Abstract Factorization Machine (FM) is an effective solution for context-aware recommender systems (CARS) which models second-order feature interactions by inner product. However, it is insufficient to capture high-order and nonlinear interaction signals. While several recent efforts have enhanced FM with neural networks, they assume the embedding dimensions are independent from each other and model high-order interactions in a rather implicit manner. In this paper, we propose Convolutional Factorization Machine (CFM) to address above limitations. Specifically, CFM models second-order interactions with outer product, resulting in “images” which capture correlations between embedding dimensions. Then all generated “images” are stacked, forming an interaction cube. 3D convolution is applied above it to learn high-order interaction signals in an explicit approach. Besides, we also leverage a self-attention mechanism to perform the pooling of features to reduce time complexity. We conduct extensive experiments on three realworld datasets, demonstrating significant improvement of CFM over competing methods for contextaware top-k recommendation