散射变换是一种基于小波的多层转换，最初是作为卷积神经网络（CNN）的模型引入的，它在我们对这些网络稳定性和不变性属性的理解中发挥了基础作用。随后，人们普遍兴趣将CNN的成功扩展到具有非欧盟结构的数据集，例如图形和歧管，从而导致了几何深度学习的新兴领域。为了提高我们对这个新领域中使用的体系结构的理解，几篇论文提出了对非欧几里得数据结构（如无方向的图形和紧凑的Riemannian歧管）的散射转换的概括。在本文中，我们介绍了一个通用的统一模型，用于测量空间上的几何散射。我们提出的框架包括以前的几何散射作品作为特殊情况，但也适用于更通用的设置，例如有向图，签名图和带边界的歧管。我们提出了一个新标准，该标准可以识别哪些有用表示应该不变的组，并表明该标准足以确保散射变换具有理想的稳定性和不变性属性。此外，我们考虑从随机采样未知歧管获得的有限度量空间。我们提出了两种构造数据驱动图的方法，在该图上相关的图形散射转换近似于基础歧管上的散射变换。此外，我们使用基于扩散图的方法来证明这些近似值之一的收敛速率的定量估计值，因为样品点的数量趋向于无穷大。最后，我们在球形图像，有向图和高维单细胞数据上展示了方法的实用性。

歧管散射变换是用于在Riemannian歧管上定义的数据的深度提取器。它是将类似卷积神经网络的操作员扩展到一般流形的第一个例子之一。该模型的初始工作主要集中在其理论稳定性和不变性属性上，但没有为其数值实现提供方法，除非具有预定义的网格的二维表面。在这项工作中，我们根据扩散图的理论提出实用方案，以实现在自然主义系统（例如单细胞遗传学）中产生的流形散射转换，其中数据是一个高度点云，该云是模仿躺在上面的高维点云。低维歧管。我们证明我们的方法对于信号分类和多种分类任务有效。

我们研究了两个基于内核的传感器融合算法，非参数规范相关性分析（NCCA）和交替扩散（AD）的行为，在非核设置下，由两个传感器收集的清洁数据集由嵌入高的常见的低维歧管建模尺寸欧几里德空间和数据集通过高维噪声损坏。假设样品尺寸和样本大小相当大，建立相关核矩阵特征值的渐近限制和收敛率，其中使用高斯内核进行NCCA和AD。事实证明，渐近限制和收敛速率都取决于每个传感器的信噪比（SNR）和所选带宽。一方面，我们表明，如果没有任何理智检查的NCCA和AD直接应用于嘈杂的点云，则可能会产生误导科学家解释的人工信息。另一方面，我们证明，如果带宽充分选择，则当SNR相对较大时，NCCA和AD都可以使NCCA和广告稳健地对高维噪声进行稳健。

我们系统地{研究基于内核的图形laplacian（gl）的光谱}，该图在非null设置中由高维和嘈杂的随机点云构成，其中点云是从低维几何对象（如歧管）中采样的，被高维噪音破坏。我们量化了信号和噪声在信号噪声比（SNR）的不同状态下如何相互作用，并报告GL的{所产生的特殊光谱行为}。此外，我们还探索了GL频谱上的内核带宽选择，而SNR的不同状态则导致带宽的自适应选择，这与实际数据中的共同实践相吻合。该结果为数据集嘈杂时的从业人员提供了理论支持。

在非参数回归中，落在欧几里德空间的限制子集中是常见的。基于典型的内核的方法，不考虑收集观察的域的内在几何学可能产生次优效果。在本文中，我们专注于在高斯过程（GP）模型的背景下解决这个问题，提出了一种新的基于Graplacian的GPS（GL-GPS），该GPS（GL-GPS），该GPS（GL-GPS）学习尊重输入域几何的协方差。随着热核的难以计算地，我们使用Prop Laplacian（GL）的有限许多特征方来近似协方差。 GL由内核构成，仅取决于输入的欧几里德坐标。因此，我们可以从关于内核的完整知识中受益，以通过NYSTR \“{o} M型扩展来将协方差结构扩展到新到达的样本。我们为GL-GP方法提供了实质性的理论支持，并说明了性能提升各种应用。

A recent study has shown a phenomenon called neural collapse in that the within-class means of features and the classifier weight vectors converge to the vertices of a simplex equiangular tight frame at the terminal phase of training for classification. In this paper, we explore the corresponding structures of the last-layer feature centers and classifiers in semantic segmentation. Based on our empirical and theoretical analysis, we point out that semantic segmentation naturally brings contextual correlation and imbalanced distribution among classes, which breaks the equiangular and maximally separated structure of neural collapse for both feature centers and classifiers. However, such a symmetric structure is beneficial to discrimination for the minor classes. To preserve these advantages, we introduce a regularizer on feature centers to encourage the network to learn features closer to the appealing structure in imbalanced semantic segmentation. Experimental results show that our method can bring significant improvements on both 2D and 3D semantic segmentation benchmarks. Moreover, our method ranks 1st and sets a new record (+6.8% mIoU) on the ScanNet200 test leaderboard. Code will be available at https://github.com/dvlab-research/Imbalanced-Learning.

Weakly-supervised object localization aims to indicate the category as well as the scope of an object in an image given only the image-level labels. Most of the existing works are based on Class Activation Mapping (CAM) and endeavor to enlarge the discriminative area inside the activation map to perceive the whole object, yet ignore the co-occurrence confounder of the object and context (e.g., fish and water), which makes the model inspection hard to distinguish object boundaries. Besides, the use of CAM also brings a dilemma problem that the classification and localization always suffer from a performance gap and can not reach their highest accuracy simultaneously. In this paper, we propose a casual knowledge distillation method, dubbed KD-CI-CAM, to address these two under-explored issues in one go. More specifically, we tackle the co-occurrence context confounder problem via causal intervention (CI), which explores the causalities among image features, contexts, and categories to eliminate the biased object-context entanglement in the class activation maps. Based on the de-biased object feature, we additionally propose a multi-teacher causal distillation framework to balance the absorption of classification knowledge and localization knowledge during model training. Extensive experiments on several benchmarks demonstrate the effectiveness of KD-CI-CAM in learning clear object boundaries from confounding contexts and addressing the dilemma problem between classification and localization performance.

Witnessing the impressive achievements of pre-training techniques on large-scale data in the field of computer vision and natural language processing, we wonder whether this idea could be adapted in a grab-and-go spirit, and mitigate the sample inefficiency problem for visuomotor driving. Given the highly dynamic and variant nature of the input, the visuomotor driving task inherently lacks view and translation invariance, and the visual input contains massive irrelevant information for decision making, resulting in predominant pre-training approaches from general vision less suitable for the autonomous driving task. To this end, we propose PPGeo (Policy Pre-training via Geometric modeling), an intuitive and straightforward fully self-supervised framework curated for the policy pretraining in visuomotor driving. We aim at learning policy representations as a powerful abstraction by modeling 3D geometric scenes on large-scale unlabeled and uncalibrated YouTube driving videos. The proposed PPGeo is performed in two stages to support effective self-supervised training. In the first stage, the geometric modeling framework generates pose and depth predictions simultaneously, with two consecutive frames as input. In the second stage, the visual encoder learns driving policy representation by predicting the future ego-motion and optimizing with the photometric error based on current visual observation only. As such, the pre-trained visual encoder is equipped with rich driving policy related representations and thereby competent for multiple visuomotor driving tasks. Extensive experiments covering a wide span of challenging scenarios have demonstrated the superiority of our proposed approach, where improvements range from 2% to even over 100% with very limited data. Code and models will be available at https://github.com/OpenDriveLab/PPGeo.

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.

Nearest-Neighbor (NN) classification has been proven as a simple and effective approach for few-shot learning. The query data can be classified efficiently by finding the nearest support class based on features extracted by pretrained deep models. However, NN-based methods are sensitive to the data distribution and may produce false prediction if the samples in the support set happen to lie around the distribution boundary of different classes. To solve this issue, we present P3DC-Shot, an improved nearest-neighbor based few-shot classification method empowered by prior-driven data calibration. Inspired by the distribution calibration technique which utilizes the distribution or statistics of the base classes to calibrate the data for few-shot tasks, we propose a novel discrete data calibration operation which is more suitable for NN-based few-shot classification. Specifically, we treat the prototypes representing each base class as priors and calibrate each support data based on its similarity to different base prototypes. Then, we perform NN classification using these discretely calibrated support data. Results from extensive experiments on various datasets show our efficient non-learning based method can outperform or at least comparable to SOTA methods which need additional learning steps.