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Spatial intelligence is a critical component of embodied AI, promoting robots to understand and interact with their environments. While recent advances have enhanced the ability of VLMs to perceive object locations and positional relationships, they still lack the capability to precisely understand object orientations-a key requirement for tasks involving fine-grained manipulations. Addressing this limitation not only requires geometric reasoning but also an expressive and intuitive way to represent orientation. In this context, we propose that natural language offers a more flexible representation space than canonical frames, making it particularly suitable for instruction-following robotic systems. In this paper, we introduce the concept of semantic orientation, which defines object orientations using natural language in a reference-frame-free manner (e.g., the ''plug-in'' direction of a USB or the ''handle'' direction of a knife). To support this, we construct OrienText300K, a large-scale dataset of 3D models annotated with semantic orientations that link geometric understanding to functional semantics. By integrating semantic orientation into a VLM system, we enable robots to generate manipulation actions with both positional and orientational constraints. Extensive experiments in simulation and real world demonstrate that our approach significantly enhances robotic manipulation capabilities, e.g., 48.7% accuracy on Open6DOR and 74.9% accuracy on SIMPLER., Comment: Project page: https://qizekun.github.io/sofar/

Driving world models have gained increasing attention due to their ability to model complex physical dynamics. However, their superb modeling capability is yet to be fully unleashed due to the limited video diversity in current driving datasets. We introduce DrivingDojo, the first dataset tailor-made for training interactive world models with complex driving dynamics. Our dataset features video clips with a complete set of driving maneuvers, diverse multi-agent interplay, and rich open-world driving knowledge, laying a stepping stone for future world model development. We further define an action instruction following (AIF) benchmark for world models and demonstrate the superiority of the proposed dataset for generating action-controlled future predictions., Comment: Accepted to NeurIPS 2024. Project page: https://drivingdojo.github.io/

In autonomous driving, end-to-end planners directly utilize raw sensor data, enabling them to extract richer scene features and reduce information loss compared to traditional planners. This raises a crucial research question: how can we develop better scene feature representations to fully leverage sensor data in end-to-end driving? Self-supervised learning methods show great success in learning rich feature representations in NLP and computer vision. Inspired by this, we propose a novel self-supervised learning approach using the LAtent World model (LAW) for end-to-end driving. LAW predicts future scene features based on current features and ego trajectories. This self-supervised task can be seamlessly integrated into perception-free and perception-based frameworks, improving scene feature learning and optimizing trajectory prediction. LAW achieves state-of-the-art performance across multiple benchmarks, including real-world open-loop benchmark nuScenes, NAVSIM, and simulator-based closed-loop benchmark CARLA. The code is released at https://github.com/BraveGroup/LAW., Comment: ICLR 2025

Let $G$ be a finite group acting faithfully on a finite set $\Omega$. For a positive integer $k$, $G$ acts naturally on the Catesian product $\Omega^k := \Omega \times ...\times \Omega$. In this paper, we prove that finite nilpotent group $G$ with $2\nmid |G|$ is a totally $k$-closed group if and only if $G$ is abelian with $n(G)\leq k-1$ or cyclic, where $n(G)$ is the number of invariant factors in the invariant factor decomposition of $G$.

Recent classification of $\frac{3}{2}$-transitive permutation groups leaves us with six families of groups which are $2$-transitive, or Frobenius, or one-dimensional affine, or the affine solvable subgroups of $ \mathrm{AGL}(2, q)$, or special projective linear group $\mathrm{PSL}(2, q)$, or $\mathrm{P\Gamma L}(2, q)$, where $q=2^p $ with $p$ prime. According to a case by case analysis, we prove that the endomorphism ring of the natural permutation module for a $\frac{3}{2}$-transitive permutation group is a symmetric algebra.

Schur rings are a type of subrings of group rings afforded by a partition of the underlined group. In this paper, Schur rings over free abelian group of rank two are classified under the assumption that one of the direct factor is a union of some basic sets. There are eight different types, and all but one type of which are traditional., Comment: arXiv admin note: text overlap with arXiv:2305.08608

While likelihood is attractive in theory, its estimates by deep generative models (DGMs) are often broken in practice, and perform poorly for out of distribution (OOD) Detection. Various recent works started to consider alternative scores and achieved better performances. However, such recipes do not come with provable guarantees, nor is it clear that their choices extract sufficient information. We attempt to change this by conducting a case study on variational autoencoders (VAEs). First, we introduce the likelihood path (LPath) principle, generalizing the likelihood principle. This narrows the search for informative summary statistics down to the minimal sufficient statistics of VAEs' conditional likelihoods. Second, introducing new theoretic tools such as nearly essential support, essential distance and co-Lipschitzness, we obtain non-asymptotic provable OOD detection guarantees for certain distillation of the minimal sufficient statistics. The corresponding LPath algorithm demonstrates SOTA performances, even using simple and small VAEs with poor likelihood estimates. To our best knowledge, this is the first provable unsupervised OOD method that delivers excellent empirical results, better than any other VAEs based techniques. We use the same model as \cite{xiao2020likelihood}, open sourced from: https://github.com/XavierXiao/Likelihood-Regret

Machine-based prediction of real-world events is garnering attention due to its potential for informed decision-making. Whereas traditional forecasting predominantly hinges on structured data like time-series, recent breakthroughs in language models enable predictions using unstructured text. In particular, (Zou et al., 2022) unveils AutoCast, a new benchmark that employs news articles for answering forecasting queries. Nevertheless, existing methods still trail behind human performance. The cornerstone of accurate forecasting, we argue, lies in identifying a concise, yet rich subset of news snippets from a vast corpus. With this motivation, we introduce AutoCast++, a zero-shot ranking-based context retrieval system, tailored to sift through expansive news document collections for event forecasting. Our approach first re-ranks articles based on zero-shot question-passage relevance, honing in on semantically pertinent news. Following this, the chosen articles are subjected to zero-shot summarization to attain succinct context. Leveraging a pre-trained language model, we conduct both the relevance evaluation and article summarization without needing domain-specific training. Notably, recent articles can sometimes be at odds with preceding ones due to new facts or unanticipated incidents, leading to fluctuating temporal dynamics. To tackle this, our re-ranking mechanism gives preference to more recent articles, and we further regularize the multi-passage representation learning to align with human forecaster responses made on different dates. Empirical results underscore marked improvements across multiple metrics, improving the performance for multiple-choice questions (MCQ) by 48% and true/false (TF) questions by up to 8%. Code is available at https://github.com/BorealisAI/Autocast-plus-plus., Comment: ICLR 2024

In currently available literature, no tracking-by-detection (TBD) paradigm-based tracking method has considered the localization confidence of detection boxes. In most TBD-based methods, it is considered that objects of low detection confidence are highly occluded and thus it is a normal practice to directly disregard such objects or to reduce their priority in matching. In addition, appearance similarity is not a factor to consider for matching these objects. However, in terms of the detection confidence fusing classification and localization, objects of low detection confidence may have inaccurate localization but clear appearance; similarly, objects of high detection confidence may have inaccurate localization or unclear appearance; yet these objects are not further classified. In view of these issues, we propose Localization-Guided Track (LG-Track). Firstly, localization confidence is applied in MOT for the first time, with appearance clarity and localization accuracy of detection boxes taken into account, and an effective deep association mechanism is designed; secondly, based on the classification confidence and localization confidence, a more appropriate cost matrix can be selected and used; finally, extensive experiments have been conducted on MOT17 and MOT20 datasets. The results show that our proposed method outperforms the compared state-of-art tracking methods. For the benefit of the community, our code has been made publicly at https://github.com/mengting2023/LG-Track., Comment: 11 pages, 4 figures

In this paper, we present an approach for explicitly constructing quasi-periodic Schr\"odinger operators with Cantor spectrum with $C^k$ potential. Additionally, we provide polynomial asymptotics on the size of spectral gaps.

With the rapid development of large models, the need for data has become increasingly crucial. Especially in 3D object detection, costly manual annotations have hindered further advancements. To reduce the burden of annotation, we study the problem of achieving 3D object detection solely based on 2D annotations. Thanks to advanced 3D reconstruction techniques, it is now feasible to reconstruct the overall static 3D scene. However, extracting precise object-level annotations from the entire scene and generalizing these limited annotations to the entire scene remain challenges. In this paper, we introduce a novel paradigm called BA$^2$-Det, encompassing pseudo label generation and multi-stage generalization. We devise the DoubleClustering algorithm to obtain object clusters from reconstructed scene-level points, and further enhance the model's detection capabilities by developing three stages of generalization: progressing from complete to partial, static to dynamic, and close to distant. Experiments conducted on the large-scale Waymo Open Dataset show that the performance of BA$^2$-Det is on par with the fully-supervised methods using 10% annotations. Additionally, using large raw videos for pretraining,BA$^2$-Det can achieve a 20% relative improvement on the KITTI dataset. The method also has great potential for detecting open-set 3D objects in complex scenes. Project page: https://ba2det.site., Comment: Project page: https://ba2det.site

Data association is a knotty problem for 2D Multiple Object Tracking due to the object occlusion. However, in 3D space, data association is not so hard. Only with a 3D Kalman Filter, the online object tracker can associate the detections from LiDAR. In this paper, we rethink the data association in 2D MOT and utilize the 3D object representation to separate each object in the feature space. Unlike the existing depth-based MOT methods, the 3D object representation can be jointly learned with the object association module. Besides, the object's 3D representation is learned from the video and supervised by the 2D tracking labels without additional manual annotations from LiDAR or pretrained depth estimator. With 3D object representation learning from Pseudo 3D object labels in monocular videos, we propose a new 2D MOT paradigm, called P3DTrack. Extensive experiments show the effectiveness of our method. We achieve new state-of-the-art performance on the large-scale Waymo Open Dataset., Comment: Technical report

Schur rings over the infinite dihedral group $\mathcal{Z}\rtimes\mathcal{Z}_2$ are studied according to properties of Schur rings over infinite groups and the classification of Schur rings over infinite cyclic groups. Schur rings over $\mathcal{Z}\rtimes{\mathcal{Z}}_2$ are classified under the assumption that $\mathcal{Z}$ is an $\mathcal{A}$-subgroup. Those Schur rings are proved to be traditional., Comment: arXiv admin note: text overlap with arXiv:2009.01443

In the classical tracking-by-detection (TBD) paradigm, detection and tracking are separately and sequentially conducted, and data association must be properly performed to achieve satisfactory tracking performance. In this paper, a new end-to-end multi-object tracking framework is proposed, which integrates object detection and multi-object tracking into a single model. The proposed tracking framework eliminates the complex data association process in the classical TBD paradigm, and requires no additional training. Secondly, the regression confidence of historical trajectories is investigated, and the possible states of a trajectory (weak object or strong object) in the current frame are predicted. Then, a confidence fusion module is designed to guide non-maximum suppression for trajectories and detections to achieve ordered and robust tracking. Thirdly, by integrating historical trajectory features, the regression performance of the detector is enhanced, which better reflects the occlusion and disappearance patterns of objects in real world. Lastly, extensive experiments are conducted on the commonly used KITTI and Waymo datasets. The results show that the proposed framework can achieve robust tracking by using only a 2D detector and a 3D detector, and it is proven more accurate than many of the state-of-the-art TBD-based multi-modal tracking methods. The source codes of the proposed method are available at https://github.com/wangxiyang2022/YONTD-MOT., Comment: 11 pages, 7 figures

We explore long-term temporal visual correspondence-based optimization for 3D video object detection in this work. Visual correspondence refers to one-to-one mappings for pixels across multiple images. Correspondence-based optimization is the cornerstone for 3D scene reconstruction but is less studied in 3D video object detection, because moving objects violate multi-view geometry constraints and are treated as outliers during scene reconstruction. We address this issue by treating objects as first-class citizens during correspondence-based optimization. In this work, we propose BA-Det, an end-to-end optimizable object detector with object-centric temporal correspondence learning and featuremetric object bundle adjustment. Empirically, we verify the effectiveness and efficiency of BA-Det for multiple baseline 3D detectors under various setups. Our BA-Det achieves SOTA performance on the large-scale Waymo Open Dataset (WOD) with only marginal computation cost. Our code is available at https://github.com/jiaweihe1996/BA-Det., Comment: CVPR2023

Data association is at the core of many computer vision tasks, e.g., multiple object tracking, image matching, and point cloud registration. however, current data association solutions have some defects: they mostly ignore the intra-view context information; besides, they either train deep association models in an end-to-end way and hardly utilize the advantage of optimization-based assignment methods, or only use an off-the-shelf neural network to extract features. In this paper, we propose a general learnable graph matching method to address these issues. Especially, we model the intra-view relationships as an undirected graph. Then data association turns into a general graph matching problem between graphs. Furthermore, to make optimization end-to-end differentiable, we relax the original graph matching problem into continuous quadratic programming and then incorporate training into a deep graph neural network with KKT conditions and implicit function theorem. In MOT task, our method achieves state-of-the-art performance on several MOT datasets. For image matching, our method outperforms state-of-the-art methods on a popular indoor dataset, ScanNet. For point cloud registration, we also achieve competitive results. Code will be available at https://github.com/jiaweihe1996/GMTracker., Comment: Accepted by TPAMI 2024. arXiv admin note: substantial text overlap with arXiv:2103.16178

The Solar Upper Transition Region Imager (SUTRI) onboard the Space Advanced Technology demonstration satellite (SATech-01), which was launched to a sun-synchronous orbit at a height of 500 km in July 2022, aims to test the on-orbit performance of our newly developed Sc-Si multi-layer reflecting mirror and the 2kx2k EUV CMOS imaging camera and to take full-disk solar images at the Ne VII 46.5 nm spectral line with a filter width of 3 nm. SUTRI employs a Ritchey-Chretien optical system with an aperture of 18 cm. The on-orbit observations show that SUTRI images have a field of view of 41.6'x41.6' and a moderate spatial resolution of 8" without an image stabilization system. The normal cadence of SUTRI images is 30 s and the solar observation time is about 16 hours each day because the earth eclipse time accounts for about 1/3 of SATech-01's orbit period. Approximately 15 GB data is acquired each day and made available online after processing. SUTRI images are valuable as the Ne VII 46.5 nm line is formed at a temperature regime of 0.5 MK in the solar atmosphere, which has rarely been sampled by existing solar imagers. SUTRI observations will establish connections between structures in the lower solar atmosphere and corona, and advance our understanding of various types of solar activity such as flares, filament eruptions, coronal jets and coronal mass ejections., Comment: 29pages,16figures

In the existing literature, most 3D multi-object tracking algorithms based on the tracking-by-detection framework employed deterministic tracks and detections for similarity calculation in the data association stage. Namely, the inherent uncertainties existing in tracks and detections are overlooked. In this work, we discard the commonly used deterministic tracks and deterministic detections for data association, instead, we propose to model tracks and detections as random vectors in which uncertainties are taken into account. Then, based on the Jensen-Shannon divergence, the similarity between two multidimensional distributions, i.e. track and detection, is evaluated for data association purposes. Lastly, the level of track uncertainty is incorporated in our cost function design to guide the data association process. Comparative experiments have been conducted on two typical datasets, KITTI and nuScenes, and the results indicated that our proposed method outperformed the compared state-of-the-art 3D tracking algorithms. For the benefit of the community, our code has been made available at https://github.com/hejiawei2023/UG3DMOT., Comment: 8 pages, 4 figures

We give a precise description of spectral types of the Mosaic Maryland model with any irrational frequency, which provides a quasi-periodic unbounded model with non-monotone potential has arithmetic phase transition., Comment: arXiv admin note: substantial text overlap with arXiv:2205.04021 by other authors

Estimating accurate 3D locations of objects from monocular images is a challenging problem because of lacking depth. Previous work shows that utilizing the object's keypoint projection constraints to estimate multiple depth candidates boosts the detection performance. However, the existing methods can only utilize vertical edges as projection constraints for depth estimation. So these methods only use a small number of projection constraints and produce insufficient depth candidates, leading to inaccurate depth estimation. In this paper, we propose a method that utilizes dense projection constraints from edges of any direction. In this way, we employ much more projection constraints and produce considerable depth candidates. Besides, we present a graph matching weighting module to merge the depth candidates. The proposed method DCD (Densely Constrained Detector) achieves state-of-the-art performance on the KITTI and WOD benchmarks. Code is released at https://github.com/BraveGroup/DCD., Comment: Accepted by ECCV2022

In the recent literature, on the one hand, many 3D multi-object tracking (MOT) works have focused on tracking accuracy and neglected computation speed, commonly by designing rather complex cost functions and feature extractors. On the other hand, some methods have focused too much on computation speed at the expense of tracking accuracy. In view of these issues, this paper proposes a robust and fast camera-LiDAR fusion-based MOT method that achieves a good trade-off between accuracy and speed. Relying on the characteristics of camera and LiDAR sensors, an effective deep association mechanism is designed and embedded in the proposed MOT method. This association mechanism realizes tracking of an object in a 2D domain when the object is far away and only detected by the camera, and updating of the 2D trajectory with 3D information obtained when the object appears in the LiDAR field of view to achieve a smooth fusion of 2D and 3D trajectories. Extensive experiments based on the typical datasets indicate that our proposed method presents obvious advantages over the state-of-the-art MOT methods in terms of both tracking accuracy and processing speed. Our code is made publicly available for the benefit of the community., Comment: 8 pages, 4 figures