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The scalar auxiliary variable (SAV) approach is a highly efficient method widely used for solving gradient flow systems. This approach offers several advantages, including linearity, unconditional energy stability, and ease of implementation. By introducing scalar auxiliary variables, a modified system that is equivalent to the original system is constructed at the continuous level. However, during temporal discretization, computational errors can lead to a loss of equivalence and accuracy. In this paper, we introduce a new Constant Scalar Auxiliary Variable (CSAV) approach in which we derive an Ordinary Differential Equation (ODE) for the constant scalar auxiliary variable r. We also introduce a stabilization parameter ({\alpha}) to improve the stability of the scheme by slowing down the dynamics of r. The CSAV approach provides additional benefits as well. We explicitly discretize the auxiliary variable in combination with the nonlinear term, enabling the solution of a single linear system with constant coefficients at each time step. This new approach also eliminates the need for assumptions about the free energy potential, removing the bounded-from-below restriction imposed by the nonlinear free energy potential in the original SAV approach. Finally, we validate the proposed method through extensive numerical simulations, demonstrating its effectiveness and accuracy.

We have developed an efficient and unconditionally energy-stable method for simulating droplet formation dynamics. Our approach involves a novel time-marching scheme based on the scalar auxiliary variable technique, specifically designed for solving the Cahn-Hilliard-Navier-Stokes phase field model with variable density and viscosity. We have successfully applied this method to simulate droplet formation in scenarios where a Newtonian fluid is injected through a vertical tube into another immiscible Newtonian fluid. To tackle the challenges posed by nonhomogeneous Dirichlet boundary conditions at the tube entrance, we have introduced additional nonlocal auxiliary variables and associated ordinary differential equations. These additions effectively eliminate the influence of boundary terms. Moreover, we have incorporated stabilization terms into the scheme to enhance its numerical effectiveness. Notably, our resulting scheme is fully decoupled, requiring the solution of only linear systems at each time step. We have also demonstrated the energy decaying property of the scheme, with suitable modifications. To assess the accuracy and stability of our algorithm, we have conducted extensive numerical simulations. Additionally, we have examined the dynamics of droplet formation and explored the impact of dimensionless parameters on the process. Overall, our work presents a refined method for simulating droplet formation dynamics, offering improved efficiency, energy stability, and accuracy.

Single object tracking aims to locate the target object in a video sequence according to the state specified by different modal references, including the initial bounding box (BBOX), natural language (NL), or both (NL+BBOX). Due to the gap between different modalities, most existing trackers are designed for single or partial of these reference settings and overspecialize on the specific modality. Differently, we present a unified tracker called UVLTrack, which can simultaneously handle all three reference settings (BBOX, NL, NL+BBOX) with the same parameters. The proposed UVLTrack enjoys several merits. First, we design a modality-unified feature extractor for joint visual and language feature learning and propose a multi-modal contrastive loss to align the visual and language features into a unified semantic space. Second, a modality-adaptive box head is proposed, which makes full use of the target reference to mine ever-changing scenario features dynamically from video contexts and distinguish the target in a contrastive way, enabling robust performance in different reference settings. Extensive experimental results demonstrate that UVLTrack achieves promising performance on seven visual tracking datasets, three vision-language tracking datasets, and three visual grounding datasets. Codes and models will be open-sourced at https://github.com/OpenSpaceAI/UVLTrack.

The Wasserstein barycenter problem is to compute the average of $m$ given probability measures, which has been widely studied in many different areas; however, real-world data sets are often noisy and huge, which impedes its applications in practice. Hence, in this paper, we focus on improving the computational efficiency of two types of robust Wasserstein barycenter problem (RWB): fixed-support RWB (fixed-RWB) and free-support RWB (free-RWB); actually, the former is a subroutine of the latter. Firstly, we improve efficiency through model reducing; we reduce RWB as an augmented Wasserstein barycenter problem, which works for both fixed-RWB and free-RWB. Especially, fixed-RWB can be computed within $\widetilde{O}(\frac{mn^2}{\epsilon_+})$ time by using an off-the-shelf solver, where $\epsilon_+$ is the pre-specified additive error and $n$ is the size of locations of input measures. Then, for free-RWB, we leverage a quality guaranteed data compression technique, coreset, to accelerate computation by reducing the data set size $m$. It shows that running algorithms on the coreset is enough instead of on the original data set. Next, by combining the model reducing and coreset techniques above, we propose an algorithm for free-RWB by updating the weights and locations alternatively. Finally, our experiments demonstrate the efficiency of our techniques., Comment: Algorithms for accelerating robust Wasserstein barycenter problem

Lexically constrained neural machine translation (LCNMT), which controls the translation generation with pre-specified constraints, is important in many practical applications. Current approaches to LCNMT typically assume that the pre-specified lexical constraints are contextually appropriate. This assumption limits their application to real-world scenarios where a source lexicon may have multiple target constraints, and disambiguation is needed to select the most suitable one. In this paper, we propose disambiguated LCNMT (D-LCNMT) to solve the problem. D-LCNMT is a robust and effective two-stage framework that disambiguates the constraints based on contexts at first, then integrates the disambiguated constraints into LCNMT. Experimental results show that our approach outperforms strong baselines including existing data augmentation based approaches on benchmark datasets, and comprehensive experiments in scenarios where a source lexicon corresponds to multiple target constraints demonstrate the constraint disambiguation superiority of our approach., Comment: Accepted at ACL 2023 as a long paper (Findings), 12 pages, 3 figures

Word alignment is to find translationally equivalent words between source and target sentences. Previous work has demonstrated that self-training can achieve competitive word alignment results. In this paper, we propose to use word alignments generated by a third-party word aligner to supervise the neural word alignment training. Specifically, source word and target word of each word pair aligned by the third-party aligner are trained to be close neighbors to each other in the contextualized embedding space when fine-tuning a pre-trained cross-lingual language model. Experiments on the benchmarks of various language pairs show that our approach can surprisingly do self-correction over the third-party supervision by finding more accurate word alignments and deleting wrong word alignments, leading to better performance than various third-party word aligners, including the currently best one. When we integrate all supervisions from various third-party aligners, we achieve state-of-the-art word alignment performances, with averagely more than two points lower alignment error rates than the best third-party aligner. We released our code at https://github.com/sdongchuanqi/Third-Party-Supervised-Aligner., Comment: 12 pages, 4 figures, findings of emnlp 2022

Multiple object tracking (MOT) is a significant task in achieving autonomous driving. Traditional works attempt to complete this task, either based on point clouds (PC) collected by LiDAR, or based on images captured from cameras. However, relying on one single sensor is not robust enough, because it might fail during the tracking process. On the other hand, feature fusion from multiple modalities contributes to the improvement of accuracy. As a result, new techniques based on different sensors integrating features from multiple modalities are being developed. Texture information from RGB cameras and 3D structure information from Lidar have respective advantages under different circumstances. However, it's not easy to achieve effective feature fusion because of completely distinct information modalities. Previous fusion methods usually fuse the top-level features after the backbones extract the features from different modalities. In this paper, we first introduce PointNet++ to obtain multi-scale deep representations of point cloud to make it adaptive to our proposed Interactive Feature Fusion between multi-scale features of images and point clouds. Specifically, through multi-scale interactive query and fusion between pixel-level and point-level features, our method, can obtain more distinguishing features to improve the performance of multiple object tracking. Besides, we explore the effectiveness of pre-training on each single modality and fine-tuning on the fusion-based model. The experimental results demonstrate that our method can achieve good performance on the KITTI benchmark and outperform other approaches without using multi-scale feature fusion. Moreover, the ablation studies indicates the effectiveness of multi-scale feature fusion and pre-training on single modality., Comment: 9 pages, 5 figures, under review

Bilingual Lexicon Induction (BLI) aims to map words in one language to their translations in another, and is typically through learning linear projections to align monolingual word representation spaces. Two classes of word representations have been explored for BLI: static word embeddings and contextual representations, but there is no studies to combine both. In this paper, we propose a simple yet effective mechanism to combine the static word embeddings and the contextual representations to utilize the advantages of both paradigms. We test the combination mechanism on various language pairs under the supervised and unsupervised BLI benchmark settings. Experiments show that our mechanism consistently improves performances over robust BLI baselines on all language pairs by averagely improving 3.2 points in the supervised setting, and 3.1 points in the unsupervised setting., Comment: Accepted to Findings of ACL2021