model in terms of its strong convergence to the optimal recommender system, showing that it achieves a fast convergence rate depending on the intrinsic dimensions of inputs features. To the best of our knowledge, this is among the first attempts to establish the statistical guarantee of the two-tower model. Through numerical experiments, we also demonstrate that the two-tower model is capable of capturing the effects of users' and items' features on ratings, leading to higher prediction accuracy over its competitors in both simulated examples and a real application data set.