Xinyi Wu

Xinyi Wu, Zhengdao Chen, William Wang et al.

Oversmoothing is a central challenge of building more powerful Graph Neural Networks (GNNs). While previous works have only demonstrated that oversmoothing is inevitable when the number of graph convolutions tends to infinity, in this paper, we precisely characterize the mechanism behind the phenomenon via a non-asymptotic analysis. Specifically, we distinguish between two different effects when applying graph convolutions -- an undesirable mixing effect that homogenizes node representations in different classes, and a desirable denoising effect that homogenizes node representations in the same class. By quantifying these two effects on random graphs sampled from the Contextual Stochastic Block Model (CSBM), we show that oversmoothing happens once the mixing effect starts to dominate the denoising effect, and the number of layers required for this transition is $O(\log N/\log (\log N))$ for sufficiently dense graphs with $N$ nodes. We also extend our analysis to study the effects of Personalized PageRank (PPR), or equivalently, the effects of initial residual connections on oversmoothing. Our results suggest that while PPR mitigates oversmoothing at deeper layers, PPR-based architectures still achieve their best performance at a shallow depth and are outperformed by the graph convolution approach on certain graphs. Finally, we support our theoretical results with numerical experiments, which further suggest that the oversmoothing phenomenon observed in practice can be magnified by the difficulty of optimizing deep GNN models.

Pingping Cai, Zhenyao Wu, Xinyi Wu et al.

Designing a point cloud upsampler, which aims to generate a clean and dense point cloud given a sparse point representation, is a fundamental and challenging problem in computer vision. A line of attempts achieves this goal by establishing a point-to-point mapping function via deep neural networks. However, these approaches are prone to produce outlier points due to the lack of explicit surface-level constraints. To solve this problem, we introduce a novel surface regularizer into the upsampler network by forcing the neural network to learn the underlying parametric surface represented by bicubic functions and rotation functions, where the new generated points are then constrained on the underlying surface. These designs are integrated into two different networks for two tasks that take advantages of upsampling layers - point cloud upsampling and point cloud completion for evaluation. The state-of-the-art experimental results on both tasks demonstrate the effectiveness of the proposed method. The code is available at https://github.com/corecai163/PSCU.

Canyu Zhang, Zhenyao Wu, Xinyi Wu et al.

3D point cloud semantic segmentation aims to group all points into different semantic categories, which benefits important applications such as point cloud scene reconstruction and understanding. Existing supervised point cloud semantic segmentation methods usually require large-scale annotated point clouds for training and cannot handle new categories. While a few-shot learning method was proposed recently to address these two problems, it suffers from high computational complexity caused by graph construction and inability to learn fine-grained relationships among points due to the use of pooling operations. In this paper, we further address these problems by developing a new multi-layer transformer network for few-shot point cloud semantic segmentation. In the proposed network, the query point cloud features are aggregated based on the class-specific support features in different scales. Without using pooling operations, our method makes full use of all pixel-level features from the support samples. By better leveraging the support features for few-shot learning, the proposed method achieves the new state-of-the-art performance, with 15\% less inference time, over existing few-shot 3D point cloud segmentation models on the S3DIS dataset and the ScanNet dataset.

Yuhang Lu, Xinyi Wu, Zhenyao Wu et al.

Few-shot segmentation (FSS) expects models trained on base classes to work on novel classes with the help of a few support images. However, when there exists a domain gap between the base and novel classes, the state-of-the-art FSS methods may even fail to segment simple objects. To improve their performance on unseen domains, we propose to transductively fine-tune the base model on a set of query images under the few-shot setting, where the core idea is to implicitly guide the segmentation of query images using support labels. Although different images are not directly comparable, their class-wise prototypes are desired to be aligned in the feature space. By aligning query and support prototypes with an uncertainty-aware contrastive loss, and using a supervised cross-entropy loss and an unsupervised boundary loss as regularizations, our method could generalize the base model to the target domain without additional labels. We conduct extensive experiments under various cross-domain settings of natural, remote sensing, and medical images. The results show that our method could consistently and significantly improve the performance of prototypical FSS models in all cross-domain tasks.

Xinyi Wu, Yifei Wang, Stefanie Jegelka et al.

Recent studies have revealed various manifestations of position bias in transformer architectures, from the "lost-in-the-middle" phenomenon to attention sinks, yet a comprehensive theoretical understanding of how attention masks and positional encodings shape these biases remains elusive. This paper presents a graph-theoretic framework for analyzing position bias in multi-layer attention. Modeling attention masks as directed graphs, we quantify how tokens interact with contextual information based on their sequential positions. We uncover two key insights: First, causal masking inherently biases attention toward earlier positions, as tokens in deeper layers attend to increasingly more contextualized representations of earlier tokens. Second, we characterize the competing effects of the causal mask and relative positional encodings, such as the decay mask and rotary positional encoding (RoPE): while both mechanisms introduce distance-based decay within individual attention maps, their aggregate effect across multiple attention layers$\unicode{x2013}$coupled with the causal mask$\unicode{x2013}$leads to a trade-off between the long-term decay effects and the cumulative importance of early sequence positions. Through controlled numerical experiments, we not only validate our theoretical findings but also reproduce position biases observed in real-world LLMs. Our framework offers a principled foundation for understanding positional biases in transformers, shedding light on the complex interplay of attention mechanism components and guiding more informed architectural design.

Xinyi Wu, Amir Ajorlou, Zihui Wu et al.

Oversmoothing in Graph Neural Networks (GNNs) refers to the phenomenon where increasing network depth leads to homogeneous node representations. While previous work has established that Graph Convolutional Networks (GCNs) exponentially lose expressive power, it remains controversial whether the graph attention mechanism can mitigate oversmoothing. In this work, we provide a definitive answer to this question through a rigorous mathematical analysis, by viewing attention-based GNNs as nonlinear time-varying dynamical systems and incorporating tools and techniques from the theory of products of inhomogeneous matrices and the joint spectral radius. We establish that, contrary to popular belief, the graph attention mechanism cannot prevent oversmoothing and loses expressive power exponentially. The proposed framework extends the existing results on oversmoothing for symmetric GCNs to a significantly broader class of GNN models, including random walk GCNs, Graph Attention Networks (GATs) and (graph) transformers. In particular, our analysis accounts for asymmetric, state-dependent and time-varying aggregation operators and a wide range of common nonlinear activation functions, such as ReLU, LeakyReLU, GELU and SiLU.

Xinyi Wu, Zhenyao Wu, Yuhang Lu et al.

In this paper, we tackle the problem of one-shot unsupervised domain adaptation (OSUDA) for semantic segmentation where the segmentors only see one unlabeled target image during training. In this case, traditional unsupervised domain adaptation models usually fail since they cannot adapt to the target domain with over-fitting to one (or few) target samples. To address this problem, existing OSUDA methods usually integrate a style-transfer module to perform domain randomization based on the unlabeled target sample, with which multiple domains around the target sample can be explored during training. However, such a style-transfer module relies on an additional set of images as style reference for pre-training and also increases the memory demand for domain adaptation. Here we propose a new OSUDA method that can effectively relieve such computational burden. Specifically, we integrate several style-mixing layers into the segmentor which play the role of style-transfer module to stylize the source images without introducing any learned parameters. Moreover, we propose a patchwise prototypical matching (PPM) method to weighted consider the importance of source pixels during the supervised training to relieve the negative adaptation. Experimental results show that our method achieves new state-of-the-art performance on two commonly used benchmarks for domain adaptive semantic segmentation under the one-shot setting and is more efficient than all comparison approaches.