Tao Wang

Yu Fan, Zicheng Zhang, Wei Sun et al.

Point cloud is one of the most widely used digital formats of 3D models, the visual quality of which is quite sensitive to distortions such as downsampling, noise, and compression. To tackle the challenge of point cloud quality assessment (PCQA) in scenarios where reference is not available, we propose a no-reference quality assessment metric for colored point cloud based on captured video sequences. Specifically, three video sequences are obtained by rotating the camera around the point cloud through three specific orbits. The video sequences not only contain the static views but also include the multi-frame temporal information, which greatly helps understand the human perception of the point clouds. Then we modify the ResNet3D as the feature extraction model to learn the correlation between the capture videos and corresponding subjective quality scores. The experimental results show that our method outperforms most of the state-of-the-art full-reference and no-reference PCQA metrics, which validates the effectiveness of the proposed method.

Chao Chao Yang, Tao Wang, Xiaoping Xie

This paper develops and analyses numerical approximation for linear-quadratic optimal control problem governed by elliptic interface equations. We adopt variational discretization concept to discretize optimal control problem, and apply an interface-unfitted finite element method due to [A. Hansbo and P. Hansbo. An unfitted finite element method, based on Nitsche's method, for elliptic interface problems. Comput. Methods Appl. Mech. Engrg., 191(47-48): 5537-5552, 2002] to discretize corresponding state and adjoint equations, where piecewise cut basis functions around interface are enriched into standard conforming finite element space. Optimal error estimates in both $L^2$ norm and a mesh-dependent norm are derived for optimal state, co-state and control under different regularity assumptions. Numerical results verify the theoretical results.

Tao Wang, Chao Chao Yang, Xiaoping Xie

This paper analyzes two eXtended finite element methods (XFEMs) for linear quadratic optimal control problems governed by Poisson equation in non-convex domains. We follow the variational discretization concept to discretize the continuous problems, and apply an XFEM with a cut-off function and a classic XFEM with a fixed enrichment area to discretize the state and co-state equations. Optimal error estimates are derived for the state, co-state and control. Numerical results confirm our theoretical results.

Tao Wang, Chaochao Yang, Xiaoping Xie

For the optimal control problem governed by elliptic equations with interfaces, we present a numerical method based on the Hansbo's Nitsche-XFEM. We followed the Hinze's variational discretization concept to discretize the continuous problem on a uniform mesh. We derive optimal error estimates of the state, co-state and control both in mesh dependent norm and L2 norm. In addition, our method is suitable for the model with non-homogeneous interface condition. Numerical results confirmed our theoretical results, with the implementation details discussed.

Georgy Noarov, Soham Mallick, Tao Wang et al.

Top-$k$ decoding is a widely used method for sampling from LLMs: at each token, only the largest $k$ next-token-probabilities are kept, and the next token is sampled after re-normalizing them to sum to unity. Top-$k$ and other sampling methods are motivated by the intuition that true next-token distributions are sparse, and the noisy LLM probabilities need to be truncated. However, to our knowledge, a precise theoretical motivation for the use of top-$k$ decoding is missing. In this work, we develop a theoretical framework that both explains and generalizes top-$k$ decoding. We view decoding at a fixed token as the recovery of a sparse probability distribution. We consider \emph{Bregman decoders} obtained by minimizing a separable Bregman divergence (for both the \emph{primal} and \emph{dual} cases) with a sparsity-inducing $\ell_0$ regularization. Despite the combinatorial nature of the objective, we show how to optimize it efficiently for a large class of divergences. We show that the optimal decoding strategies are greedy, and further that the loss function is discretely convex in $k$, so that binary search provably and efficiently finds the optimal $k$. We show that top-$k$ decoding arises as a special case for the KL divergence, and identify new decoding strategies that have distinct behaviors (e.g., non-linearly up-weighting larger probabilities after re-normalization).

Henghong Lin, Zihan Zhu, Tao Wang et al.

We address the problem of glass surface segmentation with an RGB-D camera, with a focus on effectively fusing RGB and depth information. To this end, we propose a Weighted Feature Fusion (WFF) module that dynamically and adaptively combines RGB and depth features to tackle issues such as transparency, reflections, and occlusions. This module can be seamlessly integrated with various deep neural network backbones as a plug-and-play solution. Additionally, we introduce the MJU-Glass dataset, a comprehensive RGB-D dataset collected by a service robot navigating real-world environments, providing a valuable benchmark for evaluating segmentation models. Experimental results show significant improvements in segmentation accuracy and robustness, with the WFF module enhancing performance in both mean Intersection over Union (mIoU) and boundary IoU (bIoU), achieving a 7.49% improvement in bIoU when integrated with PSPNet. The proposed module and dataset provide a robust framework for advancing glass surface segmentation in robotics and reducing the risk of collisions with glass objects.