Xin Cao

Wei Huang, Yuan Cao, Haonan Wang et al.

Graph neural networks (GNNs) have demonstrated remarkable capabilities in learning from graph-structured data, often outperforming traditional Multilayer Perceptrons (MLPs) in numerous graph-based tasks. Although existing works have demonstrated the benefits of graph convolution through Laplacian smoothing, expressivity or separability, there remains a lack of quantitative analysis comparing GNNs and MLPs from an optimization and generalization perspective. This study aims to address this gap by examining the role of graph convolution through feature learning theory. Using a signal-noise data model, we conduct a comparative analysis of the optimization and generalization between two-layer graph convolutional networks (GCNs) and their MLP counterparts. Our approach tracks the trajectory of signal learning and noise memorization in GNNs, characterizing their post-training generalization. We reveal that GNNs significantly prioritize signal learning, thus enhancing the regime of {low test error} over MLPs by $D^{q-2}$ times, where $D$ denotes a node's expected degree and $q$ is the power of ReLU activation function with $q>2$. This finding highlights a substantial and quantitative discrepancy between GNNs and MLPs in terms of optimization and generalization, a conclusion further supported by our empirical simulations on both synthetic and real-world datasets.

Wei Zhou, Xin Cao, Xiaodan Zhang et al.

The existing 3D deep learning methods adopt either individual point-based features or local-neighboring voxel-based features, and demonstrate great potential for processing 3D data. However, the point based models are inefficient due to the unordered nature of point clouds and the voxel-based models suffer from large information loss. Motivated by the success of recent point-voxel representation, such as PVCNN, we propose a new convolutional neural network, called Multi Point-Voxel Convolution (MPVConv), for deep learning on point clouds. Integrating both the advantages of voxel and point-based methods, MPVConv can effectively increase the neighboring collection between point-based features and also promote independence among voxel-based features. Moreover, most of the existing approaches aim at solving one specific task, and only a few of them can handle a variety of tasks. Simply replacing the corresponding convolution module with MPVConv, we show that MPVConv can fit in different backbones to solve a wide range of 3D tasks. Extensive experiments on benchmark datasets such as ShapeNet Part, S3DIS and KITTI for various tasks show that MPVConv improves the accuracy of the backbone (PointNet) by up to \textbf{36\%}, and achieves higher accuracy than the voxel-based model with up to \textbf{34}$\times$ speedups. In addition, MPVConv outperforms the state-of-the-art point-based models with up to \textbf{8}$\times$ speedups. Notably, our MPVConv achieves better accuracy than the newest point-voxel-based model PVCNN (a model more efficient than PointNet) with lower latency.

Wei Zhou, Xin Cao, Xiaodan Zhang et al.

We present a new convolutional neural network, called Multi Voxel-Point Neurons Convolution (MVPConv), for fast and accurate 3D deep learning. The previous works adopt either individual point-based features or local-neighboring voxel-based features to process 3D model, which limits the performance of models due to the inefficient computation. Moreover, most of the existing 3D deep learning frameworks aim at solving one specific task, and only a few of them can handle a variety of tasks. Integrating both the advantages of the voxel and point-based methods, the proposed MVPConv can effectively increase the neighboring collection between point-based features and also promote the independence among voxel-based features. Simply replacing the corresponding convolution module with MVPConv, we show that MVPConv can fit in different backbones to solve a wide range of 3D tasks. Extensive experiments on benchmark datasets such as ShapeNet Part, S3DIS and KITTI for various tasks show that MVPConv improves the accuracy of the backbone (PointNet) by up to 36%, and achieves higher accuracy than the voxel-based model with up to 34 times speedup. In addition, MVPConv also outperforms the state-of-the-art point-based models with up to 8 times speedup. Notably, our MVPConv achieves better accuracy than the newest point-voxel-based model PVCNN (a model more efficient than PointNet) with lower latency.