Title: Compact Bilinear Pooling via General Bilinear Projection. Abstract: Most factorized bilinear pooling (FBiP) employs Hadamard product-based bilinear projection to learn appropriate projecting directions to reduce the dimension of bilinear features. However, in this paper, we reveal that the Hadamard product-based bilinear projection makes FBiP miss a lot of possible projecting directions, which will significantly harm the performance of outputted compact bilinear features, including compactness and effectiveness. To address this issue, we propose a general matrix-based bilinear projection based on the rank-$k$ matrix base decomposition, where the Hadamard-based bilinear projection is a special case of our proposed one. Using the proposed bilinear projection, we design a novel low-rank factorized bilinear pooling (named RK-FBP), which does not miss any projecting directions. Thus, our RK-FBP can generate better compact bilinear features. To leverage high-order information in local features, we nest several RK-FBP modules together to formulate a multi-linear pooling that outputs compact multi-linear features. At last, we conduct experiments on several fine-grained image tasks to evaluate our models. The experiments show that our models achieve new state-of-the-art classification accuracy by the lowest dimension.