LiDAR-based place recognition (LPR) is one of the most crucial components of autonomous vehicles to identify previously visited places in GPS-denied environments. Most existing LPR methods use mundane representations of the input point cloud without considering different views, which may not fully exploit the information from LiDAR sensors. In this paper, we propose a cross-view transformer-based network, dubbed CVTNet, to fuse the range image views (RIVs) and bird's eye views (BEVs) generated from the LiDAR data. It extracts correlations within the views themselves using intra-transformers and between the two different views using inter-transformers. Based on that, our proposed CVTNet generates a yaw-angle-invariant global descriptor for each laser scan end-to-end online and retrieves previously seen places by descriptor matching between the current query scan and the pre-built database. We evaluate our approach on three datasets collected with different sensor setups and environmental conditions. The experimental results show that our method outperforms the state-of-the-art LPR methods with strong robustness to viewpoint changes and long-time spans. Furthermore, our approach has a good real-time performance that can run faster than the typical LiDAR frame rate. The implementation of our method is released as open source at: https://github.com/BIT-MJY/CVTNet.

We introduce algebraic machine reasoning, a new reasoning framework that is well-suited for abstract reasoning. Effectively, algebraic machine reasoning reduces the difficult process of novel problem-solving to routine algebraic computation. The fundamental algebraic objects of interest are the ideals of some suitably initialized polynomial ring. We shall explain how solving Raven's Progressive Matrices (RPMs) can be realized as computational problems in algebra, which combine various well-known algebraic subroutines that include: Computing the Gr\"obner basis of an ideal, checking for ideal containment, etc. Crucially, the additional algebraic structure satisfied by ideals allows for more operations on ideals beyond set-theoretic operations. Our algebraic machine reasoning framework is not only able to select the correct answer from a given answer set, but also able to generate the correct answer with only the question matrix given. Experiments on the I-RAVEN dataset yield an overall $93.2\%$ accuracy, which significantly outperforms the current state-of-the-art accuracy of $77.0\%$ and exceeds human performance at $84.4\%$ accuracy.

This paper develops a novel methodology for using symbolic knowledge in deep learning. From first principles, we derive a semantic loss function that bridges between neural output vectors and logical constraints. This loss function captures how close the neural network is to satisfying the constraints on its output. An experimental evaluation shows that our semantic loss function effectively guides the learner to achieve (near-)state-of-the-art results on semi-supervised multi-class classification. Moreover, it significantly increases the ability of the neural network to predict structured objects, such as rankings and paths. These discrete concepts are tremendously difficult to learn, and benefit from a tight integration of deep learning and symbolic reasoning methods.