Integrating first-order logic constraints (FOLCs) with neural networks is a crucial but challenging problem since it involves modeling intricate correlations to satisfy the constraints. This paper proposes a novel neural layer, LogicMP, which performs mean-field variational inference over a Markov Logic Network (MLN). It can be plugged into any off-the-shelf neural network to encode FOLCs while retaining modularity and efficiency. By exploiting the structure and symmetries in MLNs, we theoretically demonstrate that our well-designed, efficient mean-field iterations greatly mitigate the difficulty of MLN inference, reducing the inference from sequential calculation to a series of parallel tensor operations. Empirical results in three kinds of tasks over images, graphs, and text show that LogicMP outperforms advanced competitors in both performance and efficiency.

Usually, it is difficult to determine the scale and aspect ratio of anchors for anchor-based object detection methods. Current state-of-the-art object detectors either determine anchor parameters according to objects' shape and scale in a dataset, or avoid this problem by utilizing anchor-free methods, however, the former scheme is dataset-specific and the latter methods could not get better performance than the former ones. In this paper, we propose a novel anchor augmentation method named AADI, which means Augmenting Anchors by the Detector Itself. AADI is not an anchor-free method, instead, it can convert the scale and aspect ratio of anchors from a continuous space to a discrete space, which greatly alleviates the problem of anchors' designation. Furthermore, AADI is a learning-based anchor augmentation method, but it does not add any parameters or hyper-parameters, which is beneficial for research and downstream tasks. Extensive experiments on COCO dataset demonstrate the effectiveness of AADI, specifically, AADI achieves significant performance boosts on many state-of-the-art object detectors (eg. at least +2.4 box AP on Faster R-CNN, +2.2 box AP on Mask R-CNN, and +0.9 box AP on Cascade Mask R-CNN). We hope that this simple and cost-efficient method can be widely used in object detection. Code and models are available at https://github.com/WanXiaopei/aadi.