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Optimal model reduction for large-scale linear dynamical systems is studied. In contrast to most existing works, the systems under consideration are not required to be stable, neither in discrete nor in continuous time. As a consequence, the underlying rational transfer functions are allowed to have poles in general domains in the complex plane. In particular, this covers the case of specific conservative partial differential equations such as the linear Schr\"odinger and the undamped linear wave equation with spectra on the imaginary axis. By an appropriate modification of the classical continuous time Hardy space $\mathcal{H}_2$, a new $\mathcal{H}_2$ like optimal model reduction problem is introduced and first order optimality conditions are derived. As in the classical $\mathcal{H}_2$ case, these conditions exhibit a rational Hermite interpolation structure for which an iterative model reduction algorithm is proposed. Numerical examples demonstrate the effectiveness of the new method.

Assessing causal effects in the presence of unmeasured confounding is a challenging problem. Although auxiliary variables, such as instrumental variables, are commonly used to identify causal effects, they are often unavailable in practice due to stringent and untestable conditions. To address this issue, previous researches have utilized linear structural equation models to show that the causal effect can be identifiable when noise variables of the treatment and outcome are both non-Gaussian. In this paper, we investigate the problem of identifying the causal effect using auxiliary covariates and non-Gaussianity from the treatment. Our key idea is to characterize the impact of unmeasured confounders using an observed covariate, assuming they are all Gaussian. The auxiliary covariate can be an invalid instrument or an invalid proxy variable. We demonstrate that the causal effect can be identified using this measured covariate, even when the only source of non-Gaussianity comes from the treatment. We then extend the identification results to the multi-treatment setting and provide sufficient conditions for identification. Based on our identification results, we propose a simple and efficient procedure for calculating causal effects and show the $\sqrt{n}$-consistency of the proposed estimator. Finally, we evaluate the performance of our estimator through simulation studies and an application.

Previous methods solve feature matching and pose estimation using a two-stage process by first finding matches and then estimating the pose. As they ignore the geometric relationships between the two tasks, they focus on either improving the quality of matches or filtering potential outliers, leading to limited efficiency or accuracy. In contrast, we propose an iterative matching and pose estimation framework (IMP) leveraging the geometric connections between the two tasks: a few good matches are enough for a roughly accurate pose estimation; a roughly accurate pose can be used to guide the matching by providing geometric constraints. To this end, we implement a geometry-aware recurrent attention-based module which jointly outputs sparse matches and camera poses. Specifically, for each iteration, we first implicitly embed geometric information into the module via a pose-consistency loss, allowing it to predict geometry-aware matches progressively. Second, we introduce an \textbf{e}fficient IMP, called EIMP, to dynamically discard keypoints without potential matches, avoiding redundant updating and significantly reducing the quadratic time complexity of attention computation in transformers. Experiments on YFCC100m, Scannet, and Aachen Day-Night datasets demonstrate that the proposed method outperforms previous approaches in terms of accuracy and efficiency.

Current 3D object detection models follow a single dataset-specific training and testing paradigm, which often faces a serious detection accuracy drop when they are directly deployed in another dataset. In this paper, we study the task of training a unified 3D detector from multiple datasets. We observe that this appears to be a challenging task, which is mainly due to that these datasets present substantial data-level differences and taxonomy-level variations caused by different LiDAR types and data acquisition standards. Inspired by such observation, we present a Uni3D which leverages a simple data-level correction operation and a designed semantic-level coupling-and-recoupling module to alleviate the unavoidable data-level and taxonomy-level differences, respectively. Our method is simple and easily combined with many 3D object detection baselines such as PV-RCNN and Voxel-RCNN, enabling them to effectively learn from multiple off-the-shelf 3D datasets to obtain more discriminative and generalizable representations. Experiments are conducted on many dataset consolidation settings including Waymo-nuScenes, nuScenes-KITTI, Waymo-KITTI, and Waymo-nuScenes-KITTI consolidations. Their results demonstrate that Uni3D exceeds a series of individual detectors trained on a single dataset, with a 1.04x parameter increase over a selected baseline detector. We expect this work will inspire the research of 3D generalization since it will push the limits of perceptual performance.

The majority of current salient object detection (SOD) models are focused on designing a series of decoders based on fully convolutional networks (FCNs) or Transformer architectures and integrating them in a skillful manner. These models have achieved remarkable high performance and made significant contributions to the development of SOD. Their primary research objective is to develop novel algorithms that can outperform state-of-the-art models, a task that is extremely difficult and time-consuming. In contrast, this paper proposes a positive feedback method based on F-measure value for SOD, aiming to improve the accuracy of saliency prediction using existing methods. Specifically, our proposed method takes an image to be detected and inputs it into several existing models to obtain their respective prediction maps. These prediction maps are then fed into our positive feedback method to generate the final prediction result, without the need for careful decoder design or model training. Moreover, our method is adaptive and can be implemented based on existing models without any restrictions. Experimental results on five publicly available datasets show that our proposed positive feedback method outperforms the latest 12 methods in five evaluation metrics for saliency map prediction. Additionally, we conducted a robustness experiment, which shows that when at least one good prediction result exists in the selected existing model, our proposed approach can ensure that the prediction result is not worse. Our approach achieves a prediction speed of 20 frames per second (FPS) when evaluated on a low configuration host and after removing the prediction time overhead of inserted models. These results highlight the effectiveness, efficiency, and robustness of our proposed approach for salient object detection.

We introduce a technique for detecting 3D objects and estimating their position from a single image. Our method is built on top of a similar state-of-the-art technique [1], but with improved accuracy. The approach followed in this research first estimates common 3D properties of an object using a Deep Convolutional Neural Network (DCNN), contrary to other frameworks that only leverage centre-point predictions. We then combine these estimates with geometric constraints provided by a 2D bounding box to produce a complete 3D bounding box. The first output of our network estimates the 3D object orientation using a discrete-continuous loss [1]. The second output predicts the 3D object dimensions with minimal variance. Here we also present our extensions by augmenting light-weight feature extractors and a customized multibin architecture. By combining these estimates with the geometric constraints of the 2D bounding box, we can accurately (or comparatively) determine the 3D object pose better than our baseline [1] on the KITTI 3D detection benchmark [2].

Accurately estimating the 6D pose of objects is crucial for many applications, such as robotic grasping, autonomous driving, and augmented reality. However, this task becomes more challenging in poor lighting conditions or when dealing with textureless objects. To address this issue, depth images are becoming an increasingly popular choice due to their invariance to a scene's appearance and the implicit incorporation of essential geometric characteristics. However, fully leveraging depth information to improve the performance of pose estimation remains a difficult and under-investigated problem. To tackle this challenge, we propose a novel framework called SwinDePose, that uses only geometric information from depth images to achieve accurate 6D pose estimation. SwinDePose first calculates the angles between each normal vector defined in a depth image and the three coordinate axes in the camera coordinate system. The resulting angles are then formed into an image, which is encoded using Swin Transformer. Additionally, we apply RandLA-Net to learn the representations from point clouds. The resulting image and point clouds embeddings are concatenated and fed into a semantic segmentation module and a 3D keypoints localization module. Finally, we estimate 6D poses using a least-square fitting approach based on the target object's predicted semantic mask and 3D keypoints. In experiments on the LineMod and Occlusion LineMod datasets, SwinDePose outperforms existing state-of-the-art methods for 6D object pose estimation using depth images. This demonstrates the effectiveness of our approach and highlights its potential for improving performance in real-world scenarios. Our code is at //github.com/zhujunli1993/SwinDePose.

Graph Neural Networks (GNNs) have been shown to be effective models for different predictive tasks on graph-structured data. Recent work on their expressive power has focused on isomorphism tasks and countable feature spaces. We extend this theoretical framework to include continuous features - which occur regularly in real-world input domains and within the hidden layers of GNNs - and we demonstrate the requirement for multiple aggregation functions in this context. Accordingly, we propose Principal Neighbourhood Aggregation (PNA), a novel architecture combining multiple aggregators with degree-scalers (which generalize the sum aggregator). Finally, we compare the capacity of different models to capture and exploit the graph structure via a novel benchmark containing multiple tasks taken from classical graph theory, alongside existing benchmarks from real-world domains, all of which demonstrate the strength of our model. With this work, we hope to steer some of the GNN research towards new aggregation methods which we believe are essential in the search for powerful and robust models.

Many tasks in natural language processing can be viewed as multi-label classification problems. However, most of the existing models are trained with the standard cross-entropy loss function and use a fixed prediction policy (e.g., a threshold of 0.5) for all the labels, which completely ignores the complexity and dependencies among different labels. In this paper, we propose a meta-learning method to capture these complex label dependencies. More specifically, our method utilizes a meta-learner to jointly learn the training policies and prediction policies for different labels. The training policies are then used to train the classifier with the cross-entropy loss function, and the prediction policies are further implemented for prediction. Experimental results on fine-grained entity typing and text classification demonstrate that our proposed method can obtain more accurate multi-label classification results.

The task of detecting 3D objects in point cloud has a pivotal role in many real-world applications. However, 3D object detection performance is behind that of 2D object detection due to the lack of powerful 3D feature extraction methods. In order to address this issue, we propose to build a 3D backbone network to learn rich 3D feature maps by using sparse 3D CNN operations for 3D object detection in point cloud. The 3D backbone network can inherently learn 3D features from almost raw data without compressing point cloud into multiple 2D images and generate rich feature maps for object detection. The sparse 3D CNN takes full advantages of the sparsity in the 3D point cloud to accelerate computation and save memory, which makes the 3D backbone network achievable. Empirical experiments are conducted on the KITTI benchmark and results show that the proposed method can achieve state-of-the-art performance for 3D object detection.