Irreducible Cartesian tensors (ICTs) play a crucial role in the design of equivariant graph neural networks, as well as in theoretical chemistry and chemical physics. Meanwhile, the design space of available linear operations on tensors that preserve symmetry presents a significant challenge. The ICT decomposition and a basis of this equivariant space are difficult to obtain for high-order tensors. After decades of research, Bonvicini (2024) recently achieves an explicit ICT decomposition for n = 5 with factorial time/space complexity. This work, for the first time, obtains decomposition matrices for ICTs up to rank n = 9 with reduced and affordable complexity, by constructing what we call path matrices. The path matrices are obtained via performing chain-like contraction with Clebsch-Gordan matrices following the parentage scheme. We prove and leverage that the concatenation of path matrices is an orthonormal change-of-basis matrix between the Cartesian tensor product space and the spherical direct sum spaces. Furthermore, we identify a complete orthogonal basis for the equivariant space, rather than a spanning set (Pearce-Crump, 2023b), through this path matrices technique. We further extend our result to the arbitrary tensor product and direct sum spaces, enabling free design between different spaces while keeping symmetry.

Equivariant neural networks incorporate symmetries into their architecture, achieving higher generalization performance. However, constructing equivariant neural networks typically requires prior knowledge of data types and symmetries, which is difficult to achieve in most tasks. In this paper, we propose LieSD, a method for discovering symmetries via trained neural networks which approximate the input-output mappings of the tasks. It characterizes equivariance and invariance (a special case of equivariance) of continuous groups using Lie algebra and directly solves the Lie algebra space through the inputs, outputs, and gradients of the trained neural network. Then, we extend the method to make it applicable to multi-channel data and tensor data, respectively. We validate the performance of LieSD on tasks with symmetries such as the two-body problem, the moment of inertia matrix prediction, and top quark tagging. Compared with the baseline, LieSD can accurately determine the number of Lie algebra bases without the need for expensive group sampling. Furthermore, LieSD can perform well on non-uniform datasets, whereas methods based on GANs fail.

This paper explores the emerging knowledge-driven autonomous driving technologies. Our investigation highlights the limitations of current autonomous driving systems, in particular their sensitivity to data bias, difficulty in handling long-tail scenarios, and lack of interpretability. Conversely, knowledge-driven methods with the abilities of cognition, generalization and life-long learning emerge as a promising way to overcome these challenges. This paper delves into the essence of knowledge-driven autonomous driving and examines its core components: dataset \& benchmark, environment, and driver agent. By leveraging large language models, world models, neural rendering, and other advanced artificial intelligence techniques, these components collectively contribute to a more holistic, adaptive, and intelligent autonomous driving system. The paper systematically organizes and reviews previous research efforts in this area, and provides insights and guidance for future research and practical applications of autonomous driving. We will continually share the latest updates on cutting-edge developments in knowledge-driven autonomous driving along with the relevant valuable open-source resources at: \url{https://github.com/PJLab-ADG/awesome-knowledge-driven-AD}.

Multi-agent cooperative perception is an increasingly popular topic in the field of autonomous driving, where roadside LiDARs play an essential role. However, how to optimize the placement of roadside LiDARs is a crucial but often overlooked problem. This paper proposes an approach to optimize the placement of roadside LiDARs by selecting optimized positions within the scene for better perception performance. To efficiently obtain the best combination of locations, a greedy algorithm based on perceptual gain is proposed, which selects the location that can maximize the perceptual gain sequentially. We define perceptual gain as the increased perceptual capability when a new LiDAR is placed. To obtain the perception capability, we propose a perception predictor that learns to evaluate LiDAR placement using only a single point cloud frame. A dataset named Roadside-Opt is created using the CARLA simulator to facilitate research on the roadside LiDAR placement problem.

In computer vision, multi-label recognition are important tasks with many real-world applications, but classifying previously unseen labels remains a significant challenge. In this paper, we propose a novel algorithm, Aligned Dual moDality ClaSsifier (ADDS), which includes a Dual-Modal decoder (DM-decoder) with alignment between visual and textual features, for open-vocabulary multi-label classification tasks. Then we design a simple and yet effective method called Pyramid-Forwarding to enhance the performance for inputs with high resolutions. Moreover, the Selective Language Supervision is applied to further enhance the model performance. Extensive experiments conducted on several standard benchmarks, NUS-WIDE, ImageNet-1k, ImageNet-21k, and MS-COCO, demonstrate that our approach significantly outperforms previous methods and provides state-of-the-art performance for open-vocabulary multi-label classification, conventional multi-label classification and an extreme case called single-to-multi label classification where models trained on single-label datasets (ImageNet-1k, ImageNet-21k) are tested on multi-label ones (MS-COCO and NUS-WIDE).

LiDAR segmentation is crucial for autonomous driving perception. Recent trends favor point- or voxel-based methods as they often yield better performance than the traditional range view representation. In this work, we unveil several key factors in building powerful range view models. We observe that the "many-to-one" mapping, semantic incoherence, and shape deformation are possible impediments against effective learning from range view projections. We present RangeFormer -- a full-cycle framework comprising novel designs across network architecture, data augmentation, and post-processing -- that better handles the learning and processing of LiDAR point clouds from the range view. We further introduce a Scalable Training from Range view (STR) strategy that trains on arbitrary low-resolution 2D range images, while still maintaining satisfactory 3D segmentation accuracy. We show that, for the first time, a range view method is able to surpass the point, voxel, and multi-view fusion counterparts in the competing LiDAR semantic and panoptic segmentation benchmarks, i.e., SemanticKITTI, nuScenes, and ScribbleKITTI.

Although Domain Generalization (DG) problem has been fast-growing in the 2D image tasks, its exploration on 3D point cloud data is still insufficient and challenged by more complex and uncertain cross-domain variances with uneven inter-class modality distribution. In this paper, different from previous 2D DG works, we focus on the 3D DG problem and propose a Single-dataset Unified Generalization (SUG) framework that only leverages a single source dataset to alleviate the unforeseen domain differences faced by a well-trained source model. Specifically, we first design a Multi-grained Sub-domain Alignment (MSA) method, which can constrain the learned representations to be domain-agnostic and discriminative, by performing a multi-grained feature alignment process between the splitted sub-domains from the single source dataset. Then, a Sample-level Domain-aware Attention (SDA) strategy is presented, which can selectively enhance easy-to-adapt samples from different sub-domains according to the sample-level inter-domain distance to avoid the negative transfer. Experiments demonstrate that our SUG can boost the generalization ability for unseen target domains, even outperforming the existing unsupervised domain adaptation methods that have to access extensive target domain data. Our code is available at https://github.com/SiyuanHuang95/SUG.

With the growing popularity of digital twin and autonomous driving in transportation, the demand for simulation systems capable of generating high-fidelity and reliable scenarios is increasing. Existing simulation systems suffer from a lack of support for different types of scenarios, and the vehicle models used in these systems are too simplistic. Thus, such systems fail to represent driving styles and multi-vehicle interactions, and struggle to handle corner cases in the dataset. In this paper, we propose LimSim, the Long-term Interactive Multi-scenario traffic Simulator, which aims to provide a long-term continuous simulation capability under the urban road network. LimSim can simulate fine-grained dynamic scenarios and focus on the diverse interactions between multiple vehicles in the traffic flow. This paper provides a detailed introduction to the framework and features of the LimSim, and demonstrates its performance through case studies and experiments. LimSim is now open source on GitHub: https://www.github.com/PJLab-ADG/LimSim .

With the commercial application of automated vehicles (AVs), the sharing of roads between AVs and human-driven vehicles (HVs) becomes a common occurrence in the future. While research has focused on improving the safety and reliability of autonomous driving, it's also crucial to consider collaboration between AVs and HVs. Human-like interaction is a required capability for AVs, especially at common unsignalized intersections, as human drivers of HVs expect to maintain their driving habits for inter-vehicle interactions. This paper uses the social value orientation (SVO) in the decision-making of vehicles to describe the social interaction among multiple vehicles. Specifically, we define the quantitative calculation of the conflict-involved SVO at unsignalized intersections to enhance decision-making based on the reinforcement learning method. We use naturalistic driving scenarios with highly interactive motions for performance evaluation of the proposed method. Experimental results show that SVO is more effective in characterizing inter-vehicle interactions than conventional motion state parameters like velocity, and the proposed method can accurately reproduce naturalistic driving trajectories compared to behavior cloning.

The research on extrinsic calibration between Light Detection and Ranging(LiDAR) and camera are being promoted to a more accurate, automatic and generic manner. Since deep learning has been employed in calibration, the restrictions on the scene are greatly reduced. However, data driven method has the drawback of low transfer-ability. It cannot adapt to dataset variations unless additional training is taken. With the advent of foundation model, this problem can be significantly mitigated. By using the Segment Anything Model(SAM), we propose a novel LiDAR-camera calibration method, which requires zero extra training and adapts to common scenes. With an initial guess, we opimize the extrinsic parameter by maximizing the consistency of points that are projected inside each image mask. The consistency includes three properties of the point cloud: the intensity, normal vector and categories derived from some segmentation methods. The experiments on different dataset have demonstrated the generality and comparable accuracy of our method. The code is available at https://github.com/OpenCalib/CalibAnything.