We present a unified hard-constraint framework for solving geometrically complex PDEs with neural networks, where the most commonly used Dirichlet, Neumann, and Robin boundary conditions (BCs) are considered. Specifically, we first introduce the "extra fields" from the mixed finite element method to reformulate the PDEs so as to equivalently transform the three types of BCs into linear forms. Based on the reformulation, we derive the general solutions of the BCs analytically, which are employed to construct an ansatz that automatically satisfies the BCs. With such a framework, we can train the neural networks without adding extra loss terms and thus efficiently handle geometrically complex PDEs, alleviating the unbalanced competition between the loss terms corresponding to the BCs and PDEs. We theoretically demonstrate that the "extra fields" can stabilize the training process. Experimental results on real-world geometrically complex PDEs showcase the effectiveness of our method compared with state-of-the-art baselines.

基于深度学习的方法，例如物理知识的神经网络（PINN）和DeepOnets已显示出解决PDE受约束优化（PDECO）问题的希望。但是，现有方法不足以处理对优化目标具有复杂或非线性依赖性的PDE约束。在本文中，我们提出了一个新颖的双层优化框架，以通过将目标和约束的优化解耦来解决挑战。对于内部循环优化，我们采用PINN仅解决PDE约束。对于外循环，我们通过基于隐式函数定理（IFT）使用Broyden的方法来设计一种新颖的方法，该方法对于近似高度级别而言是有效且准确的。我们进一步介绍了高度级计算的理论解释和误差分析。在多个大规模和非线性PDE约束优化问题上进行了广泛的实验表明，与强基础相比，我们的方法可实现最新的结果。

近年来，Experts（MOE）的混合物已成为一种有前途的深度学习技术，可以将模型能力扩展为万亿多个参数，同时通过稀疏计算降低计算成本。虽然MoE开设了一个非常大的模型的新领域，但由于MOE的动态性质与系统的静态平行性/管道层之间的不匹配，因此其数以千计的GPU的实现受到限制。我们提出了Tutel，这是一种具有动态自适应并行性和管道的高度可扩展的堆栈设计和实现。 TUTEL在运行时提供自适应并行性切换和自适应管道，分别达到1.74倍和2.00倍的单MOE层加速度。我们还提出了一种用于MOE通信速度的新颖的二维层次结构算法，该算法的表现超过了2,048 GPU的先前最先前的最新时间。 Tutel汇总了所有技术，最终在16 GPU和2,048 GPU上分别提供了4.96倍和5.75倍的加速度，分别通过Fairseq：Meta的Facebook AI AI研究序列到序列工具Kit（Tutel（Tutel）（Tutel）（Tutel）（现在由Fairseq部分采用）。 Tutel源代码可在公共场所获得：https：//github.com/microsoft/tutel。我们的评估表明，Tutel有效，有效地运行了一个基于现实的MOE模型，名为Swinv2-Moe，建立在Swin Transformer V2上，这是一种最先进的计算机视觉体系结构。在效率方面，Tutel加速了Swinv2-MoE，在FairSeq的训练和推理中分别达到1.55倍和2.11倍的速度。关于有效性，SWINV2-MOE模型在预训练和下游计算机视觉任务（例如可可对象检测）方面都比对应的密度密度模型都达到了卓越的精度，这表明Tutel准备对端到端现实世界模型训练的准备就绪和推理。 Swinv2-Moe在https://github.com/microsoft/swin-transformer中开放。

Panoptic Part Segmentation (PPS) unifies panoptic segmentation and part segmentation into one task. Previous works utilize separated approaches to handle thing, stuff, and part predictions without shared computation and task association. We aim to unify these tasks at the architectural level, designing the first end-to-end unified framework named Panoptic-PartFormer. Moreover, we find the previous metric PartPQ biases to PQ. To handle both issues, we make the following contributions: Firstly, we design a meta-architecture that decouples part feature and things/stuff feature, respectively. We model things, stuff, and parts as object queries and directly learn to optimize all three forms of prediction as a unified mask prediction and classification problem. We term our model as Panoptic-PartFormer. Secondly, we propose a new metric Part-Whole Quality (PWQ) to better measure such task from both pixel-region and part-whole perspectives. It can also decouple the error for part segmentation and panoptic segmentation. Thirdly, inspired by Mask2Former, based on our meta-architecture, we propose Panoptic-PartFormer++ and design a new part-whole cross attention scheme to further boost part segmentation qualities. We design a new part-whole interaction method using masked cross attention. Finally, the extensive ablation studies and analysis demonstrate the effectiveness of both Panoptic-PartFormer and Panoptic-PartFormer++. Compared with previous Panoptic-PartFormer, our Panoptic-PartFormer++ achieves 2% PartPQ and 3% PWQ improvements on the Cityscapes PPS dataset and 5% PartPQ on the Pascal Context PPS dataset. On both datasets, Panoptic-PartFormer++ achieves new state-of-the-art results with a significant cost drop of 70% on GFlops and 50% on parameters. Our models can serve as a strong baseline and aid future research in PPS. Code will be available.

Rankings are widely collected in various real-life scenarios, leading to the leakage of personal information such as users' preferences on videos or news. To protect rankings, existing works mainly develop privacy protection on a single ranking within a set of ranking or pairwise comparisons of a ranking under the $\epsilon$-differential privacy. This paper proposes a novel notion called $\epsilon$-ranking differential privacy for protecting ranks. We establish the connection between the Mallows model (Mallows, 1957) and the proposed $\epsilon$-ranking differential privacy. This allows us to develop a multistage ranking algorithm to generate synthetic rankings while satisfying the developed $\epsilon$-ranking differential privacy. Theoretical results regarding the utility of synthetic rankings in the downstream tasks, including the inference attack and the personalized ranking tasks, are established. For the inference attack, we quantify how $\epsilon$ affects the estimation of the true ranking based on synthetic rankings. For the personalized ranking task, we consider varying privacy preferences among users and quantify how their privacy preferences affect the consistency in estimating the optimal ranking function. Extensive numerical experiments are carried out to verify the theoretical results and demonstrate the effectiveness of the proposed synthetic ranking algorithm.

In this work, we focus on instance-level open vocabulary segmentation, intending to expand a segmenter for instance-wise novel categories without mask annotations. We investigate a simple yet effective framework with the help of image captions, focusing on exploiting thousands of object nouns in captions to discover instances of novel classes. Rather than adopting pretrained caption models or using massive caption datasets with complex pipelines, we propose an end-to-end solution from two aspects: caption grounding and caption generation. In particular, we devise a joint Caption Grounding and Generation (CGG) framework based on a Mask Transformer baseline. The framework has a novel grounding loss that performs explicit and implicit multi-modal feature alignments. We further design a lightweight caption generation head to allow for additional caption supervision. We find that grounding and generation complement each other, significantly enhancing the segmentation performance for novel categories. We conduct extensive experiments on the COCO dataset with two settings: Open Vocabulary Instance Segmentation (OVIS) and Open Set Panoptic Segmentation (OSPS). The results demonstrate the superiority of our CGG framework over previous OVIS methods, achieving a large improvement of 6.8% mAP on novel classes without extra caption data. Our method also achieves over 15% PQ improvements for novel classes on the OSPS benchmark under various settings.

Temporal sentence grounding (TSG) aims to identify the temporal boundary of a specific segment from an untrimmed video by a sentence query. All existing works first utilize a sparse sampling strategy to extract a fixed number of video frames and then conduct multi-modal interactions with query sentence for reasoning. However, we argue that these methods have overlooked two indispensable issues: 1) Boundary-bias: The annotated target segment generally refers to two specific frames as corresponding start and end timestamps. The video downsampling process may lose these two frames and take the adjacent irrelevant frames as new boundaries. 2) Reasoning-bias: Such incorrect new boundary frames also lead to the reasoning bias during frame-query interaction, reducing the generalization ability of model. To alleviate above limitations, in this paper, we propose a novel Siamese Sampling and Reasoning Network (SSRN) for TSG, which introduces a siamese sampling mechanism to generate additional contextual frames to enrich and refine the new boundaries. Specifically, a reasoning strategy is developed to learn the inter-relationship among these frames and generate soft labels on boundaries for more accurate frame-query reasoning. Such mechanism is also able to supplement the absent consecutive visual semantics to the sampled sparse frames for fine-grained activity understanding. Extensive experiments demonstrate the effectiveness of SSRN on three challenging datasets.

Brain midline shift (MLS) is one of the most critical factors to be considered for clinical diagnosis and treatment decision-making for intracranial hemorrhage. Existing computational methods on MLS quantification not only require intensive labeling in millimeter-level measurement but also suffer from poor performance due to their dependence on specific landmarks or simplified anatomical assumptions. In this paper, we propose a novel semi-supervised framework to accurately measure the scale of MLS from head CT scans. We formulate the MLS measurement task as a deformation estimation problem and solve it using a few MLS slices with sparse labels. Meanwhile, with the help of diffusion models, we are able to use a great number of unlabeled MLS data and 2793 non-MLS cases for representation learning and regularization. The extracted representation reflects how the image is different from a non-MLS image and regularization serves an important role in the sparse-to-dense refinement of the deformation field. Our experiment on a real clinical brain hemorrhage dataset has achieved state-of-the-art performance and can generate interpretable deformation fields.

It is crucial to evaluate the quality and determine the optimal number of clusters in cluster analysis. In this paper, the multi-granularity characterization of the data set is carried out to obtain the hyper-balls. The cluster internal evaluation index based on hyper-balls(HCVI) is defined. Moreover, a general method for determining the optimal number of clusters based on HCVI is proposed. The proposed methods can evaluate the clustering results produced by the several classic methods and determine the optimal cluster number for data sets containing noises and clusters with arbitrary shapes. The experimental results on synthetic and real data sets indicate that the new index outperforms existing ones.

Normalizing flow is a class of deep generative models for efficient sampling and density estimation. In practice, the flow often appears as a chain of invertible neural network blocks; to facilitate training, existing works have regularized flow trajectories and designed special network architectures. The current paper develops a neural ODE flow network inspired by the Jordan-Kinderleherer-Otto (JKO) scheme, which allows efficient block-wise training of the residual blocks and avoids inner loops of score matching or variational learning. As the JKO scheme unfolds the dynamic of gradient flow, the proposed model naturally stacks residual network blocks one-by-one, reducing the memory load and difficulty of performing end-to-end training of deep flow networks. We also develop adaptive time reparameterization of the flow network with a progressive refinement of the trajectory in probability space, which improves the model training efficiency and accuracy in practice. Using numerical experiments with synthetic and real data, we show that the proposed JKO-iFlow model achieves similar or better performance in generating new samples compared with existing flow and diffusion models at a significantly reduced computational and memory cost.