  Learning representations for feature interactions to model user behaviors is
critical for recommendation system and click-trough rate (CTR) predictions.
Recent advances in this area are empowered by deep learning methods which could
learn sophisticated feature interactions and achieve the state-of-the-art
result in an end-to-end manner. These approaches require large number of
training parameters integrated with the low-level representations, and thus are
memory and computational inefficient. In this paper, we propose a new model
named "LorentzFM" that can learn feature interactions embedded in a hyperbolic
space in which the violation of triangle inequality for Lorentz distances is
available. To this end, the learned representation is benefited by the peculiar
geometric properties of hyperbolic triangles, and result in a significant
reduction in the number of parameters (20\% to 80\%) because all the top deep
learning layers are not required. With such a lightweight architecture,
LorentzFM achieves comparable and even materially better results than the deep
learning methods such as DeepFM, xDeepFM and Deep \& Cross in both
recommendation and CTR prediction tasks.
